From ab9f014579006d60dd295905d28c569bd0fa486e Mon Sep 17 00:00:00 2001 From: Johnnie Gray Date: Tue, 15 Oct 2024 17:23:16 -0700 Subject: [PATCH 1/5] add Tensor.rand_reduce --- docs/changelog.md | 49 +++++++++++++++++++++ quimb/tensor/tensor_core.py | 63 ++++++++++++++++++++++----- tests/test_tensor/test_tensor_core.py | 9 ++++ 3 files changed, 109 insertions(+), 12 deletions(-) diff --git a/docs/changelog.md b/docs/changelog.md index 8d689321..f1607372 100644 --- a/docs/changelog.md +++ b/docs/changelog.md @@ -9,6 +9,9 @@ Release notes for `quimb`. - expose [`qtn.edge_coloring`](quimb.tensor.tensor_arbgeom_tebd.edge_coloring) as top level function and allow layers to be returned grouped. - add docstring for [`tn.contract_compressed`](quimb.tensor.tensor_core.TensorNetwork.contract_compressed) +- add [`Tensor.rand_reduce`](quimb.tensor.tensor_core.Tensor.rand_reduce) for randomly removing a tensor index by contracting a random vector into it. One can also supply the value `"r"` to `isel` selectors to use this. + +--- (whats-new-1-8-4)= @@ -19,6 +22,8 @@ Release notes for `quimb`. - fix for MPS sampling with fixed seed ({issue}`247` and {pull}`248`) - fix for `mps_gate_with_mpo_lazy` ({issue}`246`). +--- + (whats-new-1-8-3)= ## v1.8.3 (2024-07-10) @@ -31,6 +36,8 @@ Release notes for `quimb`. - add [`edges_1d_chain`](quimb.tensor.geometry.edges_1d_chain) for generating 1D chain edges - [operatorbuilder](quimb.experimental.operatorbuilder): better coefficient placement for long range MPO building +--- + (whats-new-1-8-2)= ## v1.8.2 (2024-06-12) @@ -48,6 +55,9 @@ Release notes for `quimb`. - [`approx_spectral_function`](quimb.linalg.approx_spectral.approx_spectral_function) add plotting and tracking - add dispatching to various tensor primitives to allow overriding +--- + + (whats-new-1-8-1)= ## v1.8.1 (2024-05-06) @@ -76,6 +86,9 @@ Release notes for `quimb`. - fix for retrieving `opt_einsum.PathInfo` for single scalar contraction ({issue}`231`) +--- + + (whats-new-1-8-0)= ## v1.8.0 (2024-04-10) @@ -160,6 +173,9 @@ Release notes for `quimb`. - fix autoblock bug where connected sectors were not being merged ({issue}`223`) +--- + + (whats-new-1-7-3)= ## v1.7.3 (2024-02-08) @@ -173,6 +189,9 @@ Release notes for `quimb`. - restore fallback (to `scipy.linalg.svd` with driver='gesvd') behavior for truncated SVD with numpy backend. +--- + + (whats-new-1-7-2)= ## v1.7.2 (2024-01-30) @@ -186,6 +205,9 @@ Release notes for `quimb`. - removed import of deprecated `numba.generated_jit` decorator. +--- + + (whats-new-1-7-1)= ## v1.7.1 (2024-01-30) @@ -219,6 +241,9 @@ Release notes for `quimb`. - fix bug in quantum discord computation when the state was diagonal ({issue}`217`) +--- + + (whats-new-1-7-0)= ## v1.7.0 (2023-12-08) @@ -269,6 +294,9 @@ Release notes for `quimb`. performing tensor network simplifications. +--- + + (whats-new-1-6-0)= ## v1.6.0 (2023-09-10) @@ -293,6 +321,9 @@ Release notes for `quimb`. - fix gauge size check for some backends +--- + + (whats-new-1-5-1)= ## v1.5.1 (2023-07-28) @@ -313,6 +344,9 @@ Release notes for `quimb`. - fix for {meth}`gate_with_auto_swap` for `i > j`. - fix bug where calling `tn.norm()` would mangle indices. +--- + + (whats-new-1-5-0)= ## v1.5.0 (2023-05-03) @@ -377,6 +411,9 @@ Release notes for `quimb`. - fix {func}`~quimb.tensor.decomp.qr_stabilized` bug for strictly upper triangular R factors. +--- + + (whats-new-1-4-2)= ## v1.4.2 (2022-11-28) @@ -385,6 +422,9 @@ Release notes for `quimb`. - move from versioneer to to [setuptools_scm](https://pypi.org/project/setuptools-scm/) for versioning +--- + + (whats-new-1-4-1)= ## v1.4.1 (2022-11-28) @@ -418,6 +458,9 @@ Release notes for `quimb`. > - fix force atlas 2 and `weight_attr` bug ({issue}`126`) > - allow unpickling of `PTensor` objects ({issue}`128`, {pull}`131`) +--- + + (whats-new-1-4-0)= ## v1.4.0 (2022-06-14) @@ -437,6 +480,9 @@ Release notes for `quimb`. - Various memory and performance improvements - Various graph generators and TN builders +--- + + (whats-new-1-3-0)= ## v1.3.0 (2020-02-18) @@ -473,6 +519,9 @@ Release notes for `quimb`. - Add environment variable `QUIMB_NUMBA_PAR` to set whether numba should use automatic parallelization - mainly to fix travis segfaults. - Make cache import and initilization of `petsc4py` and `slepc4py` more robust. +--- + + (whats-new-1-2-0)= ## v1.2.0 (2019-06-06) diff --git a/quimb/tensor/tensor_core.py b/quimb/tensor/tensor_core.py index e3bcf8ef..982d7ab2 100644 --- a/quimb/tensor/tensor_core.py +++ b/quimb/tensor/tensor_core.py @@ -1626,8 +1626,15 @@ def isel(self, selectors, inplace=False): Parameters ---------- - selectors : dict[str, int], dict[str, slice] - Mapping of index(es) to which value to take. + selectors : dict[str, int or slice or "r"] + Mapping of index(es) to which value to take. The values can be: + + - int: select a specific value for that index. + - slice: select a range of values for that index. + - "r": contract a random vector in. + + The mapping can contain indices that don't appear on this tensor, + in which case they are ignored. inplace : bool, optional Whether to select inplace or not. @@ -1643,18 +1650,29 @@ def isel(self, selectors, inplace=False): See Also -------- - TensorNetwork.isel + TensorNetwork.isel, Tensor.rand_reduce """ T = self if inplace else self.copy() - new_inds = tuple( - ix - for ix in self.inds - if (ix not in selectors) or isinstance(selectors[ix], slice) - ) + new_inds = [] + data_loc = [] - data_loc = tuple(selectors.get(ix, slice(None)) for ix in self.inds) - T.modify(apply=lambda x: x[data_loc], inds=new_inds, left_inds=None) + for ix in T.inds: + sel = selectors.get(ix, slice(None)) + if isinstance(sel, slice): + # index will be kept (including a partial slice of entries) + new_inds.append(ix) + data_loc.append(sel) + elif sel == "r": + # eagerly remove any 'random' selections + T.rand_reduce_(ix) + else: + # index will be removed by selecting a specific index + data_loc.append(sel) + + T.modify( + apply=lambda x: x[tuple(data_loc)], inds=new_inds, left_inds=None + ) return T isel_ = functools.partialmethod(isel, inplace=True) @@ -2200,6 +2218,22 @@ def vector_reduce(self, ind, v, inplace=False): vector_reduce_ = functools.partialmethod(vector_reduce, inplace=True) + def rand_reduce(self, ind, dtype=None, inplace=False, **kwargs): + """Contract the index ``ind`` of this tensor with a random vector, + removing it. + + Parameters + ---------- + """ + if dtype is None: + dtype = self.dtype + + v = randn(self.ind_size(ind), dtype=self.dtype, **kwargs) + + return self.vector_reduce(ind, v, inplace=inplace) + + rand_reduce_ = functools.partialmethod(rand_reduce, inplace=True) + def collapse_repeated(self, inplace=False): """Take the diagonals of any repeated indices, such that each index only appears once. @@ -7983,8 +8017,13 @@ def isel(self, selectors, inplace=False): Parameters ---------- - selectors : dict[str, int] - Mapping of index(es) to which value to take. + selectors : dict[str, int or slice or "r"] + Mapping of index(es) to which value to take. The values can be: + + - int: select a specific value for that index. + - slice: select a range of values for that index. + - "r": contract a random vector in. + inplace : bool, optional Whether to select inplace or not. diff --git a/tests/test_tensor/test_tensor_core.py b/tests/test_tensor/test_tensor_core.py index f9877e74..bf6950cb 100644 --- a/tests/test_tensor/test_tensor_core.py +++ b/tests/test_tensor/test_tensor_core.py @@ -1909,6 +1909,15 @@ def test_gen_inds_connected(self): patches = tuple(tn.gen_inds_connected(2)) assert len(patches) == 34 + def test_tn_isel_rand(self): + mps = qtn.MPS_rand_state(6, 7) + ramp = mps.isel({mps.site_ind(i): "r" for i in mps.sites}) + assert ramp.outer_inds() == () + # check we haven't selected an computation basis amplitude + rx = ramp.contract() + xs = mps.to_dense().ravel() + assert not any(np.allclose(rx, x) for x in xs) + class TestTensorNetworkSimplifications: def test_rank_simplify(self): From d57eb5356989910e589a0defda6332be71f8e396 Mon Sep 17 00:00:00 2001 From: Johnnie Gray Date: Thu, 17 Oct 2024 22:12:01 -0700 Subject: [PATCH 2/5] add gate by gate sampling and MPS local expectation methods --- docs/_static/amplitude.png | Bin 0 -> 105126 bytes docs/_static/branching.png | Bin 0 -> 128534 bytes docs/_static/compute_marginal.png | Bin 0 -> 193219 bytes docs/_static/local_expectation.png | Bin 0 -> 125952 bytes docs/_static/partial_trace.png | Bin 0 -> 111028 bytes docs/_static/sample.png | Bin 0 -> 220094 bytes docs/_static/sample_chaotic.png | Bin 0 -> 75501 bytes docs/_static/sample_gate_by_gate.png | Bin 0 -> 153002 bytes docs/_static/to_dense.png | Bin 0 -> 35905 bytes docs/changelog.md | 18 +- docs/tensor-circuit.ipynb | 59219 +------------------------ quimb/calc.py | 5 +- quimb/schematic.py | 21 + quimb/tensor/__init__.py | 2 + quimb/tensor/circuit.py | 593 +- quimb/tensor/circuit_gen.py | 72 +- quimb/tensor/tensor_1d.py | 408 +- quimb/tensor/tensor_core.py | 15 +- tests/test_tensor/test_circuit.py | 22 + 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" @@ -25481,6 +382,7 @@ }, { "cell_type": "markdown", + "id": "1cb9fa40-f203-42d3-816d-f09f7ee042ad", "metadata": {}, "source": [ "All of these might be helpful when addressing only certain tensors:" @@ -25489,12 +391,13 @@ { "cell_type": "code", "execution_count": 8, + "id": "f28e2b10-7455-4b2e-a2fc-5d47214f1392", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
TensorNetworkGenVector(tensors=1, indices=3)
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TensorNetworkGenVector(tensors=1, indices=3)
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByq, _438f3aAABzD, _438f3aAAByp], tags={GATE_69, ROUND_3, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642+0.j, 0. +0.j],\n", " [ 0. +0.j, 0.84089642+0.j]],\n", "\n", " [[-0. +0.j, -0.84089642+0.j],\n", @@ -25516,6 +419,7 @@ }, { "cell_type": "markdown", + "id": "9160495c-c8a5-4693-9d4d-63be1213aa1b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -25531,6 +435,7 @@ { "cell_type": "code", "execution_count": 9, + "id": "3174cadd-b595-4544-90d5-771a19ee7c30", "metadata": {}, "outputs": [ { @@ -25542,6 +447,7 @@ "CCY\n", "CCZ\n", "CNOT\n", + "CPHASE\n", "CRX\n", "CRY\n", "CRZ\n", @@ -25563,6 +469,7 @@ "IDEN\n", "IS\n", "ISWAP\n", + "PHASE\n", "RX\n", "RXX\n", "RY\n", @@ -25595,6 +502,7 @@ }, { "cell_type": "markdown", + "id": "6252031b-dece-40c9-bebc-595b5577fe25", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -25611,1346 +519,13 @@ { "cell_type": "code", "execution_count": 10, + "id": "ef8b6097-4698-4044-bfc1-5428ad69c6eb", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - 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" @@ -26978,6 +553,7 @@ }, { "cell_type": "markdown", + "id": "c5e2d670-03ec-4fd9-8be7-38db6a8b4fcf", "metadata": {}, "source": [ "We've used the ``contract=False`` option which doesn't try and split the gate tensor in any way,\n", @@ -26989,26 +565,27 @@ { "cell_type": "code", "execution_count": 11, + "id": "d087d620-f7be-4507-9fad-1bf3bd88324b", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
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" ], "text/plain": [ - "PTensor(shape=(2, 2, 2, 2), inds=('_119073AASiy', '_119073AASiu', '_119073AASio', '_119073AASip'), tags=oset(['GATE_0', 'FSIM', 'I0', 'I1']))" + "PTensor(shape=(2, 2, 2, 2), inds=('_438f3aAACEb', '_438f3aAACEX', '_438f3aAACER', '_438f3aAACES'), tags=oset(['GATE_0', 'FSIM', 'I0', 'I1']))" ] }, "execution_count": 11, @@ -27022,6 +599,7 @@ }, { "cell_type": "markdown", + "id": "fca0e3f5-ad88-4142-891a-88a5f2c8c363", "metadata": {}, "source": [ "For most tasks like contraction these are transparently handled like normal tensors:" @@ -27030,12 +608,13 @@ { "cell_type": "code", "execution_count": 12, + "id": "94cd7bda-556b-496b-8451-2f527f43f754", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(-0.07115178600720336+0.02949649184357368j)" + "np.complex128(0.027649938444653424-0.003473153420318573j)" ] }, "execution_count": 12, @@ -27049,6 +628,7 @@ }, { "cell_type": "markdown", + "id": "fc21f9a4-47ac-4654-8138-6d829e6d369b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -27068,10 +648,7 @@ "\n", "### Compute an amplitude\n", "\n", - ":::{figure} https://i.imgur.com/3mcnDNp.png\n", - ":alt: amplitude\n", - ":width: 300\n", - ":::\n", + "\n", "\n", "- [Circuit.amplitude](quimb.tensor.circuit.Circuit.amplitude)\n", "\n", @@ -27089,20 +666,13 @@ { "cell_type": "code", "execution_count": 13, + "id": "21fc92a3-ef33-492c-864f-3680566c8af3", "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/kjs/.pyenv/versions/3.11.9/envs/quimb/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", - " from .autonotebook import tqdm as notebook_tqdm\n" - ] - }, { "data": { "text/plain": [ - "(-0.0062675896452940244+0.012702244544177444j)" + "(-0.006267589645294032+0.012702244544177538j)" ] }, "execution_count": 13, @@ -27116,16 +686,14 @@ }, { "cell_type": "markdown", + "id": "6dd8eac0-d1e9-4e96-baf0-fbd541117fbd", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "### Compute a local expectation\n", "\n", - ":::{figure} https://i.imgur.com/XuXmTMM.png\n", - ":alt: local_expectation\n", - ":width: 300\n", - ":::\n", + "\n", "\n", "- [`Circuit.local_expectation`](quimb.tensor.circuit.Circuit.local_expectation)\n", "\n", @@ -27146,12 +714,13 @@ { "cell_type": "code", "execution_count": 14, + "id": "6418b631-2e29-430c-bd4c-de92f04d820c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-0.018188965185456228" + "-0.01818896518545991" ] }, "execution_count": 14, @@ -27165,6 +734,7 @@ }, { "cell_type": "markdown", + "id": "d647790b-3287-48ab-bcbd-e477a67addb0", "metadata": {}, "source": [ "You can compute several individual expectations on the same sites by supplying a list (they are computed in a single contraction):" @@ -27173,14 +743,15 @@ { "cell_type": "code", "execution_count": 15, + "id": "86452eee-1016-46fc-ab48-eef68cbbbdc7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "((-0.005784719259097598+4.9439619065339e-17j),\n", - " (0.05890188167924251+1.6046192152785466e-17j),\n", - " (-0.018188965185456277-1.474514954580286e-17j))" + "(np.complex128(-0.005784719259098372-2.3124976814589107e-17j),\n", + " np.complex128(0.05890188167925037+7.043679869776645e-17j),\n", + " np.complex128(-0.018188965185458657-6.705296660729364e-18j))" ] }, "execution_count": 15, @@ -27199,16 +770,14 @@ }, { "cell_type": "markdown", + "id": "a111262e-4d41-4914-9ad2-3db14cbe8c05", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "### Compute a reduced density matrix\n", "\n", - ":::{figure} https://i.imgur.com/DAbEdXg.png\n", - ":alt: partial_trace\n", - ":width: 300\n", - ":::\n", + "\n", "\n", "- [`Circuit.partial_trace`](quimb.tensor.circuit.Circuit.partial_trace)\n", "\n", @@ -27225,12 +794,13 @@ "and so it can be more efficient than repeatedly calling\n", "{meth}`~quimb.tensor.circuit.Circuit.local_expectation`.\n", "\n", - "**Example usage:**\n" + "**Example usage:**" ] }, { "cell_type": "code", "execution_count": 16, + "id": "eb58f4dd-a5d9-44b4-a50a-a8fcb010b35f", "metadata": {}, "outputs": [ { @@ -27253,16 +823,14 @@ }, { "cell_type": "markdown", + "id": "e1b3bf8a-f827-40a0-b1c1-68ea845bd51d", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "### Compute a marginal probability distribution\n", "\n", - ":::{figure} https://i.imgur.com/stoZ3v8.png\n", - ":alt: compute_marginal\n", - ":width: 400\n", - ":::\n", + "\n", "\n", "- {meth}`~quimb.tensor.circuit.Circuit.compute_marginal`\n", "\n", @@ -27284,12 +852,13 @@ "The result is a $2^{|\\bar{q}|}$ dimensional tensor containing the probabilites for each\n", "bit-string $x_{\\bar{q}}$, given that we have already 'measured' $x_{\\bar{f}}$.\n", "\n", - "**Example usage:**\n" + "**Example usage:**" ] }, { "cell_type": "code", "execution_count": 17, + "id": "d082168d-6bf3-4efc-a297-a6c1a2e676fb", "metadata": {}, "outputs": [ { @@ -27312,12 +881,13 @@ { "cell_type": "code", "execution_count": 18, + "id": "4dd589bc-976f-46d9-a65d-164ec3df1cff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "'01'" + "'10'" ] }, "execution_count": 18, @@ -27331,16 +901,14 @@ }, { "cell_type": "markdown", + "id": "3e0aea44-1484-46d3-9e73-b3b7d4211678", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "### Generate unbiased samples\n", "\n", - ":::{figure} https://i.imgur.com/egpytOg.png\n", - ":alt: sample\n", - ":width: 800\n", - ":::\n", + "\n", "\n", "- [`Circuit.sample`](quimb.tensor.circuit.Circuit.sample)\n", "\n", @@ -27378,7 +946,7 @@ "\n", ":::{note}\n", "You can set the group size to be that of the whole sytem, which is equivalent to sampling from the full wavefunction,\n", - "if you want to do this, it would be more efficient to call \n", + "if you want to do this, it would be more efficient to call\n", "[`Circuit.simulate_counts`](quimb.tensor.circuit.Circuit.simulate_counts), which\n", "doesn't draw the samples individually.\n", ":::\n", @@ -27386,10 +954,7 @@ "2. **Once we have computed a particular marginal we can cache the result, meaning if we come across the same sub-string result,\n", " we don't need to contract anything again, the trivial example being the first marginal we compute.**\n", "\n", - ":::{figure} https://i.imgur.com/4jnATD2.png\n", - ":alt: branching\n", - ":width: 300\n", - ":::\n", + "\n", "\n", "The second point is easy to understand if we think of the sampling process as the repeated exploration of a\n", "probability tree as above - which is shown for 3 qubits grouped individually, with a first sample of $011$ drawn.\n", @@ -27403,42 +968,87 @@ { "cell_type": "code", "execution_count": 19, + "id": "da48f88a-5cdb-4b5f-bc02-511ba920350b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0011011010\n", - "0101100000\n", - "0100001010\n", - "0110011111\n", - "1000000001\n", - "1011000100\n", - "1111010101\n", - "0011101001\n", - "0011010001\n", - "0101110000\n" + "1010101000\n", + "0001000000\n", + "1110100111\n", + "0101111110\n", + "1110100000\n", + "1100111000\n", + "1001000111\n", + "1101111000\n", + "0111110001\n", + "1000111011\n" ] } ], "source": [ - "for b in circ.sample(10, group_size=3):\n", + "for b in circ.sample(10):\n", " print(b)" ] }, { "cell_type": "markdown", + "id": "442e97aa-3316-48cc-843a-f621ba9607fc", + "metadata": {}, + "source": [ + "### Generate unbiased samples using the *'gate-by-gate'* method\n", + "\n", + "\n", + "\n", + "- [`Circuit.sample_gate_by_gate`](quimb.tensor.circuit.Circuit.sample_gate_by_gate)\n", + "\n", + "There is an alternative way to compute unbiased samples first introduced in *\"How to simulate quantum measurement without computing marginals\"* by Sergey Bravyi, David Gosset, Yinchen Liu (https://arxiv.org/abs/2112.08499). As illustrated above this essentially propagates a bit-string by sequentially adding more and more gates from the target circuit, and resampling parts of the bit-string corresponding to qubits that are acted on by the added gates. The upshot is that every contraction is no more expensive than computing a single amplitude, though the number of contractions we have to do scales linearly with the depth of the circuit. In many cases the theoretical total flop count of this 'gate-by-gate' method, as compared to the 'qubit-by-qubit' approach above, is significantly better, though practically the computation can still be dominated by subleading steps such as TN simplification - so it is worth comparing the two explicitly!\n", + "\n", + "This method makes use of being to reorder the gates so that groups of adjacent qubits are acted in in close succession. If you call the gate by gate rehearse methods you can access the sequence of circuits used.\n", + "\n", + "**Example usage:**" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "4c2b79b7-4be4-4a0b-bc46-a17fd5122fe5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0110011101\n", + "0010100101\n", + "0010000001\n", + "0101001010\n", + "1101010011\n", + "1110010011\n", + "0001111111\n", + "0100111110\n", + "0001001010\n", + "0001010110\n" + ] + } + ], + "source": [ + "for b in circ.sample_gate_by_gate(10):\n", + " print(b)" + ] + }, + { + "cell_type": "markdown", + "id": "a2cefa76-2121-4436-ae44-760ed8371cbb", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "### Generate samples from a chaotic circuit\n", "\n", - ":::{figure} https://i.imgur.com/vIw74uS.png\n", - ":alt: sample_chaotic\n", - ":width: 310\n", - ":::\n", + "\n", "\n", "- [`Circuit.sample_chaotic`](quimb.tensor.circuit.Circuit.sample_chaotic)\n", "\n", @@ -27464,28 +1074,29 @@ "superconducting processor\"](https://www.nature.com/articles/s41586-019-1666-5).\n", ":::\n", "\n", - "**Example usage:**\n" + "**Example usage:**" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, + "id": "9a03b9f0-9223-44d1-8f06-6b83f29c4833", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1000111100\n", - "1001110110\n", - "0101101101\n", - "1110100010\n", - "0101111000\n", - "0001101011\n", - "0000111011\n", - "0110001111\n", - "0110111010\n", - "0110101110\n" + "1100110110\n", + "1111011001\n", + "1101010111\n", + "0010101011\n", + "1110100001\n", + "0100100001\n", + "0010111100\n", + "1101010011\n", + "1111001110\n", + "0010000001\n" ] } ], @@ -27496,6 +1107,7 @@ }, { "cell_type": "markdown", + "id": "0cb43e41-62cd-4a16-99f6-7f3a48ea260b", "metadata": {}, "source": [ "Five of these qubits will now be sampled completely randomly." @@ -27503,16 +1115,14 @@ }, { "cell_type": "markdown", + "id": "42d6c608-571e-4de9-a889-f0b26024574d", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "### Compute the dense vector representation of the state\n", "\n", - ":::{figure} https://i.imgur.com/2lak43W.png\n", - ":alt: to_dense\n", - ":width: 500\n", - ":::\n", + "\n", "\n", "- {meth}`~quimb.tensor.circuit.Circuit.to_dense`\n", "\n", @@ -27533,12 +1143,13 @@ "the circuit geometry once.\n", ":::\n", "\n", - "**Example usage:**\n" + "**Example usage:**" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 22, + "id": "a9211ff2-99ff-4731-b0a4-d03baa0b577a", "metadata": {}, "outputs": [ { @@ -27553,7 +1164,7 @@ " [-0.033285-0.030653j]]" ] }, - "execution_count": 21, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -27564,6 +1175,7 @@ }, { "cell_type": "markdown", + "id": "f9e5e4f7-d071-48cd-af5e-8c7a37991fc6", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -27585,12 +1197,13 @@ "These each return a `dict` with the tensor network that *would* be\n", "contracted in the main part of the computation (with the key `'tn'`),\n", "and the {class}`cotengra.ContractionTree` object describing the contraction\n", - "path found for that tensor network (with the key `'tree'`). For example:\n" + "path found for that tensor network (with the key `'tree'`). For example:" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 23, + "id": "9407796a-c065-423c-aab9-2f7e1b8ff802", "metadata": {}, "outputs": [ { @@ -27599,7 +1212,7 @@ "7.0" ] }, - "execution_count": 22, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -27614,6 +1227,7 @@ }, { "cell_type": "markdown", + "id": "556c0538-87cf-41b5-adee-52744b27fc81", "metadata": {}, "source": [ "Upper twenties is the limit for standard (~10GB) amounts of RAM." @@ -27621,16 +1235,17 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 24, + "id": "7c85fdf4-e27e-413e-8baf-e9bf54f70707", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "3.93791890264778" + "4.059487684274447" ] }, - "execution_count": 23, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -27646,16 +1261,17 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 25, + "id": "c250012c-4aaf-4941-955f-f061131e2f66", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(0.0074846830625545525+0.030157252558037258j)" + "(44.57893837175564-2.968763081936263j)" ] }, - "execution_count": 24, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -27667,6 +1283,7 @@ }, { "cell_type": "markdown", + "id": "3b436cc9-b5be-47f0-b313-f7d89098197b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -27681,7 +1298,8 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 26, + "id": "e486939e-b454-43a3-a33a-4b525136b3e6", "metadata": {}, "outputs": [ { @@ -27690,7 +1308,7 @@ "dict_keys([(0, 1, 2), (3, 4, 9), (5, 6, 7), (8,)])" ] }, - "execution_count": 25, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -27702,7 +1320,8 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 27, + "id": "d00259ba-fd44-4f8b-9ee7-1cd511682fa4", "metadata": {}, "outputs": [ { @@ -27711,7 +1330,7 @@ "dict_keys(['tn', 'tree', 'W', 'C'])" ] }, - "execution_count": 26, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -27722,6 +1341,7 @@ }, { "cell_type": "markdown", + "id": "f88238f6-b8c4-4d0c-a8be-89df869ad89b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -27747,12 +1367,13 @@ "Whilst such simplifications can be found by the local simplifications (see below) its\n", "easier and quicker to drop these explicitly.\n", "\n", - "You can see which gate tags are in the reverse lightcone of which regions of qubits by calling:\n" + "You can see which gate tags are in the reverse lightcone of which regions of qubits by calling:" ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 28, + "id": "c88842ca-cef7-44c0-9eb3-7dd40fcee81d", "metadata": {}, "outputs": [ { @@ -27770,7 +1391,7 @@ " 'GATE_8')" ] }, - "execution_count": 27, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -27783,7993 +1404,14 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 29, + "id": "33ed1894-2893-45b5-8689-7ad53de24b97", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2024-08-19T07:32:43.548255\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.9.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - 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" @@ -50133,3902 +1538,23 @@ }, { "cell_type": "markdown", + "id": "b98b3875-32bd-425d-9abd-d9f90b456023", "metadata": {}, "source": [ - "You can see that only 3+ dimensional tensors remain. Now if we turn on all the \n", + "You can see that only 3+ dimensional tensors remain. 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" @@ -54052,6 +1578,7 @@ }, { "cell_type": "markdown", + "id": "9595e91f-d8fb-4c84-bc22-23d7fdec1b46", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54071,219 +1598,220 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 33, + "id": "12df083a-eea4-44f8-84c6-c18a66191e35", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
TensorNetworkGen(tensors=668, indices=802)
Tensor(shape=(2), inds=[_119073AASbJ], tags={I0, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbK], tags={I1, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbL], tags={I2, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbM], tags={I3, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbN], tags={I4, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbO], tags={I5, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbP], tags={I6, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbQ], tags={I7, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbR], tags={I8, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_119073AASbS], tags={I9, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2, 2), inds=[_119073AASbT, _119073AASbJ], tags={GATE_0, ROUND_0, H, I0}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbU, _119073AASbK], tags={GATE_1, ROUND_0, H, I1}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbV, _119073AASbL], tags={GATE_2, ROUND_0, H, I2}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbW, _119073AASbM], tags={GATE_3, ROUND_0, H, I3}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbY, _119073AASbN], tags={GATE_4, ROUND_0, H, I4}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbZ, _119073AASbO], tags={GATE_5, ROUND_0, H, I5}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbb, _119073AASbP], tags={GATE_6, ROUND_0, H, I6}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbc, _119073AASbQ], tags={GATE_7, ROUND_0, H, I7}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbe, _119073AASbR], tags={GATE_8, ROUND_0, H, I8}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_119073AASbf, _119073AASbS], tags={GATE_9, ROUND_0, H, I9}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", - " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbh, _119073AASbT, b], tags={GATE_10, ROUND_1, CX, I0}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + "
TensorNetworkGen(tensors=668, indices=802)
Tensor(shape=(2), inds=[_438f3aAABwm], tags={I0, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwn], tags={I1, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwo], tags={I2, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwp], tags={I3, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwq], tags={I4, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwr], tags={I5, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABws], tags={I6, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwt], tags={I7, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwu], tags={I8, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2), inds=[_438f3aAABwv], tags={I9, PSI0}),backend=numpy, dtype=complex128, data=array([1.-0.j, 0.-0.j])
Tensor(shape=(2, 2), inds=[_438f3aAABww, _438f3aAABwm], tags={GATE_0, ROUND_0, H, I0}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABwx, _438f3aAABwn], tags={GATE_1, ROUND_0, H, I1}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABwy, _438f3aAABwo], tags={GATE_2, ROUND_0, H, I2}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABwz, _438f3aAABwp], tags={GATE_3, ROUND_0, H, I3}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxB, _438f3aAABwq], tags={GATE_4, ROUND_0, H, I4}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxC, _438f3aAABwr], tags={GATE_5, ROUND_0, H, I5}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxE, _438f3aAABws], tags={GATE_6, ROUND_0, H, I6}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxF, _438f3aAABwt], tags={GATE_7, ROUND_0, H, I7}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxH, _438f3aAABwu], tags={GATE_8, ROUND_0, H, I8}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxI, _438f3aAABwv], tags={GATE_9, ROUND_0, H, I9}),backend=numpy, dtype=complex128, data=array([[ 0.70710678-0.j, 0.70710678-0.j],\n", + " [ 0.70710678-0.j, -0.70710678-0.j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxK, _438f3aAABww, b], tags={GATE_10, ROUND_1, CX, I0}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[b, _119073AASbi, _119073AASbU], tags={GATE_10, ROUND_1, CX, I1}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[b, _438f3aAABxL, _438f3aAABwx], tags={GATE_10, ROUND_1, CX, I1}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbj, _119073AASbV, _119073AASbX], tags={GATE_11, ROUND_1, CX, I2}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxM, _438f3aAABwy, _438f3aAABxA], tags={GATE_11, ROUND_1, CX, I2}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbX, _119073AASbk, _119073AASbW], tags={GATE_11, ROUND_1, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxA, _438f3aAABxN, _438f3aAABwz], tags={GATE_11, ROUND_1, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbl, _119073AASbY, _119073AASba], tags={GATE_12, ROUND_1, CX, I4}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxO, _438f3aAABxB, _438f3aAABxD], tags={GATE_12, ROUND_1, CX, I4}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASba, _119073AASbm, _119073AASbZ], tags={GATE_12, ROUND_1, CX, I5}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxD, _438f3aAABxP, _438f3aAABxC], tags={GATE_12, ROUND_1, CX, I5}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbn, _119073AASbb, _119073AASbd], tags={GATE_13, ROUND_1, CX, I6}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxQ, _438f3aAABxE, _438f3aAABxG], tags={GATE_13, ROUND_1, CX, I6}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbd, _119073AASbo, _119073AASbc], tags={GATE_13, ROUND_1, CX, I7}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxG, _438f3aAABxR, _438f3aAABxF], tags={GATE_13, ROUND_1, CX, I7}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbp, _119073AASbe, _119073AASbg], tags={GATE_14, ROUND_1, CX, I8}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxS, _438f3aAABxH, _438f3aAABxJ], tags={GATE_14, ROUND_1, CX, I8}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbg, _119073AASbq, _119073AASbf], tags={GATE_14, ROUND_1, CX, I9}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxJ, _438f3aAABxT, _438f3aAABxI], tags={GATE_14, ROUND_1, CX, I9}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2), inds=[_119073AAScD, _119073AASbh], tags={GATE_15, ROUND_1, RZ, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASbr, _119073AASbi], tags={GATE_16, ROUND_1, RZ, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASbs, _119073AASbj], tags={GATE_17, ROUND_1, RZ, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASbu, _119073AASbk], tags={GATE_18, ROUND_1, RZ, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASbv, _119073AASbl], tags={GATE_19, ROUND_1, RZ, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASbx, _119073AASbm], tags={GATE_20, ROUND_1, RZ, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASby, _119073AASbn], tags={GATE_21, ROUND_1, RZ, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScA, _119073AASbo], tags={GATE_22, ROUND_1, RZ, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScB, _119073AASbp], tags={GATE_23, ROUND_1, RZ, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScM, _119073AASbq], tags={GATE_24, ROUND_1, RZ, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScE, _119073AASbr, _119073AASbt], tags={GATE_25, ROUND_1, CZ, I1}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2), inds=[_438f3aAABxg, _438f3aAABxK], tags={GATE_15, ROUND_1, RZ, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxU, _438f3aAABxL], tags={GATE_16, ROUND_1, RZ, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxV, _438f3aAABxM], tags={GATE_17, ROUND_1, RZ, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxX, _438f3aAABxN], tags={GATE_18, ROUND_1, RZ, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxY, _438f3aAABxO], tags={GATE_19, ROUND_1, RZ, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxa, _438f3aAABxP], tags={GATE_20, ROUND_1, RZ, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxb, _438f3aAABxQ], tags={GATE_21, ROUND_1, RZ, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxd, _438f3aAABxR], tags={GATE_22, ROUND_1, RZ, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxe, _438f3aAABxS], tags={GATE_23, ROUND_1, RZ, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABxp, _438f3aAABxT], tags={GATE_24, ROUND_1, RZ, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxh, _438f3aAABxU, _438f3aAABxW], tags={GATE_25, ROUND_1, CZ, I1}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbt, _119073AAScF, _119073AASbs], tags={GATE_25, ROUND_1, CZ, I2}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxW, _438f3aAABxi, _438f3aAABxV], tags={GATE_25, ROUND_1, CZ, I2}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScG, _119073AASbu, _119073AASbw], tags={GATE_26, ROUND_1, CZ, I3}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxj, _438f3aAABxX, _438f3aAABxZ], tags={GATE_26, ROUND_1, CZ, I3}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbw, _119073AAScH, _119073AASbv], tags={GATE_26, ROUND_1, CZ, I4}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxZ, _438f3aAABxk, _438f3aAABxY], tags={GATE_26, ROUND_1, CZ, I4}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScI, _119073AASbx, _119073AASbz], tags={GATE_27, ROUND_1, CZ, I5}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxl, _438f3aAABxa, _438f3aAABxc], tags={GATE_27, ROUND_1, CZ, I5}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASbz, _119073AAScJ, _119073AASby], tags={GATE_27, ROUND_1, CZ, I6}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxc, _438f3aAABxm, _438f3aAABxb], tags={GATE_27, ROUND_1, CZ, I6}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScK, _119073AAScA, _119073AAScC], tags={GATE_28, ROUND_1, CZ, I7}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxn, _438f3aAABxd, _438f3aAABxf], tags={GATE_28, ROUND_1, CZ, I7}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScC, _119073AAScL, _119073AAScB], tags={GATE_28, ROUND_1, CZ, I8}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxf, _438f3aAABxo, _438f3aAABxe], tags={GATE_28, ROUND_1, CZ, I8}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2), inds=[_119073AAScN, _119073AAScD], tags={GATE_29, ROUND_1, RX, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScO, _119073AAScE], tags={GATE_30, ROUND_1, RX, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScQ, _119073AAScF], tags={GATE_31, ROUND_1, RX, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScR, _119073AAScG], tags={GATE_32, ROUND_1, RX, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScT, _119073AAScH], tags={GATE_33, ROUND_1, RX, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScU, _119073AAScI], tags={GATE_34, ROUND_1, RX, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScW, _119073AAScJ], tags={GATE_35, ROUND_1, RX, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScX, _119073AAScK], tags={GATE_36, ROUND_1, RX, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AAScZ, _119073AAScL], tags={GATE_37, ROUND_1, RX, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASca, _119073AAScM], tags={GATE_38, ROUND_1, RX, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScc, _119073AAScN, _119073AAScP], tags={GATE_39, ROUND_2, CX, I0}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2), inds=[_438f3aAABxq, _438f3aAABxg], tags={GATE_29, ROUND_1, RX, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABxr, _438f3aAABxh], tags={GATE_30, ROUND_1, RX, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABxt, _438f3aAABxi], tags={GATE_31, ROUND_1, RX, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABxu, _438f3aAABxj], tags={GATE_32, ROUND_1, RX, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABxw, _438f3aAABxk], tags={GATE_33, ROUND_1, RX, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABxx, _438f3aAABxl], tags={GATE_34, ROUND_1, RX, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABxz, _438f3aAABxm], tags={GATE_35, ROUND_1, RX, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByA, _438f3aAABxn], tags={GATE_36, ROUND_1, RX, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByC, _438f3aAABxo], tags={GATE_37, ROUND_1, RX, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByD, _438f3aAABxp], tags={GATE_38, ROUND_1, RX, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByF, _438f3aAABxq, _438f3aAABxs], tags={GATE_39, ROUND_2, CX, I0}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScP, _119073AAScd, _119073AAScO], tags={GATE_39, ROUND_2, CX, I1}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxs, _438f3aAAByG, _438f3aAABxr], tags={GATE_39, ROUND_2, CX, I1}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASce, _119073AAScQ, _119073AAScS], tags={GATE_40, ROUND_2, CX, I2}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByH, _438f3aAABxt, _438f3aAABxv], tags={GATE_40, ROUND_2, CX, I2}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScS, _119073AAScf, _119073AAScR], tags={GATE_40, ROUND_2, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxv, _438f3aAAByI, _438f3aAABxu], tags={GATE_40, ROUND_2, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScg, _119073AAScT, _119073AAScV], tags={GATE_41, ROUND_2, CX, I4}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByJ, _438f3aAABxw, _438f3aAABxy], tags={GATE_41, ROUND_2, CX, I4}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScV, _119073AASch, _119073AAScU], tags={GATE_41, ROUND_2, CX, I5}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABxy, _438f3aAAByK, _438f3aAABxx], tags={GATE_41, ROUND_2, CX, I5}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASci, _119073AAScW, _119073AAScY], tags={GATE_42, ROUND_2, CX, I6}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByL, _438f3aAABxz, _438f3aAAByB], tags={GATE_42, ROUND_2, CX, I6}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScY, _119073AAScj, _119073AAScX], tags={GATE_42, ROUND_2, CX, I7}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByB, _438f3aAAByM, _438f3aAAByA], tags={GATE_42, ROUND_2, CX, I7}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASck, _119073AAScZ, _119073AAScb], tags={GATE_43, ROUND_2, CX, I8}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByN, _438f3aAAByC, _438f3aAAByE], tags={GATE_43, ROUND_2, CX, I8}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScb, _119073AAScl, _119073AASca], tags={GATE_43, ROUND_2, CX, I9}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByE, _438f3aAAByO, _438f3aAAByD], tags={GATE_43, ROUND_2, CX, I9}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2), inds=[_119073AAScy, _119073AAScc], tags={GATE_44, ROUND_2, RZ, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScm, _119073AAScd], tags={GATE_45, ROUND_2, RZ, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScn, _119073AASce], tags={GATE_46, ROUND_2, RZ, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScp, _119073AAScf], tags={GATE_47, ROUND_2, RZ, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScq, _119073AAScg], tags={GATE_48, ROUND_2, RZ, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScs, _119073AASch], tags={GATE_49, ROUND_2, RZ, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASct, _119073AASci], tags={GATE_50, ROUND_2, RZ, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScv, _119073AAScj], tags={GATE_51, ROUND_2, RZ, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAScw, _119073AASck], tags={GATE_52, ROUND_2, RZ, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASdH, _119073AAScl], tags={GATE_53, ROUND_2, RZ, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", - " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScz, _119073AAScm, _119073AASco], tags={GATE_54, ROUND_2, CZ, I1}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAByb, _438f3aAAByF], tags={GATE_44, ROUND_2, RZ, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByP, _438f3aAAByG], tags={GATE_45, ROUND_2, RZ, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByQ, _438f3aAAByH], tags={GATE_46, ROUND_2, RZ, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByS, _438f3aAAByI], tags={GATE_47, ROUND_2, RZ, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByT, _438f3aAAByJ], tags={GATE_48, ROUND_2, RZ, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByV, _438f3aAAByK], tags={GATE_49, ROUND_2, RZ, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByW, _438f3aAAByL], tags={GATE_50, ROUND_2, RZ, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByY, _438f3aAAByM], tags={GATE_51, ROUND_2, RZ, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByZ, _438f3aAAByN], tags={GATE_52, ROUND_2, RZ, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAByk, _438f3aAAByO], tags={GATE_53, ROUND_2, RZ, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179+0.57859091j, 0. -0.j ],\n", + " [0. -0.j , 0.8156179-0.57859091j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByc, _438f3aAAByP, _438f3aAAByR], tags={GATE_54, ROUND_2, CZ, I1}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASco, _119073AASdA, _119073AAScn], tags={GATE_54, ROUND_2, CZ, I2}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByR, _438f3aAAByd, _438f3aAAByQ], tags={GATE_54, ROUND_2, CZ, I2}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdB, _119073AAScp, _119073AAScr], tags={GATE_55, ROUND_2, CZ, I3}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABye, _438f3aAAByS, _438f3aAAByU], tags={GATE_55, ROUND_2, CZ, I3}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScr, _119073AASdC, _119073AAScq], tags={GATE_55, ROUND_2, CZ, I4}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByU, _438f3aAAByf, _438f3aAAByT], tags={GATE_55, ROUND_2, CZ, I4}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdD, _119073AAScs, _119073AAScu], tags={GATE_56, ROUND_2, CZ, I5}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByg, _438f3aAAByV, _438f3aAAByX], tags={GATE_56, ROUND_2, CZ, I5}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScu, _119073AASdE, _119073AASct], tags={GATE_56, ROUND_2, CZ, I6}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByX, _438f3aAAByh, _438f3aAAByW], tags={GATE_56, ROUND_2, CZ, I6}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdF, _119073AAScv, _119073AAScx], tags={GATE_57, ROUND_2, CZ, I7}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByi, _438f3aAAByY, _438f3aAABya], tags={GATE_57, ROUND_2, CZ, I7}),backend=numpy, dtype=complex128, data=array([[[-0.34461337-0.j, 1.13818065-0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAScx, _119073AASdG, _119073AAScw], tags={GATE_57, ROUND_2, CZ, I8}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", - " [ 0. -0.j, 0.5611368 -0.j]],\n", + " [-1.13818065-0.j, -0.34461337-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABya, _438f3aAAByj, _438f3aAAByZ], tags={GATE_57, ROUND_2, CZ, I8}),backend=numpy, dtype=complex128, data=array([[[-1.04849371-0.j, 0. -0.j],\n", + " [-0. -0.j, 0.5611368 -0.j]],\n", "\n", " [[ 0.5611368 -0.j, 0. -0.j],\n", - " [ 0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2), inds=[_119073AASdI, _119073AAScy], tags={GATE_58, ROUND_2, RX, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdJ, _119073AAScz], tags={GATE_59, ROUND_2, RX, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdL, _119073AASdA], tags={GATE_60, ROUND_2, RX, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdM, _119073AASdB], tags={GATE_61, ROUND_2, RX, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdO, _119073AASdC], tags={GATE_62, ROUND_2, RX, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdP, _119073AASdD], tags={GATE_63, ROUND_2, RX, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdR, _119073AASdE], tags={GATE_64, ROUND_2, RX, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdS, _119073AASdF], tags={GATE_65, ROUND_2, RX, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdU, _119073AASdG], tags={GATE_66, ROUND_2, RX, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_119073AASdV, _119073AASdH], tags={GATE_67, ROUND_2, RX, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", - " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdX, _119073AASdI, _119073AASdK], tags={GATE_68, ROUND_3, CX, I0}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0. -0.j, 1.04849371-0.j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAByl, _438f3aAAByb], tags={GATE_58, ROUND_2, RX, I0}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABym, _438f3aAAByc], tags={GATE_59, ROUND_2, RX, I1}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByo, _438f3aAAByd], tags={GATE_60, ROUND_2, RX, I2}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByp, _438f3aAABye], tags={GATE_61, ROUND_2, RX, I3}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByr, _438f3aAAByf], tags={GATE_62, ROUND_2, RX, I4}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAABys, _438f3aAAByg], tags={GATE_63, ROUND_2, RX, I5}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByu, _438f3aAAByh], tags={GATE_64, ROUND_2, RX, I6}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByv, _438f3aAAByi], tags={GATE_65, ROUND_2, RX, I7}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByx, _438f3aAAByj], tags={GATE_66, ROUND_2, RX, I8}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2), inds=[_438f3aAAByy, _438f3aAAByk], tags={GATE_67, ROUND_2, RX, I9}),backend=numpy, dtype=complex128, data=array([[0.8156179-0.j , 0. +0.57859091j],\n", + " [0. +0.57859091j, 0.8156179-0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABzA, _438f3aAAByl, _438f3aAAByn], tags={GATE_68, ROUND_3, CX, I0}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdK, _119073AASdY, _119073AASdJ], tags={GATE_68, ROUND_3, CX, I1}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByn, _438f3aAABzB, _438f3aAABym], tags={GATE_68, ROUND_3, CX, I1}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", - " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdZ, _119073AASdL, _119073AASdN], tags={GATE_69, ROUND_3, CX, I2}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", + " [-0.84089642-0.j, 0. -0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABzC, _438f3aAAByo, _438f3aAAByq], tags={GATE_69, ROUND_3, CX, I2}),backend=numpy, dtype=complex128, data=array([[[ 1.18920712-0.j, 0. -0.j],\n", " [ 0. -0.j, 0. -0.j]],\n", "\n", " [[ 0. -0.j, 0. -0.j],\n", - " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdN, _119073AASda, _119073AASdM], tags={GATE_69, ROUND_3, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", + " [ 0. -0.j, -1.18920712-0.j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByq, _438f3aAABzD, _438f3aAAByp], tags={GATE_69, ROUND_3, CX, I3}),backend=numpy, dtype=complex128, data=array([[[ 0.84089642-0.j, 0. -0.j],\n", " [ 0. -0.j, 0.84089642-0.j]],\n", "\n", " [[-0. -0.j, -0.84089642-0.j],\n", @@ -54293,7 +1821,7 @@ "TensorNetworkGen(tensors=668, indices=802)" ] }, - "execution_count": 32, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -54305,30 +1833,31 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 34, + "id": "14972121-8a36-4345-b4fc-1263fc57f2c5", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
TensorNetworkGen(tensors=87, indices=67)
Tensor(shape=(2, 2), inds=[_119073AAYDm, _119073AAYDn], tags={GATE_138, ROUND_5, RZ, I7, GATE_144, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASfo, _119073AAYDl], tags={GATE_136, ROUND_5, RZ, I5, GATE_143, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYCr, _119073AAYCs], tags={GATE_109, ROUND_4, RZ, I7, GATE_115, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYCp, _119073AAYCq], tags={GATE_107, ROUND_4, RZ, I5, GATE_114, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASer, _119073AAYCo], tags={GATE_105, ROUND_4, RZ, I3, GATE_113, CZ, I4}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYBw, _119073AAYBx], tags={GATE_80, ROUND_3, RZ, I7, GATE_86, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYBu, _119073AAYBv], tags={GATE_78, ROUND_3, RZ, I5, GATE_85, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYBs, _119073AAYBt], tags={GATE_76, ROUND_3, RZ, I3, GATE_84, CZ, I4}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASdu, _119073AAYBr], tags={GATE_74, ROUND_3, RZ, I1, GATE_83, CZ, I2}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", - " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYEh, _119073AASgm], tags={GATE_167, ROUND_6, RZ, I7, GATE_173, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASfq, _119073AASfr], tags={GATE_138, ROUND_5, RZ, I7, GATE_144, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASev, _119073AASew], tags={GATE_109, ROUND_4, RZ, I7, GATE_115, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASet, _119073AASeu], tags={GATE_107, ROUND_4, RZ, I5, GATE_114, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASeA, _119073AASeB], tags={GATE_80, ROUND_3, RZ, I7, GATE_86, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASdy, _119073AASdz], tags={GATE_78, ROUND_3, RZ, I5, GATE_85, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AASdw, _119073AASdx], tags={GATE_76, ROUND_3, RZ, I3, GATE_84, CZ, I4}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", - " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_119073AAYEi, _119073AAYDn], tags={GATE_159, ROUND_6, CX, I8, GATE_153, ROUND_5, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYEi, _119073AAYEj, _119073AAYDo], tags={GATE_168, ROUND_6, RZ, I8, GATE_169, I9, GATE_154, ROUND_5, RX, GATE_159, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", + "
TensorNetworkGen(tensors=87, indices=67)
Tensor(shape=(2, 2), inds=[_438f3aAAFVl, _438f3aAAFVm], tags={GATE_138, ROUND_5, RZ, I7, GATE_144, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAACBR, _438f3aAAFVk], tags={GATE_136, ROUND_5, RZ, I5, GATE_143, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUq, _438f3aAAFUr], tags={GATE_109, ROUND_4, RZ, I7, GATE_115, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUo, _438f3aAAFUp], tags={GATE_107, ROUND_4, RZ, I5, GATE_114, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAACAU, _438f3aAAFUn], tags={GATE_105, ROUND_4, RZ, I3, GATE_113, CZ, I4}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTv, _438f3aAAFTw], tags={GATE_80, ROUND_3, RZ, I7, GATE_86, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTt, _438f3aAAFTu], tags={GATE_78, ROUND_3, RZ, I5, GATE_85, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTr, _438f3aAAFTs], tags={GATE_76, ROUND_3, RZ, I3, GATE_84, CZ, I4}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABzX, _438f3aAAFTq], tags={GATE_74, ROUND_3, RZ, I1, GATE_83, CZ, I2}),backend=numpy, dtype=complex128, data=array([[ 0.8156179-0.57859091j, 0.8156179-0.57859091j],\n", + " [ 0.8156179+0.57859091j, -0.8156179-0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFWg, _438f3aAACCP], tags={GATE_167, ROUND_6, RZ, I7, GATE_173, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAACBT, _438f3aAACBU], tags={GATE_138, ROUND_5, RZ, I7, GATE_144, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAACAY, _438f3aAACAZ], tags={GATE_109, ROUND_4, RZ, I7, GATE_115, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAACAW, _438f3aAACAX], tags={GATE_107, ROUND_4, RZ, I5, GATE_114, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABzd, _438f3aAABze], tags={GATE_80, ROUND_3, RZ, I7, GATE_86, CZ, I8}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABzb, _438f3aAABzc], tags={GATE_78, ROUND_3, RZ, I5, GATE_85, CZ, I6}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAABzZ, _438f3aAABza], tags={GATE_76, ROUND_3, RZ, I3, GATE_84, CZ, I4}),backend=numpy, dtype=complex128, data=array([[ 0.8156179+0.57859091j, 0.8156179+0.57859091j],\n", + " [ 0.8156179-0.57859091j, -0.8156179+0.57859091j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFWh, _438f3aAAFVm], tags={GATE_159, ROUND_6, CX, I8, GATE_153, ROUND_5, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFWh, _438f3aAAFWi, _438f3aAAFVn], tags={GATE_168, ROUND_6, RZ, I8, GATE_169, I9, GATE_154, ROUND_5, RX, GATE_159, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", " -4.59200617e-01-1.60782850e-01j],\n", " [-2.51780799e-18-4.86535026e-01j,\n", " 6.85850166e-01+2.33613923e-17j]],\n", @@ -54336,12 +1865,12 @@ " [[-2.51780799e-18+4.86535026e-01j,\n", " -6.85850166e-01+2.33613923e-17j],\n", " [-2.26649549e-01-6.47317875e-01j,\n", - " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASgk, _119073AAYDm, _119073AAYEh], tags={GATE_166, ROUND_6, RZ, I6, GATE_152, ROUND_5, RX, I7, GATE_158, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACCN, _438f3aAAFVl, _438f3aAAFWg], tags={GATE_166, ROUND_6, RZ, I6, GATE_152, ROUND_5, RX, I7, GATE_158, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYDn, _119073AAYCs], tags={GATE_130, ROUND_5, CX, I8, GATE_124, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYDn, _119073AAYDo, _119073AAYCt], tags={GATE_139, ROUND_5, RZ, I8, GATE_140, I9, GATE_125, ROUND_4, RX, GATE_130, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFVm, _438f3aAAFUr], tags={GATE_130, ROUND_5, CX, I8, GATE_124, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFVm, _438f3aAAFVn, _438f3aAAFUs], tags={GATE_139, ROUND_5, RZ, I8, GATE_140, I9, GATE_125, ROUND_4, RX, GATE_130, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", " -4.59200617e-01-1.60782850e-01j],\n", " [-2.51780799e-18-4.86535026e-01j,\n", " 6.85850166e-01+2.33613923e-17j]],\n", @@ -54349,13 +1878,13 @@ " [[-2.51780799e-18+4.86535026e-01j,\n", " -6.85850166e-01+2.33613923e-17j],\n", " [-2.26649549e-01-6.47317875e-01j,\n", - " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AAYDl, _119073AAYCq], tags={GATE_129, ROUND_5, CX, I6, GATE_122, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYDl, _119073AAYCr, _119073AAYDm], tags={GATE_137, ROUND_5, RZ, I6, GATE_123, ROUND_4, RX, I7, GATE_129, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFVk, _438f3aAAFUp], tags={GATE_129, ROUND_5, CX, I6, GATE_122, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFVk, _438f3aAAFUq, _438f3aAAFVl], tags={GATE_137, ROUND_5, RZ, I6, GATE_123, ROUND_4, RX, I7, GATE_129, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYCs, _119073AAYBx], tags={GATE_101, ROUND_4, CX, I8, GATE_95, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYCs, _119073AAYCt, _119073AAYBy], tags={GATE_110, ROUND_4, RZ, I8, GATE_111, I9, GATE_96, ROUND_3, RX, GATE_101, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUr, _438f3aAAFTw], tags={GATE_101, ROUND_4, CX, I8, GATE_95, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFUr, _438f3aAAFUs, _438f3aAAFTx], tags={GATE_110, ROUND_4, RZ, I8, GATE_111, I9, GATE_96, ROUND_3, RX, GATE_101, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", " -4.59200617e-01-1.60782850e-01j],\n", " [-2.51780799e-18-4.86535026e-01j,\n", " 6.85850166e-01+2.33613923e-17j]],\n", @@ -54363,18 +1892,18 @@ " [[-2.51780799e-18+4.86535026e-01j,\n", " -6.85850166e-01+2.33613923e-17j],\n", " [-2.26649549e-01-6.47317875e-01j,\n", - " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AAYCq, _119073AAYBv], tags={GATE_100, ROUND_4, CX, I6, GATE_93, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYCq, _119073AAYBw, _119073AAYCr], tags={GATE_108, ROUND_4, RZ, I6, GATE_94, ROUND_3, RX, I7, GATE_100, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUp, _438f3aAAFTu], tags={GATE_100, ROUND_4, CX, I6, GATE_93, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFUp, _438f3aAAFTv, _438f3aAAFUq], tags={GATE_108, ROUND_4, RZ, I6, GATE_94, ROUND_3, RX, I7, GATE_100, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYCo, _119073AAYBt], tags={GATE_99, ROUND_4, CX, I4, GATE_91, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYCo, _119073AAYBu, _119073AAYCp], tags={GATE_106, ROUND_4, RZ, I4, GATE_92, ROUND_3, RX, I5, GATE_99, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUn, _438f3aAAFTs], tags={GATE_99, ROUND_4, CX, I4, GATE_91, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFUn, _438f3aAAFTt, _438f3aAAFUo], tags={GATE_106, ROUND_4, RZ, I4, GATE_92, ROUND_3, RX, I5, GATE_99, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYBx, _119073AAYBC], tags={GATE_72, ROUND_3, CX, I8, GATE_66, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYBx, _119073AAYBy, _119073AAYBD], tags={GATE_81, ROUND_3, RZ, I8, GATE_82, I9, GATE_67, ROUND_2, RX, GATE_72, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTw, _438f3aAAFTB], tags={GATE_72, ROUND_3, CX, I8, GATE_66, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFTw, _438f3aAAFTx, _438f3aAAFTC], tags={GATE_81, ROUND_3, RZ, I8, GATE_82, I9, GATE_67, ROUND_2, RX, GATE_72, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01-6.47317875e-01j,\n", " -4.59200617e-01-1.60782850e-01j],\n", " [-2.51780799e-18-4.86535026e-01j,\n", " 6.85850166e-01+2.33613923e-17j]],\n", @@ -54382,27 +1911,27 @@ " [[-2.51780799e-18+4.86535026e-01j,\n", " -6.85850166e-01+2.33613923e-17j],\n", " [-2.26649549e-01-6.47317875e-01j,\n", - " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AAYBv, _119073AAYBA], tags={GATE_71, ROUND_3, CX, I6, GATE_64, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYBv, _119073AAYBB, _119073AAYBw], tags={GATE_79, ROUND_3, RZ, I6, GATE_65, ROUND_2, RX, I7, GATE_71, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " -4.59200617e-01+1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTu, _438f3aAAFSz], tags={GATE_71, ROUND_3, CX, I6, GATE_64, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFTu, _438f3aAAFTA, _438f3aAAFTv], tags={GATE_79, ROUND_3, RZ, I6, GATE_65, ROUND_2, RX, I7, GATE_71, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYBt, _119073AAYAy], tags={GATE_70, ROUND_3, CX, I4, GATE_62, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYBt, _119073AAYAz, _119073AAYBu], tags={GATE_77, ROUND_3, RZ, I4, GATE_63, ROUND_2, RX, I5, GATE_70, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTs, _438f3aAAFSx], tags={GATE_70, ROUND_3, CX, I4, GATE_62, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFTs, _438f3aAAFSy, _438f3aAAFTt], tags={GATE_77, ROUND_3, RZ, I4, GATE_63, ROUND_2, RX, I5, GATE_70, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYBr, _119073AAYAw], tags={GATE_69, ROUND_3, CX, I2, GATE_60, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", - " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYBr, _119073AAYAx, _119073AAYBs], tags={GATE_75, ROUND_3, RZ, I2, GATE_61, ROUND_2, RX, I3, GATE_69, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTq, _438f3aAAFSv], tags={GATE_69, ROUND_3, CX, I2, GATE_60, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.j , 0. -0.68806443j],\n", + " [ 0. +0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFTq, _438f3aAAFSw, _438f3aAAFTr], tags={GATE_75, ROUND_3, RZ, I2, GATE_61, ROUND_2, RX, I3, GATE_69, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYBC, _119073AAYBB], tags={GATE_43, ROUND_2, CX, I8, GATE_51, RZ, I7, GATE_57, CZ}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.68806443j, 0.96993861+0.68806443j],\n", - " [-0.96993861+0.68806443j, 0.96993861+0.68806443j]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYBA, _119073AAYAG, _119073AAYBB], tags={GATE_50, ROUND_2, RZ, I6, GATE_36, ROUND_1, RX, I7, GATE_42, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFTB, _438f3aAAFTA], tags={GATE_43, ROUND_2, CX, I8, GATE_51, RZ, I7, GATE_57, CZ}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.68806443j, 0.96993861+0.68806443j],\n", + " [-0.96993861+0.68806443j, 0.96993861+0.68806443j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFSz, _438f3aAAFSF, _438f3aAAFTA], tags={GATE_50, ROUND_2, RZ, I6, GATE_36, ROUND_1, RX, I7, GATE_42, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167-0.39682667j, -0.28150475-0.39682667j],\n", " [-0.28150475-0.39682667j, 0.55939167-0.39682667j]],\n", "\n", " [[-0.28150475+0.39682667j, -0.55939167-0.39682667j],\n", - " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAShh, _119073AAYFe, _119073AASgn], tags={GATE_197, ROUND_7, RZ, I8, GATE_198, I9, GATE_183, ROUND_6, RX, GATE_188, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", + " [-0.55939167-0.39682667j, -0.28150475+0.39682667j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACDK, _438f3aAAFXd, _438f3aAACCQ], tags={GATE_197, ROUND_7, RZ, I8, GATE_198, I9, GATE_183, ROUND_6, RX, GATE_188, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", " -4.59200617e-01+1.60782850e-01j],\n", " [-2.51780799e-18+4.86535026e-01j,\n", " 6.85850166e-01-2.33613923e-17j]],\n", @@ -54410,8 +1939,8 @@ " [[-2.51780799e-18-4.86535026e-01j,\n", " -6.85850166e-01-2.33613923e-17j],\n", " [-2.26649549e-01+6.47317875e-01j,\n", - " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AASgm, _119073AASfr], tags={GATE_159, ROUND_6, CX, I8, GATE_153, ROUND_5, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASgm, _119073AASgn, _119073AASfs], tags={GATE_168, ROUND_6, RZ, I8, GATE_169, I9, GATE_154, ROUND_5, RX, GATE_159, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", + " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACCP, _438f3aAACBU], tags={GATE_159, ROUND_6, CX, I8, GATE_153, ROUND_5, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACCP, _438f3aAACCQ, _438f3aAACBV], tags={GATE_168, ROUND_6, RZ, I8, GATE_169, I9, GATE_154, ROUND_5, RX, GATE_159, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", " -4.59200617e-01+1.60782850e-01j],\n", " [-2.51780799e-18+4.86535026e-01j,\n", " 6.85850166e-01-2.33613923e-17j]],\n", @@ -54419,12 +1948,12 @@ " [[-2.51780799e-18-4.86535026e-01j,\n", " -6.85850166e-01-2.33613923e-17j],\n", " [-2.26649549e-01+6.47317875e-01j,\n", - " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASgk, _119073AASfq, _119073AAYEh], tags={GATE_166, ROUND_6, RZ, I6, GATE_152, ROUND_5, RX, I7, GATE_158, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACCN, _438f3aAACBT, _438f3aAAFWg], tags={GATE_166, ROUND_6, RZ, I6, GATE_152, ROUND_5, RX, I7, GATE_158, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASfr, _119073AASew], tags={GATE_130, ROUND_5, CX, I8, GATE_124, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASfr, _119073AASfs, _119073AASex], tags={GATE_139, ROUND_5, RZ, I8, GATE_140, I9, GATE_125, ROUND_4, RX, GATE_130, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACBU, _438f3aAACAZ], tags={GATE_130, ROUND_5, CX, I8, GATE_124, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACBU, _438f3aAACBV, _438f3aAACAa], tags={GATE_139, ROUND_5, RZ, I8, GATE_140, I9, GATE_125, ROUND_4, RX, GATE_130, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", " -4.59200617e-01+1.60782850e-01j],\n", " [-2.51780799e-18+4.86535026e-01j,\n", " 6.85850166e-01-2.33613923e-17j]],\n", @@ -54432,18 +1961,18 @@ " [[-2.51780799e-18-4.86535026e-01j,\n", " -6.85850166e-01-2.33613923e-17j],\n", " [-2.26649549e-01+6.47317875e-01j,\n", - " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AASfp, _119073AASeu], tags={GATE_129, ROUND_5, CX, I6, GATE_122, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASfp, _119073AASev, _119073AASfq], tags={GATE_137, ROUND_5, RZ, I6, GATE_123, ROUND_4, RX, I7, GATE_129, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACBS, _438f3aAACAX], tags={GATE_129, ROUND_5, CX, I6, GATE_122, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACBS, _438f3aAACAY, _438f3aAACBT], tags={GATE_137, ROUND_5, RZ, I6, GATE_123, ROUND_4, RX, I7, GATE_129, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYDj, _119073AASes], tags={GATE_128, ROUND_5, CX, I4, GATE_120, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYDj, _119073AASet, _119073AASfo], tags={GATE_135, ROUND_5, RZ, I4, GATE_121, ROUND_4, RX, I5, GATE_128, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFVi, _438f3aAACAV], tags={GATE_128, ROUND_5, CX, I4, GATE_120, ROUND_4, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFVi, _438f3aAACAW, _438f3aAACBR], tags={GATE_135, ROUND_5, RZ, I4, GATE_121, ROUND_4, RX, I5, GATE_128, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASew, _119073AASeB], tags={GATE_101, ROUND_4, CX, I8, GATE_95, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASew, _119073AASex, _119073AASeC], tags={GATE_110, ROUND_4, RZ, I8, GATE_111, I9, GATE_96, ROUND_3, RX, GATE_101, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACAZ, _438f3aAABze], tags={GATE_101, ROUND_4, CX, I8, GATE_95, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACAZ, _438f3aAACAa, _438f3aAABzf], tags={GATE_110, ROUND_4, RZ, I8, GATE_111, I9, GATE_96, ROUND_3, RX, GATE_101, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", " -4.59200617e-01+1.60782850e-01j],\n", " [-2.51780799e-18+4.86535026e-01j,\n", " 6.85850166e-01-2.33613923e-17j]],\n", @@ -54451,23 +1980,23 @@ " [[-2.51780799e-18-4.86535026e-01j,\n", " -6.85850166e-01-2.33613923e-17j],\n", " [-2.26649549e-01+6.47317875e-01j,\n", - " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AASeu, _119073AASdz], tags={GATE_100, ROUND_4, CX, I6, GATE_93, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASeu, _119073AASeA, _119073AASev], tags={GATE_108, ROUND_4, RZ, I6, GATE_94, ROUND_3, RX, I7, GATE_100, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACAX, _438f3aAABzc], tags={GATE_100, ROUND_4, CX, I6, GATE_93, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACAX, _438f3aAABzd, _438f3aAACAY], tags={GATE_108, ROUND_4, RZ, I6, GATE_94, ROUND_3, RX, I7, GATE_100, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASes, _119073AASdx], tags={GATE_99, ROUND_4, CX, I4, GATE_91, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASes, _119073AASdy, _119073AASet], tags={GATE_106, ROUND_4, RZ, I4, GATE_92, ROUND_3, RX, I5, GATE_99, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACAV, _438f3aAABza], tags={GATE_99, ROUND_4, CX, I4, GATE_91, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACAV, _438f3aAABzb, _438f3aAACAW], tags={GATE_106, ROUND_4, RZ, I4, GATE_92, ROUND_3, RX, I5, GATE_99, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AAYCm, _119073AASdv], tags={GATE_98, ROUND_4, CX, I2, GATE_89, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYCm, _119073AASdw, _119073AASer], tags={GATE_104, ROUND_4, RZ, I2, GATE_90, ROUND_3, RX, I3, GATE_98, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUl, _438f3aAABzY], tags={GATE_98, ROUND_4, CX, I2, GATE_89, ROUND_3, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFUl, _438f3aAABzZ, _438f3aAACAU], tags={GATE_104, ROUND_4, RZ, I2, GATE_90, ROUND_3, RX, I3, GATE_98, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASeB, _119073AASdG], tags={GATE_72, ROUND_3, CX, I8, GATE_66, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASeB, _119073AASeC, _119073AASdH], tags={GATE_81, ROUND_3, RZ, I8, GATE_82, I9, GATE_67, ROUND_2, RX, GATE_72, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAABze, _438f3aAAByj], tags={GATE_72, ROUND_3, CX, I8, GATE_66, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABze, _438f3aAABzf, _438f3aAAByk], tags={GATE_81, ROUND_3, RZ, I8, GATE_82, I9, GATE_67, ROUND_2, RX, GATE_72, CX}),backend=numpy, dtype=complex128, data=array([[[ 2.26649549e-01+6.47317875e-01j,\n", " -4.59200617e-01+1.60782850e-01j],\n", " [-2.51780799e-18+4.86535026e-01j,\n", " 6.85850166e-01-2.33613923e-17j]],\n", @@ -54475,87 +2004,87 @@ " [[-2.51780799e-18-4.86535026e-01j,\n", " -6.85850166e-01-2.33613923e-17j],\n", " [-2.26649549e-01+6.47317875e-01j,\n", - " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AASdz, _119073AASdE], tags={GATE_71, ROUND_3, CX, I6, GATE_64, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdz, _119073AASdF, _119073AASeA], tags={GATE_79, ROUND_3, RZ, I6, GATE_65, ROUND_2, RX, I7, GATE_71, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " -4.59200617e-01-1.60782850e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAABzc, _438f3aAAByh], tags={GATE_71, ROUND_3, CX, I6, GATE_64, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABzc, _438f3aAAByi, _438f3aAABzd], tags={GATE_79, ROUND_3, RZ, I6, GATE_65, ROUND_2, RX, I7, GATE_71, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASdx, _119073AASdC], tags={GATE_70, ROUND_3, CX, I4, GATE_62, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdx, _119073AASdD, _119073AASdy], tags={GATE_77, ROUND_3, RZ, I4, GATE_63, ROUND_2, RX, I5, GATE_70, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAABza, _438f3aAAByf], tags={GATE_70, ROUND_3, CX, I4, GATE_62, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABza, _438f3aAAByg, _438f3aAABzb], tags={GATE_77, ROUND_3, RZ, I4, GATE_63, ROUND_2, RX, I5, GATE_70, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASdv, _119073AASdA], tags={GATE_69, ROUND_3, CX, I2, GATE_60, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", - " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdv, _119073AASdB, _119073AASdw], tags={GATE_75, ROUND_3, RZ, I2, GATE_61, ROUND_2, RX, I3, GATE_69, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAABzY, _438f3aAAByd], tags={GATE_69, ROUND_3, CX, I2, GATE_60, ROUND_2, RX}),backend=numpy, dtype=complex128, data=array([[ 0.96993861-0.j , 0. +0.68806443j],\n", + " [ 0. -0.68806443j, -0.96993861+0.j ]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABzY, _438f3aAABye, _438f3aAABzZ], tags={GATE_75, ROUND_3, RZ, I2, GATE_61, ROUND_2, RX, I3, GATE_69, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASdG, _119073AASdF], tags={GATE_43, ROUND_2, CX, I8, GATE_51, RZ, I7, GATE_57, CZ}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.68806443j, 0.96993861-0.68806443j],\n", - " [-0.96993861-0.68806443j, 0.96993861-0.68806443j]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdE, _119073AAScK, _119073AASdF], tags={GATE_50, ROUND_2, RZ, I6, GATE_36, ROUND_1, RX, I7, GATE_42, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAAByj, _438f3aAAByi], tags={GATE_43, ROUND_2, CX, I8, GATE_51, RZ, I7, GATE_57, CZ}),backend=numpy, dtype=complex128, data=array([[ 0.96993861+0.68806443j, 0.96993861-0.68806443j],\n", + " [-0.96993861-0.68806443j, 0.96993861-0.68806443j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByh, _438f3aAABxn, _438f3aAAByi], tags={GATE_50, ROUND_2, RZ, I6, GATE_36, ROUND_1, RX, I7, GATE_42, CX}),backend=numpy, dtype=complex128, data=array([[[ 0.55939167+0.39682667j, -0.28150475+0.39682667j],\n", " [-0.28150475+0.39682667j, 0.55939167+0.39682667j]],\n", "\n", " [[-0.28150475-0.39682667j, -0.55939167+0.39682667j],\n", - " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdG, _119073AAScK, _119073AASdH], tags={GATE_52, ROUND_2, RZ, I8, GATE_14, ROUND_1, CX, GATE_22, I7, GATE_28, CZ, GATE_37, RX, GATE_23, GATE_8, ROUND_0, H, GATE_53, I9, GATE_38, GATE_43, GATE_24, GATE_9, GATE_21, I6, GATE_6, GATE_7, GATE_13}),backend=numpy, dtype=complex128, data=array([[[ 0.5027836 +0.11370736j, -0.02428325-0.12148106j],\n", + " [-0.55939167+0.39682667j, -0.28150475-0.39682667j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByj, _438f3aAABxn, _438f3aAAByk], tags={GATE_52, ROUND_2, RZ, I8, GATE_14, ROUND_1, CX, GATE_22, I7, GATE_28, CZ, GATE_37, RX, GATE_23, GATE_8, ROUND_0, H, GATE_53, I9, GATE_38, GATE_43, GATE_24, GATE_9, GATE_21, I6, GATE_6, GATE_7, GATE_13}),backend=numpy, dtype=complex128, data=array([[[ 0.5027836 +0.11370736j, -0.02428325-0.12148106j],\n", " [-0.02428325-0.12148106j, -0.02428325+0.01722628j]],\n", "\n", " [[ 0.02428325+0.01722628j, 0.1226808 +0.01722628j],\n", - " [-0.02428325+0.12148106j, 0.142557 +0.49537684j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYBC, _119073AAYAG, _119073AAYBD], tags={GATE_52, ROUND_2, RZ, I8, GATE_14, ROUND_1, CX, GATE_22, I7, GATE_28, CZ, GATE_37, RX, GATE_23, GATE_8, ROUND_0, H, GATE_53, I9, GATE_38, GATE_43, GATE_24, GATE_9, GATE_21, I6, GATE_6, GATE_7, GATE_13}),backend=numpy, dtype=complex128, data=array([[[ 0.5027836 -0.11370736j, -0.02428325+0.12148106j],\n", + " [-0.02428325+0.12148106j, 0.142557 +0.49537684j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFTB, _438f3aAAFSF, _438f3aAAFTC], tags={GATE_52, ROUND_2, RZ, I8, GATE_14, ROUND_1, CX, GATE_22, I7, GATE_28, CZ, GATE_37, RX, GATE_23, GATE_8, ROUND_0, H, GATE_53, I9, GATE_38, GATE_43, GATE_24, GATE_9, GATE_21, I6, GATE_6, GATE_7, GATE_13}),backend=numpy, dtype=complex128, data=array([[[ 0.5027836 -0.11370736j, -0.02428325+0.12148106j],\n", " [-0.02428325+0.12148106j, -0.02428325-0.01722628j]],\n", "\n", " [[ 0.02428325-0.01722628j, 0.1226808 -0.01722628j],\n", - " [-0.02428325-0.12148106j, 0.142557 -0.49537684j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdB, _119073AASdC, _119073AASdA], tags={GATE_47, ROUND_2, RZ, I3, GATE_55, CZ, I4, GATE_41, CX, GATE_33, ROUND_1, RX, GATE_12, GATE_18, GATE_26, GATE_19, GATE_4, ROUND_0, H, GATE_5, I5, GATE_46, I2, GATE_32, GATE_40, GATE_17, GATE_2, GATE_3, GATE_11}),backend=numpy, dtype=complex128, data=array([[[-0.53798078+3.63434853e-01j, 0.28016385-2.68095775e-17j],\n", + " [-0.02428325-0.12148106j, 0.142557 -0.49537684j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAABye, _438f3aAAByf, _438f3aAAByd], tags={GATE_47, ROUND_2, RZ, I3, GATE_55, CZ, I4, GATE_41, CX, GATE_33, ROUND_1, RX, GATE_12, GATE_18, GATE_26, GATE_19, GATE_4, ROUND_0, H, GATE_5, I5, GATE_46, I2, GATE_32, GATE_40, GATE_17, GATE_2, GATE_3, GATE_11}),backend=numpy, dtype=complex128, data=array([[[-0.53798078+3.63434853e-01j, 0.28016385+6.06362953e-18j],\n", " [ 0.09258438+2.64423745e-01j, -0.16523255+6.27858598e-01j]],\n", "\n", - " [[-0.28016385+7.81422312e-17j, -0.64718797-5.15358662e-02j],\n", - " [-0.16523255+6.27858598e-01j, 0.09258438-2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdD, _119073AASdE, _119073AASdC], tags={GATE_49, ROUND_2, RZ, I5, GATE_56, CZ, I6, GATE_42, CX, GATE_35, ROUND_1, RX, GATE_13, GATE_20, GATE_27, GATE_21, GATE_6, ROUND_0, H, GATE_7, I7, GATE_48, I4, GATE_34, GATE_41, GATE_19, GATE_4, GATE_5, GATE_12}),backend=numpy, dtype=complex128, data=array([[[-0.53798078+3.63434853e-01j, 0.28016385-2.68095775e-17j],\n", + " [[-0.28016385+6.57395498e-17j, -0.64718797-5.15358662e-02j],\n", + " [-0.16523255+6.27858598e-01j, 0.09258438-2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAByg, _438f3aAAByh, _438f3aAAByf], tags={GATE_49, ROUND_2, RZ, I5, GATE_56, CZ, I6, GATE_42, CX, GATE_35, ROUND_1, RX, GATE_13, GATE_20, GATE_27, GATE_21, GATE_6, ROUND_0, H, GATE_7, I7, GATE_48, I4, GATE_34, GATE_41, GATE_19, GATE_4, GATE_5, GATE_12}),backend=numpy, dtype=complex128, data=array([[[-0.53798078+3.63434853e-01j, 0.28016385+6.06362953e-18j],\n", " [ 0.09258438+2.64423745e-01j, -0.16523255+6.27858598e-01j]],\n", "\n", - " [[-0.28016385+7.81422312e-17j, -0.64718797-5.15358662e-02j],\n", - " [-0.16523255+6.27858598e-01j, 0.09258438-2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYAx, _119073AAYAy, _119073AAYAw], tags={GATE_47, ROUND_2, RZ, I3, GATE_55, CZ, I4, GATE_41, CX, GATE_33, ROUND_1, RX, GATE_12, GATE_18, GATE_26, GATE_19, GATE_4, ROUND_0, H, GATE_5, I5, GATE_46, I2, GATE_32, GATE_40, GATE_17, GATE_2, GATE_3, GATE_11}),backend=numpy, dtype=complex128, data=array([[[-0.53798078-3.63434853e-01j, 0.28016385+2.68095775e-17j],\n", + " [[-0.28016385+6.57395498e-17j, -0.64718797-5.15358662e-02j],\n", + " [-0.16523255+6.27858598e-01j, 0.09258438-2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFSw, _438f3aAAFSx, _438f3aAAFSv], tags={GATE_47, ROUND_2, RZ, I3, GATE_55, CZ, I4, GATE_41, CX, GATE_33, ROUND_1, RX, GATE_12, GATE_18, GATE_26, GATE_19, GATE_4, ROUND_0, H, GATE_5, I5, GATE_46, I2, GATE_32, GATE_40, GATE_17, GATE_2, GATE_3, GATE_11}),backend=numpy, dtype=complex128, data=array([[[-0.53798078-3.63434853e-01j, 0.28016385-6.06362953e-18j],\n", " [ 0.09258438-2.64423745e-01j, -0.16523255-6.27858598e-01j]],\n", "\n", - " [[-0.28016385-7.81422312e-17j, -0.64718797+5.15358662e-02j],\n", - " [-0.16523255-6.27858598e-01j, 0.09258438+2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYAz, _119073AAYBA, _119073AAYAy], tags={GATE_49, ROUND_2, RZ, I5, GATE_56, CZ, I6, GATE_42, CX, GATE_35, ROUND_1, RX, GATE_13, GATE_20, GATE_27, GATE_21, GATE_6, ROUND_0, H, GATE_7, I7, GATE_48, I4, GATE_34, GATE_41, GATE_19, GATE_4, GATE_5, GATE_12}),backend=numpy, dtype=complex128, data=array([[[-0.53798078-3.63434853e-01j, 0.28016385+2.68095775e-17j],\n", + " [[-0.28016385-6.57395498e-17j, -0.64718797+5.15358662e-02j],\n", + " [-0.16523255-6.27858598e-01j, 0.09258438+2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFSy, _438f3aAAFSz, _438f3aAAFSx], tags={GATE_49, ROUND_2, RZ, I5, GATE_56, CZ, I6, GATE_42, CX, GATE_35, ROUND_1, RX, GATE_13, GATE_20, GATE_27, GATE_21, GATE_6, ROUND_0, H, GATE_7, I7, GATE_48, I4, GATE_34, GATE_41, GATE_19, GATE_4, GATE_5, GATE_12}),backend=numpy, dtype=complex128, data=array([[[-0.53798078-3.63434853e-01j, 0.28016385-6.06362953e-18j],\n", " [ 0.09258438-2.64423745e-01j, -0.16523255-6.27858598e-01j]],\n", "\n", - " [[-0.28016385-7.81422312e-17j, -0.64718797+5.15358662e-02j],\n", - " [-0.16523255-6.27858598e-01j, 0.09258438+2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AAShh, _119073AAYFe, _119073AAYEj], tags={GATE_197, ROUND_7, RZ, I8, GATE_198, I9, GATE_183, ROUND_6, RX, GATE_188, CX, GATE_212, GATE_217, ROUND_8, GATE_227, GATE_241, GATE_251, ROUND_9, H}),backend=numpy, dtype=complex128, data=array([[[-1.90588793e-01+5.44327281e-01j,\n", + " [[-0.28016385-6.57395498e-17j, -0.64718797+5.15358662e-02j],\n", + " [-0.16523255-6.27858598e-01j, 0.09258438+2.64423745e-01j]]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAACDK, _438f3aAAFXd, _438f3aAAFWi], tags={GATE_197, ROUND_7, RZ, I8, GATE_198, I9, GATE_183, ROUND_6, RX, GATE_188, CX, GATE_212, GATE_217, ROUND_8, GATE_227, GATE_241, GATE_251, ROUND_9, H}),backend=numpy, dtype=complex128, data=array([[[-1.90588793e-01+5.44327281e-01j,\n", " 3.86140152e-01+1.35201722e-01j],\n", - " [ 2.11721571e-18+4.09125559e-01j,\n", - " -5.76728946e-01-1.96445111e-17j]],\n", + " [ 4.47512346e-18+4.09125559e-01j,\n", + " -5.76728946e-01-1.63206570e-17j]],\n", "\n", - " [[ 2.11721571e-18-4.09125559e-01j,\n", - " 5.76728946e-01-1.96445111e-17j],\n", + " [[-2.40692041e-19-4.09125559e-01j,\n", + " 5.76728946e-01-2.29683651e-17j],\n", " [ 1.90588793e-01+5.44327281e-01j,\n", - " 3.86140152e-01-1.35201722e-01j]]])
Tensor(shape=(2, 2), inds=[_119073AAShh, _119073AASgm], tags={GATE_188, ROUND_7, CX, I8, GATE_182, ROUND_6, RX, GATE_217, ROUND_8, GATE_211, GATE_212, I9, GATE_227, RZ, GATE_241, GATE_251, ROUND_9, H, GATE_226, GATE_240, GATE_250, GATE_231, CZ, I7, GATE_225}),backend=numpy, dtype=complex128, data=array([[ 0.9407809 -0.66738026j, 0.47343266+0.66738026j],\n", - " [-0.47343266-0.66738026j, -0.9407809 +0.66738026j]])
Tensor(shape=(2, 2), inds=[_119073AAShh, _119073AAYEi], tags={GATE_188, ROUND_7, CX, I8, GATE_182, ROUND_6, RX, GATE_196, RZ, I7, GATE_202, CZ}),backend=numpy, dtype=complex128, data=array([[-9.69938606e-01+0.00000000e+00j, 0.00000000e+00+6.88064432e-01j],\n", - " [-5.07964202e-18-6.88064432e-01j, 9.69938606e-01-7.16058072e-18j]])
Tensor(shape=(2, 2), inds=[_119073AAYEh, _119073AAYEi], tags={GATE_167, ROUND_6, RZ, I7, GATE_173, CZ, I8, GATE_195, ROUND_7, I6, GATE_181, RX, GATE_187, CX, GATE_210, GATE_216, ROUND_8, GATE_224, GATE_238, GATE_248, ROUND_9, H, GATE_225, GATE_239, GATE_249, GATE_226, GATE_231, GATE_196, GATE_202}),backend=numpy, dtype=complex128, data=array([[-0.62892738+0.44615459j, -0.62892738+0.44615459j],\n", - " [-0.62892738-0.44615459j, 0.62892738+0.44615459j]])
Tensor(shape=(2, 2), inds=[_119073AASgk, _119073AASfp], tags={GATE_158, ROUND_6, CX, I6, GATE_151, ROUND_5, RX, GATE_187, ROUND_7, GATE_180, GATE_195, RZ, GATE_181, I7, GATE_210, GATE_216, ROUND_8, GATE_224, GATE_238, GATE_248, ROUND_9, H, GATE_225, GATE_239, GATE_249, GATE_226, I8, GATE_231, CZ, GATE_196, GATE_202, GATE_209, GATE_230, I5, GATE_223, GATE_194, GATE_201, GATE_208, GATE_215, GATE_222, I4, GATE_236, GATE_246, GATE_237, GATE_247}),backend=numpy, dtype=complex128, data=array([[ 1.15345789e+00-5.31640927e-17j, 3.77140584e-17+8.18251118e-01j],\n", - " [-4.66651456e-17-8.18251118e-01j, -1.15345789e+00+6.57821044e-17j]])
Tensor(shape=(2, 2), inds=[_119073AASgk, _119073AAYDl], tags={GATE_158, ROUND_6, CX, I6, GATE_151, ROUND_5, RX, GATE_165, RZ, I5, GATE_172, CZ}),backend=numpy, dtype=complex128, data=array([[-9.69938606e-01+0.00000000e+00j, 0.00000000e+00+6.88064432e-01j],\n", - " [ 5.07964202e-18-6.88064432e-01j, 9.69938606e-01+7.16058072e-18j]])
Tensor(shape=(2, 2), inds=[_119073AASfo, _119073AASfp], tags={GATE_136, ROUND_5, RZ, I5, GATE_143, CZ, I6, GATE_164, ROUND_6, I4, GATE_150, RX, GATE_157, CX, GATE_193, ROUND_7, GATE_179, GATE_186, GATE_194, GATE_201, GATE_208, GATE_215, ROUND_8, GATE_222, GATE_236, GATE_246, ROUND_9, H, GATE_223, GATE_237, GATE_247, GATE_224, GATE_230, GATE_165, GATE_172}),backend=numpy, dtype=complex128, data=array([[ 0.61545076+0.43659441j, 0.61545076+0.43659441j],\n", - " [ 0.61545076-0.43659441j, -0.61545076+0.43659441j]])
Tensor(shape=(2, 2), inds=[_119073AAYDj, _119073AAYCo], tags={GATE_128, ROUND_5, CX, I4, GATE_120, ROUND_4, RX, GATE_157, ROUND_6, GATE_149, GATE_164, RZ, GATE_150, I5, GATE_193, ROUND_7, GATE_179, GATE_186, GATE_194, GATE_201, CZ, I6, GATE_208, GATE_215, ROUND_8, GATE_222, GATE_236, GATE_246, ROUND_9, H, GATE_223, GATE_237, GATE_247, GATE_224, GATE_230, GATE_165, GATE_172, GATE_178, GATE_192, I3, GATE_200, GATE_206, GATE_214, GATE_220, I2, GATE_234, GATE_244, GATE_221, GATE_235, GATE_245, GATE_229, GATE_207, GATE_163, GATE_171, GATE_191, GATE_177, GATE_185}),backend=numpy, dtype=complex128, data=array([[ 1.15345789e+00-6.10152182e-17j, -4.32835657e-17-8.18251118e-01j],\n", - " [ 5.45687982e-17+8.18251118e-01j, -1.15345789e+00+7.69235868e-17j]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYDj, _119073AAYCp, _119073AASfo], tags={GATE_135, ROUND_5, RZ, I4, GATE_121, ROUND_4, RX, I5, GATE_128, CX, GATE_134, I3, GATE_142, CZ}),backend=numpy, dtype=complex128, data=array([[[-0.55939167+0.39682667j, 0.28150475+0.39682667j],\n", + " 3.86140152e-01-1.35201722e-01j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACDK, _438f3aAACCP], tags={GATE_188, ROUND_7, CX, I8, GATE_182, ROUND_6, RX, GATE_217, ROUND_8, GATE_211, GATE_212, I9, GATE_227, RZ, GATE_241, GATE_251, ROUND_9, H, GATE_226, GATE_240, GATE_250, GATE_231, CZ, I7, GATE_225}),backend=numpy, dtype=complex128, data=array([[ 0.9407809 -0.66738026j, 0.47343266+0.66738026j],\n", + " [-0.47343266-0.66738026j, -0.9407809 +0.66738026j]])
Tensor(shape=(2, 2), inds=[_438f3aAACDK, _438f3aAAFWh], tags={GATE_188, ROUND_7, CX, I8, GATE_182, ROUND_6, RX, GATE_196, RZ, I7, GATE_202, CZ}),backend=numpy, dtype=complex128, data=array([[-9.69938606e-01+0.00000000e+00j, 0.00000000e+00+6.88064432e-01j],\n", + " [-5.07964202e-18-6.88064432e-01j, 9.69938606e-01-7.16058072e-18j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFWg, _438f3aAAFWh], tags={GATE_167, ROUND_6, RZ, I7, GATE_173, CZ, I8, GATE_195, ROUND_7, I6, GATE_181, RX, GATE_187, CX, GATE_210, GATE_216, ROUND_8, GATE_224, GATE_238, GATE_248, ROUND_9, H, GATE_225, GATE_239, GATE_249, GATE_226, GATE_231, GATE_196, GATE_202}),backend=numpy, dtype=complex128, data=array([[-0.62892738+0.44615459j, -0.62892738+0.44615459j],\n", + " [-0.62892738-0.44615459j, 0.62892738+0.44615459j]])
Tensor(shape=(2, 2), inds=[_438f3aAACCN, _438f3aAACBS], tags={GATE_158, ROUND_6, CX, I6, GATE_151, ROUND_5, RX, GATE_187, ROUND_7, GATE_180, GATE_195, RZ, GATE_181, I7, GATE_210, GATE_216, ROUND_8, GATE_224, GATE_238, GATE_248, ROUND_9, H, GATE_225, GATE_239, GATE_249, GATE_226, I8, GATE_231, CZ, GATE_196, GATE_202, GATE_209, GATE_230, I5, GATE_223, GATE_194, GATE_201, GATE_208, GATE_215, GATE_222, I4, GATE_236, GATE_246, GATE_237, GATE_247}),backend=numpy, dtype=complex128, data=array([[ 1.15345789e+00+3.08719276e-17j, -2.19002267e-17+8.18251118e-01j],\n", + " [ 5.29450912e-17-8.18251118e-01j, -1.15345789e+00-7.46347080e-17j]])
Tensor(shape=(2, 2), inds=[_438f3aAACCN, _438f3aAAFVk], tags={GATE_158, ROUND_6, CX, I6, GATE_151, ROUND_5, RX, GATE_165, RZ, I5, GATE_172, CZ}),backend=numpy, dtype=complex128, data=array([[-9.69938606e-01+0.00000000e+00j, 0.00000000e+00+6.88064432e-01j],\n", + " [ 5.07964202e-18-6.88064432e-01j, 9.69938606e-01+7.16058072e-18j]])
Tensor(shape=(2, 2), inds=[_438f3aAACBR, _438f3aAACBS], tags={GATE_136, ROUND_5, RZ, I5, GATE_143, CZ, I6, GATE_164, ROUND_6, I4, GATE_150, RX, GATE_157, CX, GATE_193, ROUND_7, GATE_179, GATE_186, GATE_194, GATE_201, GATE_208, GATE_215, ROUND_8, GATE_222, GATE_236, GATE_246, ROUND_9, H, GATE_223, GATE_237, GATE_247, GATE_224, GATE_230, GATE_165, GATE_172}),backend=numpy, dtype=complex128, data=array([[ 0.61545076+0.43659441j, 0.61545076+0.43659441j],\n", + " [ 0.61545076-0.43659441j, -0.61545076+0.43659441j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFVi, _438f3aAAFUn], tags={GATE_128, ROUND_5, CX, I4, GATE_120, ROUND_4, RX, GATE_157, ROUND_6, GATE_149, GATE_164, RZ, GATE_150, I5, GATE_193, ROUND_7, GATE_179, GATE_186, GATE_194, GATE_201, CZ, I6, GATE_208, GATE_215, ROUND_8, GATE_222, GATE_236, GATE_246, ROUND_9, H, GATE_223, GATE_237, GATE_247, GATE_224, GATE_230, GATE_165, GATE_172, GATE_178, GATE_192, I3, GATE_200, GATE_206, GATE_214, GATE_220, I2, GATE_234, GATE_244, GATE_221, GATE_235, GATE_245, GATE_229, GATE_207, GATE_163, GATE_171, GATE_191, GATE_177, GATE_185}),backend=numpy, dtype=complex128, data=array([[ 1.15345789e+00+4.06113858e-17j, 2.88092977e-17-8.18251118e-01j],\n", + " [-3.50891981e-17+8.18251118e-01j, -1.15345789e+00-4.94639256e-17j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFVi, _438f3aAAFUo, _438f3aAACBR], tags={GATE_135, ROUND_5, RZ, I4, GATE_121, ROUND_4, RX, I5, GATE_128, CX, GATE_134, I3, GATE_142, CZ}),backend=numpy, dtype=complex128, data=array([[[-0.55939167+0.39682667j, 0.28150475+0.39682667j],\n", " [ 0.28150475+0.39682667j, -0.55939167+0.39682667j]],\n", "\n", " [[ 0.28150475-0.39682667j, 0.55939167+0.39682667j],\n", - " [ 0.55939167+0.39682667j, 0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_119073AASer, _119073AASes], tags={GATE_105, ROUND_4, RZ, I3, GATE_113, CZ, I4, GATE_133, ROUND_5, I2, GATE_119, RX, GATE_127, CX, GATE_162, ROUND_6, GATE_148, GATE_156, GATE_163, GATE_171, GATE_191, ROUND_7, GATE_177, GATE_185, GATE_192, GATE_200, GATE_206, GATE_214, ROUND_8, GATE_220, GATE_234, GATE_244, ROUND_9, H, GATE_221, GATE_235, GATE_245, GATE_222, GATE_229, GATE_134, GATE_142}),backend=numpy, dtype=complex128, data=array([[ 0.61212697+0.43423655j, 0.61212697+0.43423655j],\n", - " [ 0.61212697-0.43423655j, -0.61212697+0.43423655j]])
Tensor(shape=(2, 2), inds=[_119073AAYCm, _119073AAYBr], tags={GATE_98, ROUND_4, CX, I2, GATE_89, ROUND_3, RX, GATE_127, ROUND_5, GATE_118, GATE_133, RZ, GATE_119, I3, GATE_162, ROUND_6, GATE_148, GATE_156, GATE_163, GATE_171, CZ, I4, GATE_191, ROUND_7, GATE_177, GATE_185, GATE_192, GATE_200, GATE_206, GATE_214, ROUND_8, GATE_220, GATE_234, GATE_244, ROUND_9, H, GATE_221, GATE_235, GATE_245, GATE_222, GATE_229, GATE_134, GATE_142, GATE_132, I1, GATE_141, GATE_160, I0, GATE_146, GATE_155, GATE_161, GATE_170, GATE_189, GATE_175, GATE_184, GATE_190, GATE_199, GATE_219, GATE_233, GATE_243, GATE_204, GATE_213, GATE_218, GATE_228, GATE_147, GATE_176, GATE_205}),backend=numpy, dtype=complex128, data=array([[ 1.02947075e+00+1.00729510e-17j, 7.14564743e-18-7.30295919e-01j],\n", - " [-1.41994610e-17+7.30295919e-01j, -1.02947075e+00-2.00164473e-17j]])
Tensor(shape=(2, 2, 2), inds=[_119073AAYCm, _119073AAYBs, _119073AASer], tags={GATE_104, ROUND_4, RZ, I2, GATE_90, ROUND_3, RX, I3, GATE_98, CX, GATE_103, I1, GATE_112, CZ}),backend=numpy, dtype=complex128, data=array([[[-0.55939167+0.39682667j, 0.28150475+0.39682667j],\n", + " [ 0.55939167+0.39682667j, 0.28150475-0.39682667j]]])
Tensor(shape=(2, 2), inds=[_438f3aAACAU, _438f3aAACAV], tags={GATE_105, ROUND_4, RZ, I3, GATE_113, CZ, I4, GATE_133, ROUND_5, I2, GATE_119, RX, GATE_127, CX, GATE_162, ROUND_6, GATE_148, GATE_156, GATE_163, GATE_171, GATE_191, ROUND_7, GATE_177, GATE_185, GATE_192, GATE_200, GATE_206, GATE_214, ROUND_8, GATE_220, GATE_234, GATE_244, ROUND_9, H, GATE_221, GATE_235, GATE_245, GATE_222, GATE_229, GATE_134, GATE_142}),backend=numpy, dtype=complex128, data=array([[ 0.61212697+0.43423655j, 0.61212697+0.43423655j],\n", + " [ 0.61212697-0.43423655j, -0.61212697+0.43423655j]])
Tensor(shape=(2, 2), inds=[_438f3aAAFUl, _438f3aAAFTq], tags={GATE_98, ROUND_4, CX, I2, GATE_89, ROUND_3, RX, GATE_127, ROUND_5, GATE_118, GATE_133, RZ, GATE_119, I3, GATE_162, ROUND_6, GATE_148, GATE_156, GATE_163, GATE_171, CZ, I4, GATE_191, ROUND_7, GATE_177, GATE_185, GATE_192, GATE_200, GATE_206, GATE_214, ROUND_8, GATE_220, GATE_234, GATE_244, ROUND_9, H, GATE_221, GATE_235, GATE_245, GATE_222, GATE_229, GATE_134, GATE_142, GATE_132, I1, GATE_141, GATE_160, I0, GATE_146, GATE_155, GATE_161, GATE_170, GATE_189, GATE_175, GATE_184, GATE_190, GATE_199, GATE_219, GATE_233, GATE_243, GATE_204, GATE_213, GATE_218, GATE_228, GATE_147, GATE_176, GATE_205}),backend=numpy, dtype=complex128, data=array([[ 1.02947075e+00+7.76633283e-17j, 5.50935632e-17-7.30295919e-01j],\n", + " [-1.09479079e-16+7.30295919e-01j, -1.02947075e+00-1.54328549e-16j]])
Tensor(shape=(2, 2, 2), inds=[_438f3aAAFUl, _438f3aAAFTr, _438f3aAACAU], tags={GATE_104, ROUND_4, RZ, I2, GATE_90, ROUND_3, RX, I3, GATE_98, CX, GATE_103, I1, GATE_112, CZ}),backend=numpy, dtype=complex128, data=array([[[-0.55939167+0.39682667j, 0.28150475+0.39682667j],\n", " [ 0.28150475+0.39682667j, -0.55939167+0.39682667j]],\n", "\n", " [[ 0.28150475-0.39682667j, 0.55939167+0.39682667j],\n", - " [ 0.55939167+0.39682667j, 0.28150475-0.39682667j]]])
Tensor(shape=(2, 2, 2), inds=[_119073AASdu, _119073AAYAw, _119073AASdA], tags={GATE_97, ROUND_4, CX, I0, GATE_87, ROUND_3, RX, GATE_73, RZ, GATE_59, ROUND_2, I1, GATE_68, GATE_45, GATE_54, CZ, I2, GATE_40, GATE_31, ROUND_1, GATE_11, GATE_39, GATE_16, GATE_25, GATE_30, GATE_10, GATE_0, ROUND_0, H, GATE_1, GATE_15, GATE_29, GATE_44, GATE_58, GATE_17, GATE_2, GATE_3, I3, GATE_126, ROUND_5, GATE_116, GATE_155, ROUND_6, GATE_145, GATE_184, ROUND_7, GATE_174, GATE_213, ROUND_8, GATE_203, GATE_218, GATE_232, GATE_242, ROUND_9, GATE_219, GATE_233, GATE_243, GATE_204, GATE_220, GATE_228, GATE_189, GATE_175, GATE_190, GATE_199, GATE_160, GATE_146, GATE_161, GATE_170, GATE_131, GATE_117, GATE_132, GATE_141, GATE_156, GATE_147, GATE_185, GATE_176, GATE_214, GATE_205, GATE_206, GATE_234, GATE_244, GATE_221, GATE_235, GATE_245, GATE_222, I4, GATE_229, GATE_191, GATE_177, GATE_192, GATE_200, GATE_162, GATE_148, GATE_163, GATE_171, GATE_102, GATE_88, GATE_103, GATE_112}),backend=numpy, dtype=complex128, data=array([[[ 0.9367917 -0.66455036j, -0.01811946-0.44375959j],\n", + " [ 0.55939167+0.39682667j, 0.28150475-0.39682667j]]])
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" ], "text/plain": [ "TensorNetworkGen(tensors=87, indices=67)" ] }, - "execution_count": 33, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -54566,6 +2095,7 @@ }, { "cell_type": "markdown", + "id": "482fff96-b375-421b-81b7-ddbdc75ce84c", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54577,16 +2107,17 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 35, + "id": "87a331aa-9186-49a8-bd7d-d51ca4f78c10", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.99999999999996" + "0.9999999999999576" ] }, - "execution_count": 34, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" } @@ -54598,6 +2129,7 @@ }, { "cell_type": "markdown", + "id": "38655ea1-568c-46df-aae5-b960816b7c4d", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54627,12 +2159,13 @@ "\n", "$$\n", "\\langle \\psi_{3, 4} | Z_3 \\otimes Z_4 | \\psi_{3, 4} \\rangle\n", - "$$\n" + "$$" ] }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 36, + "id": "3c59eda8-d59f-4af4-9225-86ec3b3bdc82", "metadata": {}, "outputs": [], "source": [ @@ -54643,6 +2176,7 @@ }, { "cell_type": "markdown", + "id": "6461bb03-5a06-4f21-bee8-44d8887fbc3d", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54654,16 +2188,17 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 37, + "id": "d078cd57-7712-4ab5-bd59-e17b3780771e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "222176" + "228328" ] }, - "execution_count": 36, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } @@ -54676,6 +2211,7 @@ }, { "cell_type": "markdown", + "id": "64bdd81b-6ba2-4e11-8d86-44070722b7b5", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54688,14 +2224,15 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 38, + "id": "f902f982-3ffd-4e5d-a338-7477e85c9b8d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "43.8 ms ± 713 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + "16.1 ms ± 118 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], @@ -54706,6 +2243,7 @@ }, { "cell_type": "markdown", + "id": "72e8ad06-9e3c-4dcf-a224-c43ad707f1ca", "metadata": {}, "source": [ "We can compare this to just performing the main contraction:" @@ -54713,14 +2251,15 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 39, + "id": "e8136022-0b6f-487d-b90d-fe2b91dd325d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "3.73 ms ± 137 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + "1.21 ms ± 10.3 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] } ], @@ -54731,6 +2270,7 @@ }, { "cell_type": "markdown", + "id": "19c8c68c-1557-470c-a02e-b1ceb97bf2f5", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54742,21 +2282,22 @@ "You can also supply a customized `PathOptimizer` instance here, an example of which\n", "is the `opt_einsum.RandomGreedy`\n", "[optimizer](https://optimized-einsum.readthedocs.io/en/stable/random_greedy_path.html)\n", - "(which is itself called by `'auto-hq'` in fact).\n" + "(which is itself called by `'auto-hq'` in fact)." ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 40, + "id": "1a3ebbdc-43fd-4f95-a9df-5f3b4fd94603", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "222176" + "228328" ] }, - "execution_count": 39, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -54774,6 +2315,7 @@ }, { "cell_type": "markdown", + "id": "12c44773-7681-471a-a846-d12417070fdd", "metadata": {}, "source": [ "We see it has found a much better path than `'greedy'`, which is not so surprising.\n", @@ -54784,16 +2326,17 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 41, + "id": "12ec5f53-aaac-4731-b9b7-154be4ff91a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.04035324286371912" + "0.04035324286372618" ] }, - "execution_count": 40, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -54804,27 +2347,26 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 42, + "id": "db73fe14-5df4-4fd3-b2d1-f299e6822bcd", "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "0.04035324286371912" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" + "name": "stdout", + "output_type": "stream", + "text": [ + "14.4 ms ± 95.6 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] } ], "source": [ - "# %%timeit\n", + "%%timeit\n", "circ.local_expectation(ZZ, where, optimize=tree)" ] }, { "cell_type": "markdown", + "id": "192ca463-0d59-4076-a45a-ef7068f9925b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -54857,23 +2399,24 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 43, + "id": "f0ed7460-3834-4bdf-9d9e-46a652c17171", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "F=4.64 C=5.94 S=10.00 P=11.63: 100%|██████████| 16/16 [00:09<00:00, 1.65it/s]\n" + "F=4.60 C=5.89 S=10.00 P=11.31: 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████| 16/16 [00:04<00:00, 3.80it/s]\n" ] }, { "data": { "text/plain": [ - "{'flops': 43442, 'write': 12995, 'size': 1024}" + "{'flops': 40212, 'write': 11365, 'size': 1024}" ] }, - "execution_count": 42, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -54897,6 +2440,7 @@ }, { "cell_type": "markdown", + "id": "d5355777-74b8-4993-8afd-9ae419c377bc", "metadata": {}, "source": [ "We can see even for this small contraction it has improved on the `RandomGreedy` path cost.\n", @@ -54907,14 +2451,15 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 44, + "id": "dd970b4e-0bfc-497c-9d57-a579776c284b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "40.7 ms ± 1.25 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + "15.3 ms ± 54.3 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], @@ -54925,6 +2470,7 @@ }, { "cell_type": "markdown", + "id": "dabf0797-3a9e-49ed-b86d-f95d0e03dd37", "metadata": {}, "source": [ "Again, since the main contraction is very small, we don't see any real improvement." @@ -54932,6 +2478,7 @@ }, { "cell_type": "markdown", + "id": "a10637f4-8148-4869-aa3f-eacec3b77c2c", "metadata": {}, "source": [ "`cotengra` also has a `ContractionTree` object for manipulating and visualizing\n", @@ -54940,5759 +2487,14 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 46, + "id": "a1c1fd3e-7be2-4070-91e8-790e5143b0cf", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - 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" @@ -60709,7 +2511,7 @@ "(
, )" ] }, - "execution_count": 44, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -60720,15 +2522,54 @@ }, { "cell_type": "markdown", + "id": "fc6cd08a-45d3-489a-b2ae-ba824fcec1fc", "metadata": {}, "source": [ "Here the, grey network at the bottom is the TN to be contracted, and the tree\n", "above it depicts the series of pairwise contractions and their individual cost\n", - "needed to find the output answer (the node at the top)." + "needed to find the output answer (the node at the top).\n", + "\n", + "See https://cotengra.readthedocs.io/en/latest/visualization.html for other methods:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "e97ec69a-7ea5-4108-a28d-c7bd91e48e41", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "" + ], + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "(
, )" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tree.plot_rubberband()" ] }, { "cell_type": "markdown", + "id": "457270d8-6c28-44bb-8323-bb260a701998", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -60741,7 +2582,8 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 47, + "id": "42a00fb4-5733-403b-949a-017f85618295", "metadata": {}, "outputs": [ { @@ -60750,7 +2592,7 @@ "{2, 4, 8}" ] }, - "execution_count": 45, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -60761,12 +2603,13 @@ }, { "cell_type": "markdown", + "id": "f347fa46-918a-49cd-9be8-5f8c5a51b89d", "metadata": {}, "source": [ "When it comes to the actual contraction however, where large tensors will appear, it can be advantageous to\n", "use a different library to perform the contractions. If you specify a ``backend`` kwarg, before contraction,\n", "the arrays will converted to the ``backend``, then the contraction performed, and the result converted back\n", - "to ``numpy``. \n", + "to ``numpy``.\n", "[The list of available backends is here](https://optimized-einsum.readthedocs.io/en/stable/backends.html#special-gpu-backends-for-numpy-arrays), including:\n", "\n", "\n", @@ -60778,42 +2621,45 @@ }, { "cell_type": "markdown", + "id": "d161043c-ae26-4d50-a7e4-de2f85326b6c", "metadata": {}, "source": [ "Sampling is an excellent candidate for GPU acceleration as the same geometry TNs\n", - "are contracted over and over again and since sampling is inherently a low \n", + "are contracted over and over again and since sampling is inherently a low\n", "precision task, single precision arrays are a natural fit." ] }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 48, + "id": "d99ed8d4-b137-4ce1-b401-6991e95d78b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1011111001\n", - "1101000001\n", - "1000100011\n", - "0011101000\n", - "0010100101\n", - "1100001101\n", - "1111011010\n", - "0001111101\n", - "0111001001\n", - "1001000000\n" + "1001000111\n", + "0111100001\n", + "1011000000\n", + "0101101000\n", + "0101110101\n", + "0011001001\n", + "1001100000\n", + "1010011001\n", + "1111101000\n", + "1000010010\n" ] } ], "source": [ "for b in circ.sample(10, backend='jax', dtype='complex64'):\n", - " print(b)\n" + " print(b)" ] }, { "cell_type": "markdown", + "id": "865bc679-0bdf-4f58-8dab-ec17853093b2", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -60831,17 +2677,20 @@ "Here's a list of things to check if you want to ensure you are getting the\n", "most performance out of your circuit simulation:\n", "\n", - "- What contraction path optimizer are you using? If performance isn't great, have you tried `cotengra`?\n", - "- How are you applying the gates? For example, `gate_opts={'contract': False}` (no decomposition) can be better for diagonal 2-qubit gates.\n", - "- How are you grouping the qubits? For sampling, there is a sweet spot for `group_size` usually. For chaotic sampling, you might try the *last* \\$M\\$ marginal qubits rather than the *first*, for example.\n", - "- What local simplifications are you using, and in what order? `simplify_sequence='SADCR'` is also good sometimes.\n", - "- If the computation is contraction dominated, can you run it on a GPU?\n" + "- If you are sampling:\n", + " - [ ] Have you tried the *gate-by-gate* method?\n", + " - [ ] How are you grouping the qubits? For sampling, there is a sweet spot for `group_size` usually. For chaotic sampling, you might try the *last* \\$M\\$ marginal qubits rather than the *first*, for example.\n", + "- [ ] What contraction path optimizer are you using? If performance isn't great, have you tried [`cotengra`](https://cotengra.readthedocs.io)?\n", + " - [ ] if you are using `cotengra` and subtree-reconfiguration / dynamic slicing, have you installed [`cotengrust`](https://github.com/jcmgray/cotengrust)?\n", + "- [ ] How are you applying the gates? For example, `gate_opts={'contract': False}` (no decomposition) can be better for diagonal 2-qubit gates.\n", + "- [ ] What local simplifications are you using, and in what order? `simplify_sequence='SADCR'` is also good sometimes.\n", + "- [ ] If the computation is contraction dominated, can you run it on a GPU?" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -60855,7 +2704,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.8" + "version": "3" } }, "nbformat": 4, diff --git a/quimb/calc.py b/quimb/calc.py index 1979e62a..87d7f72e 100644 --- a/quimb/calc.py +++ b/quimb/calc.py @@ -357,8 +357,7 @@ def simulate_counts(p, C, phys_dim=2, seed=None): {'000': 514, '111': 510} """ - if seed is not None: - np.random.seed(seed) + rng = np.random.default_rng(seed) n = infer_size(p, phys_dim) d = phys_dim**n @@ -372,7 +371,7 @@ def simulate_counts(p, C, phys_dim=2, seed=None): pi = pi.reshape(-1) # raw counts in terms of integers - raw_counts = np.random.choice(np.arange(d), size=C, p=pi) + raw_counts = rng.choice(d, size=C, p=pi) # convert to frequencies of binary bin_str = "{:0>" + str(n) + "b}" diff --git a/quimb/schematic.py b/quimb/schematic.py index e2d827d5..27f7b00b 100644 --- a/quimb/schematic.py +++ b/quimb/schematic.py @@ -430,6 +430,9 @@ def marker(self, coo, preset=None, **kwargs): coo, preset=preset, n=n, orientation=orientation, **style ) + def square(self, coo, preset=None, **kwargs): + return self.marker(coo, preset=preset, marker="s", **kwargs) + def cube(self, coo, preset=None, **kwargs): """Draw a cube at the specified coordinate, which must be 3D. @@ -825,6 +828,24 @@ def shape(self, coos, preset=None, **kwargs): for coo in coos: self._adjust_lims(*coo) + def rectangle(self, cooa, coob, preset=None, **kwargs): + style = parse_style_preset(self.presets, preset, **kwargs) + radius = style.pop("radius", 0.25) + + forward, inverse = get_rotator_and_inverse(cooa, coob) + + # rotate both onto y=0 + xa, _ = forward(*cooa) + xb, _ = forward(*coob) + points = [ + (xa - radius, -radius), + (xa - radius, +radius), + (xb + radius, +radius), + (xb + radius, -radius), + ] + points = [inverse(*coo) for coo in points] + self.shape(points, **style) + def patch(self, coos, preset=None, **kwargs): """Draw a closed smooth patch through given coordinates. diff --git a/quimb/tensor/__init__.py b/quimb/tensor/__init__.py index da946f8c..a34316d7 100644 --- a/quimb/tensor/__init__.py +++ b/quimb/tensor/__init__.py @@ -8,6 +8,7 @@ Gate, ) from .circuit_gen import ( + circ_a2a_rand, circ_ansatz_1D_brickwork, circ_ansatz_1D_rand, circ_ansatz_1D_zigzag, @@ -222,6 +223,7 @@ "array_contract", "bonds_size", "bonds", + "circ_a2a_rand", "circ_ansatz_1D_brickwork", "circ_ansatz_1D_rand", "circ_ansatz_1D_zigzag", diff --git a/quimb/tensor/circuit.py b/quimb/tensor/circuit.py index 113fe104..e8a988c4 100644 --- a/quimb/tensor/circuit.py +++ b/quimb/tensor/circuit.py @@ -1361,7 +1361,7 @@ def __repr__(self): ) -def sample_bitstring_from_prob_ndarray(p): +def sample_bitstring_from_prob_ndarray(p, seed=None): """Sample a bitstring from n-dimensional tensor ``p`` of probabilities. Examples @@ -1373,7 +1373,8 @@ def sample_bitstring_from_prob_ndarray(p): >>> sample_bitstring_from_prob_ndarray(p) '01011' """ - b = np.random.choice(p.size, p=p.flat) + rng = np.random.default_rng(seed) + b = rng.choice(p.size, p=p.ravel()) return f"{b:0>{p.ndim}b}" @@ -2642,7 +2643,7 @@ def amplitude( optimize="auto-hq", simplify_sequence="ADCRS", simplify_atol=1e-12, - simplify_equalize_norms=False, + simplify_equalize_norms=True, backend=None, dtype="complex128", rehearse=False, @@ -2701,7 +2702,7 @@ def amplitude( # fix the output indices to the correct bitstring for i, x in zip(range(self.N), b): - psi_b.isel_({psi_b.site_ind(i): int(x)}) + psi_b.isel_({psi_b.site_ind(i): x}) # perform a final simplification and cast psi_b.full_simplify_(**fs_opts) @@ -2727,7 +2728,7 @@ def amplitude_rehearse( b="random", simplify_sequence="ADCRS", simplify_atol=1e-12, - simplify_equalize_norms=False, + simplify_equalize_norms=True, optimize="auto-hq", dtype="complex128", rehearse=True, @@ -2766,9 +2767,7 @@ def amplitude_rehearse( """ if b == "random": - import random - - b = [random.choice("01") for _ in range(self.N)] + b = "r" * self.N return self.amplitude( b=b, @@ -2788,7 +2787,7 @@ def partial_trace( optimize="auto-hq", simplify_sequence="ADCRS", simplify_atol=1e-12, - simplify_equalize_norms=False, + simplify_equalize_norms=True, backend=None, dtype="complex128", rehearse=False, @@ -2885,7 +2884,7 @@ def local_expectation( optimize="auto-hq", simplify_sequence="ADCRS", simplify_atol=1e-12, - simplify_equalize_norms=False, + simplify_equalize_norms=True, backend=None, dtype="complex128", rehearse=False, @@ -3078,7 +3077,7 @@ def compute_marginal( if fix: # project (slice) fixed tensors with bitstring # this severs the indices connecting bra and ket on fixed sites - nm_lc.isel_({self.ket_site_ind(i): int(b) for i, b in fix.items()}) + nm_lc.isel_({self.ket_site_ind(i): b for i, b in fix.items()}) # having sliced we can do a final simplify nm_lc.full_simplify_(output_inds=output_inds, **fs_opts) @@ -3215,12 +3214,149 @@ def _group_order(self, order, group_size=1): tuple(sorted(g)) for g in partition_all(group_size, order) ) + def get_qubit_distances(self, method="dijkstra", alpha=2): + """Get a nested dictionary of qubit distances. This is computed from a + graph representing qubit interactions. The graph has an edge between + qubits if they are acted on by the same gate, and the distance-weight + of the edge is exponentially small in the number of gates between them. + + Parameters + ---------- + method : {'dijkstra', 'resistance'}, optional + The method to use to compute the qubit distances. See + :func:`networkx.all_pairs_dijkstra_path_length` and + :func:`networkx.resistance_distance`. + alpha : float, optional + The distance weight between qubits is ``alpha**(num_gates - 1 )``. + + Returns + ------- + dict[int, dict[int, float]] + The distance between each pair of qubits, accessed like + ``distances[q1][q2]``. If two qubits are not connected, the + distance is missing. + """ + import networkx as nx + + G = nx.Graph() + for g in self.gates: + for q1, q2 in itertools.combinations(g.qubits, 2): + if G.has_edge(q1, q2): + G[q1][q2]["weight"] /= alpha + else: + G.add_edge(q1, q2, weight=1) + + if method == "dijkstra": + distances = dict( + nx.all_pairs_dijkstra_path_length(G, weight="weight") + ) + elif method == "resistance": + distances = nx.resistance_distance(G, weight="weight") + else: + raise ValueError(f"Unknown method {method}.") + + return distances + + def reordered_gates_dfs_clustered(self): + """Get the gates reordered by a depth first search traversal of the + multi-qubit gate graph that greedily selects successive gates which + are 'close' in graph distance, and shifts single qubit gates to be + adjacent to multi-qubit gates where possible. + """ + # first we make a directed graph of the multi-qubit gates + successors = {} + predecessors = {} + single_qubit_stacks = {} + single_qubit_predecessors = {} + last_gates = {} + queue = [] + + for i, g in enumerate(self.gates): + if g.total_qubit_count == 1: + # lazily accumulate single qubit gates + (q,) = g.qubits + single_qubit_stacks.setdefault(q, []).append(i) + + else: + pi = predecessors[i] = [] + sqpi = single_qubit_predecessors[i] = [] + + for q in g.qubits: + # collect any single qubit gates acting on this qubit + sqpi.extend(single_qubit_stacks.pop(q, [])) + + if q in last_gates: + # qubit has already been acted on -> have an edge + h = last_gates[q] + # mark h as a predecessor of i + pi.append(h) + # mark i as a successor of h + successors.setdefault(h, []).append(i) + + # mark qubit as acted on + last_gates[q] = i + + if len(pi) == 0: + # no predecessors -> is possible starting multiqubit gate + queue.append(i) + + # then we traverse the multi-qubit gates in a depth first, topological + # order, breaking ties by minimizing the distance between active qubits + distances = self.get_qubit_distances() + + def gate_distance(i, j): + qis = self.gates[i].qubits + qjs = self.gates[j].qubits + return min( + distances[q1].get(q2, float("inf")) for q1 in qis for q2 in qjs + ) + + # sort initial queue by qubit with smallest index + queue.sort(key=lambda i: min(self.gates[i].qubits)) + new_gates = [] + + while queue: + i = queue.pop(0) + + # first flush any single qubit gates acting on the qubits of gate i + new_gates.extend( + self.gates[j] for j in single_qubit_predecessors.pop(i, []) + ) + # then add the gate itself + new_gates.append(self.gates[i]) + + # then remove i as a predecessor of its successors + for j in successors.pop(i, []): + pj = predecessors[j] + pj.remove(i) + if not pj: + # j has no more predecessors -> can be added to queue + queue.append(j) + + # check if this is the last time q is acted on, + # if so flush any remaining single qubit gates + for q in self.gates[i].qubits: + if last_gates[q] == i: + # qubit has been acted on for the last time + new_gates.extend( + self.gates[j] for j in single_qubit_stacks.pop(q, []) + ) + + # sort the queue of possible next gates + queue.sort(key=lambda k: gate_distance(i, k)) + + # flush any remaining single qubit gates + for q in sorted(single_qubit_stacks): + new_gates.extend(self.gates[j] for j in single_qubit_stacks.pop(q)) + + return new_gates + def sample( self, C, qubits=None, order=None, - group_size=1, + group_size=10, max_marginal_storage=2**20, seed=None, optimize="auto-hq", @@ -3228,7 +3364,7 @@ def sample( dtype="complex64", simplify_sequence="ADCRS", simplify_atol=1e-6, - simplify_equalize_norms=False, + simplify_equalize_norms=True, ): r"""Sample the circuit given by ``gates``, ``C`` times, using lightcone cancelling and caching marginal distribution results. This is a @@ -3319,15 +3455,14 @@ def sample( # init TN norms, contraction trees, and marginals self._maybe_init_storage() + rng = np.random.default_rng(seed) + # which qubits and an ordering e.g. (2, 3, 4, 5), (5, 3, 4, 2) qubits, order = self._parse_qubits_order(qubits, order) # group the ordering e.g. ((5, 3), (4, 2)) groups = self._group_order(order, group_size) - if seed is not None: - np.random.seed(seed) - result = dict() for _ in range(C): for where in groups: @@ -3360,7 +3495,7 @@ def sample( p = self._sampled_conditionals[key] # the sampled bitstring e.g. '1' or '001010101' - b_where = sample_bitstring_from_prob_ndarray(p) + b_where = sample_bitstring_from_prob_ndarray(p, seed=rng) # split back into individual qubit results for q, b in zip(where, b_where): @@ -3373,12 +3508,12 @@ def sample_rehearse( self, qubits=None, order=None, - group_size=1, + group_size=10, result=None, optimize="auto-hq", simplify_sequence="ADCRS", simplify_atol=1e-6, - simplify_equalize_norms=False, + simplify_equalize_norms=True, rehearse=True, progbar=False, ): @@ -3431,7 +3566,7 @@ def sample_rehearse( groups = self._group_order(order, group_size) if result is None: - result = {q: "0" for q in qubits} + result = {q: "r" for q in qubits} fix = {} tns_and_trees = {} @@ -3459,6 +3594,7 @@ def sample_chaotic( self, C, marginal_qubits, + fix=None, max_marginal_storage=2**20, seed=None, optimize="auto-hq", @@ -3466,7 +3602,7 @@ def sample_chaotic( dtype="complex64", simplify_sequence="ADCRS", simplify_atol=1e-6, - simplify_equalize_norms=False, + simplify_equalize_norms=True, ): r"""Sample from this circuit, *assuming* it to be chaotic. Which is to say, only compute and sample correctly from the final marginal, @@ -3502,6 +3638,9 @@ def sample_chaotic( The number of qubits to treat as marginal, or the actual qubits. If an int is given then the qubits treated as marginal will be ``circuit.calc_qubit_ordering()[:marginal_qubits]``. + fix : None or dict[int, str], optional + Measurement results on other qubits to fix. These will be randomly + sampled if ``fix`` is not given or a qubit is missing. seed : None or int, optional A random seed, passed to ``numpy.random.seed`` if given. optimize : str, optional @@ -3531,8 +3670,7 @@ def sample_chaotic( self._maybe_init_storage() qubits = tuple(range(self.N)) - if seed is not None: - np.random.seed(seed) + rng = np.random.default_rng(seed) # choose which qubits to treat as marginal - ideally 'towards one side' # to increase contraction efficiency @@ -3547,7 +3685,10 @@ def sample_chaotic( for _ in range(C): # generate a random bit-string for the fixed qubits for q in fix_qubits: - result[q] = np.random.choice(("0", "1")) + if (fix is None) or (q not in fix): + result[q] = rng.choice(("0", "1")) + else: + result[q] = fix[q] # compute the remaining marginal key = (where, tuple(sorted(result.items()))) @@ -3588,7 +3729,7 @@ def sample_chaotic_rehearse( optimize="auto-hq", simplify_sequence="ADCRS", simplify_atol=1e-6, - simplify_equalize_norms=False, + simplify_equalize_norms=True, dtype="complex64", rehearse=True, ): @@ -3664,13 +3805,275 @@ def sample_chaotic_rehearse( sample_chaotic_rehearse, rehearse="tn" ) + def get_gate_by_gate_circuits(self, group_size=10): + """Get a sequence of circuits by partitioning the gates into groups + such circuit `i + 1` acts on at most ``group_size`` new qubits compared + to circuit `i`. + + Parameters + ---------- + group_size : int, optional + The maximum number of new qubits that can be acted on by a circuit + compared to its predecessor. + + Returns + ------- + Sequence[dict] + A sequence of dicts, each with keys ``'circuit'`` and ``'where'``, + where the former is a :class:`~quimb.tensor.circuit.Circuit` and + the latter the tuple of new qubits that it acts on comparaed to + the previous circuit. + """ + circs = [self.__class__(self.N)] + groups = [] + current_group = set() + + # this ensures that single qubit gates are always adjacent to + # multi-qubit gates and will thus always be included in the same group + gates = self.reordered_gates_dfs_clustered() + + for gate in gates: + # if we were to add next gate, how many new qubits would we have? + next_group = current_group.union(gate.qubits) + if len(next_group) > group_size: + # over the limit: flush a copy of the current circuit and group + groups.append(tuple(sorted(current_group))) + circs.append(circs[-1].copy()) + # start a new group + current_group = set(gate.qubits) + else: + # add the gate to the current group + current_group = next_group + circs[-1].apply_gate(gate) + + # add the final group corresponding to circs[-1] + groups.append(tuple(sorted(current_group))) + + return tuple({"circuit": c, "where": g} for c, g in zip(circs, groups)) + + def sample_gate_by_gate( + self, + C, + group_size=10, + seed=None, + max_marginal_storage=2**20, + optimize="auto-hq", + backend=None, + dtype="complex64", + simplify_sequence="ADCRS", + simplify_atol=1e-6, + simplify_equalize_norms=True, + ): + """Sample this circuit using the gate-by-gate method, where we 'evolve' + a result bitstring by sequentially including more and more gates, at + each step updating the result by computing a full conditional marginal. + See "How to simulate quantum measurement without computing marginals" + by Sergey Bravyi, David Gosset, Yinchen Liu + (https://arxiv.org/abs/2112.08499). The overall complexity of this is + guaranteed to be similar to that of computing a single amplitude which + can be much better than the naive "qubit-by-qubit" (`.sample`) method. + However, it requires evaluting a number of tensor networks that scales + linearly with the number of gates which can offset any practical + advantages for shallow circuits for example. + + Parameters + ---------- + C : int + The number of samples to generate. + group_size : int, optional + The maximum number of qubits that can be acted on by a circuit + compared to its predecessor. This will be the dimension of the + marginal computed at each step. + seed : None or int, optional + A random seed, passed to ``numpy.random.seed`` if given. + max_marginal_storage : int, optional + The total cumulative number of marginal probabilites to cache, once + this is exceeded caching will be turned off. + optimize : str, optional + Contraction path optimizer to use for the marginals, shouldn't be + a non-reusable path optimizer as called on many different TNs. + Passed to :func:`cotengra.array_contract_tree`. + backend : str, optional + Backend to perform the marginal contraction with, e.g. ``'numpy'``, + ``'cupy'`` or ``'jax'``. Passed to ``cotengra``. + dtype : str, optional + Data type to cast the TN to before contraction. + simplify_sequence : str, optional + Which local tensor network simplifications to perform and in which + order, see + :meth:`~quimb.tensor.tensor_core.TensorNetwork.full_simplify`. + simplify_atol : float, optional + The tolerance with which to compare to zero when applying + :meth:`~quimb.tensor.tensor_core.TensorNetwork.full_simplify`. + simplify_equalize_norms : bool, optional + Actively renormalize tensor norms during simplification. + rehearse : bool, optional + If ``True``, generate and cache the simplified tensor network and + contraction tree but don't actually perform the contraction. + Returns a dict with keys ``'tn'`` and ``'tree'`` with the tensor + network that will be contracted and the corresponding contraction + tree if so. + + Yields + ------ + str + """ + self._maybe_init_storage() + + rng = np.random.default_rng(seed) + + key = ("gate_by_gate_circuits", group_size) + try: + circs_wheres = self._storage[key] + except KeyError: + circs_wheres = self.get_gate_by_gate_circuits(group_size) + self._storage[key] = circs_wheres + + for _ in range(C): + # start with all qubits in the |0> state + result = {q: "0" for q in range(self.N)} + + for circ_where in circs_wheres: + # get the next circuit and the new group of qubits + circ_g = circ_where["circuit"] + where = circ_where["where"] + + # remove the new group of qubits from our current result + for q in where: + result.pop(q) + + # check if we have already computed the conditional + key = (where, tuple(sorted(result.items()))) + + if key not in circ_g._sampled_conditionals: + p = circ_g.compute_marginal( + where, + fix=result, + optimize=optimize, + backend=backend, + dtype=dtype, + simplify_sequence=simplify_sequence, + simplify_atol=simplify_atol, + simplify_equalize_norms=simplify_equalize_norms, + ) + p /= p.sum() + + if circ_g._marginal_storage_size <= max_marginal_storage: + circ_g._sampled_conditionals[key] = p + circ_g._marginal_storage_size += p.size + else: + p = circ_g._sampled_conditionals[key] + + # sample a configuration for our new group + b_where = sample_bitstring_from_prob_ndarray(p, seed=rng) + + # update the fixed qubits given new group result + for q, qx in zip(where, b_where): + result[q] = qx + + yield "".join(result[i] for i in range(self.N)) + + def sample_gate_by_gate_rehearse( + self, + group_size=10, + optimize="auto-hq", + dtype="complex64", + simplify_sequence="ADCRS", + simplify_atol=1e-6, + simplify_equalize_norms=True, + rehearse=True, + progbar=False, + ): + """Perform the preparations and contraction tree findings for + :meth:`~quimb.tensor.circuit.Circuit.sample_gate_by_gate`, caching + various intermedidate objects, but don't perform the main contractions. + + Parameters + ---------- + group_size : int, optional + The maximum number of qubits that can be acted on by a circuit + compared to its predecessor. This will be the dimension of the + marginal computed at each step. + optimize : str, optional + Contraction path optimizer to use for the marginals, shouldn't be + a non-reusable path optimizer as called on many different TNs. + Passed to :func:`cotengra.array_contract_tree`. + dtype : str, optional + Data type to cast the TN to before contraction. + simplify_sequence : str, optional + Which local tensor network simplifications to perform and in which + order, see + :meth:`~quimb.tensor.tensor_core.TensorNetwork.full_simplify`. + simplify_atol : float, optional + The tolerance with which to compare to zero when applying + :meth:`~quimb.tensor.tensor_core.TensorNetwork.full_simplify`. + simplify_equalize_norms : bool, optional + Actively renormalize tensor norms during simplification. + rehearse : True or "tn", optional + If ``True``, generate and cache the simplified tensor network and + contraction tree but don't actually perform the contraction. If + "tn", only generate the simplified tensor networks. + + Returns + ------- + Sequence[dict] or Sequence[TensorNetwork] + """ + self._maybe_init_storage() + + key = ("gate_by_gate_circuits", group_size) + try: + circs_wheres = self._storage[key] + except KeyError: + circs_wheres = self.get_gate_by_gate_circuits(group_size) + self._storage[key] = circs_wheres + + rehs = [] + result = {q: "0" for q in range(self.N)} + + for circs_wheres in _progbar(circs_wheres, disable=not progbar): + # get the next circuit and the new group of qubits + circ_g = circs_wheres["circuit"] + where = circs_wheres["where"] + + # remove the new group of qubits from our current result + for q in where: + result.pop(q) + + r = circ_g.compute_marginal( + where, + fix=result, + optimize=optimize, + dtype=dtype, + simplify_sequence=simplify_sequence, + simplify_atol=simplify_atol, + simplify_equalize_norms=simplify_equalize_norms, + rehearse=rehearse, + ) + + if rehearse != "tn": + r["where"] = where + r["circuit"] = circ_g + + rehs.append(r) + + # update the fixed qubits with randomly rotated results so we + # don't get zero probability networks when simplifying + for q in where: + result[q] = "r" + + return rehs + + sample_gate_by_gate_tns = functools.partialmethod( + sample_gate_by_gate_rehearse, rehearse="tn" + ) + def to_dense( self, reverse=False, optimize="auto-hq", simplify_sequence="R", simplify_atol=1e-12, - simplify_equalize_norms=False, + simplify_equalize_norms=True, backend=None, dtype=None, rehearse=False, @@ -3846,7 +4249,7 @@ def xeb_ex( optimize="auto-hq", simplify_sequence="R", simplify_atol=1e-12, - simplify_equalize_norms=False, + simplify_equalize_norms=True, dtype=None, backend=None, autojit=False, @@ -3957,6 +4360,112 @@ def update_params_from(self, tn): self.clear_storage() + def draw( + self, + figsize=None, + radius=1 / 3, + drawcolor=(0.5, 0.5, 0.5), + linewidth=1, + ): + """Draw a simple linear schematic of the circuit. + + Parameters + ---------- + figsize : tuple, optional + The size of the figure, if not given will be set based on the + number of gates and qubits. + radius : float, optional + The radius of the gates. + drawcolor : tuple, optional + The color of the wires. + linewidth : float, optional + The linewidth of the wires. + + Returns + ------- + fig : matplotlib.Figure + The figure object. + ax : matplotlib.Axes + The axis object. + """ + from quimb.schematic import Drawing, hash_to_color + + if figsize is None: + figsize = (self.num_gates / 6, self.N / 6) + + d = Drawing( + figsize=figsize, + presets=dict( + wire=dict( + color=drawcolor, + linewidth=linewidth, + ), + gate=dict( + radius=radius, + ), + ), + ) + + depths = {} + for i, g in enumerate(self.gates): + # level = max(depths.get(q, 0) for q in g.qubits) + 1 + level = i + + if len(g.qubits) == 1: + (q,) = g.qubits + # draw line from previous gate to this one + d.line( + (depths.get(q, -1) + radius, q), + (level - radius, q), + preset="wire", + zorder=level, + ) + # draw the gate + d.marker( + (level, q), + color=hash_to_color(g.label), + zorder=0, + preset="gate", + ) + # record last gate on this qubit + depths[q] = level + else: + # stretch a box over all qubits + qmin = min(g.qubits) + qmax = max(g.qubits) + d.rectangle( + (level, qmin), + (level, qmax), + color=hash_to_color(g.label), + zorder=0, + alpha=1 / 3, + preset="gate", + ) + for q in g.qubits: + # draw markers on each qubit acted on + d.marker( + (level, q), + color=hash_to_color(g.label), + zorder=0, + preset="gate", + ) + # draw lines from previous gate to this one + d.line( + (depths.get(q, -1) + radius, q), + (level - radius, q), + preset="wire", + zorder=level, + ) + # record last gate on this qubit + depths[q] = level + + # draw final lines to the right + level = max(depths.values(), default=0) + 1 + for q in depths: + d.line((depths.get(q, -1), q), (level, q), preset="wire") + + return d.fig, d.ax + def __repr__(self): r = "" return r.format(self.N, self.num_gates, self.gate_opts) @@ -4152,6 +4661,36 @@ def error_estimate(self): """ return 1 - self.fidelity_estimate() + def local_expectation( + self, + G, + where, + normalized=False, + **contract_opts, + ): + """Compute the local expectation value of a local operator at ``where`` + (via forming the reduced density matrix). Note this moves the + orthogonality around inplace, and records it in `info`. + + Parameters + ---------- + G : Tensor + The local operator tensor. + where : int + The qubit to compute the expectation value at. + + Returns + ------- + float + """ + return self._psi.local_expectation_canonical( + G, + where, + normalized=normalized, + info=self.gate_opts["info"], + **contract_opts, + ) + class CircuitPermMPS(CircuitMPS): """Quantum circuit simulation keeping the state always in an MPS form, but diff --git a/quimb/tensor/circuit_gen.py b/quimb/tensor/circuit_gen.py index 8639a800..e4d93fff 100644 --- a/quimb/tensor/circuit_gen.py +++ b/quimb/tensor/circuit_gen.py @@ -1,5 +1,4 @@ -"""Functions for generating specific, e.g. ansatz, circuits. -""" +"""Functions for generating specific, e.g. ansatz, circuits.""" import math import random @@ -10,7 +9,7 @@ def inject_u3s( ent_gates, - gate2='cz', + gate2="cz", avoid_doubling=False, seed=None, ): @@ -65,11 +64,10 @@ def inject_u3s( gates = [] # consume list of pairs to entangle while ent_gates: - # break up entanling gates with U3s where necesary for i in range(n): if needs_u3[i]: - gates.append(('U3', *rand(3, scale=2 * math.pi), i)) + gates.append(("U3", *rand(3, scale=2 * math.pi), i)) needs_u3[i] = False # try and get the next entanling gate which is not 'doubled' @@ -91,8 +89,7 @@ def inject_u3s( # ^ ^ ^ ^ if avoid_doubling: just_entangled = { - ij for ij in just_entangled - if (i not in ij) and (j not in ij) + ij for ij in just_entangled if (i not in ij) and (j not in ij) } just_entangled.add((i, j)) @@ -102,12 +99,12 @@ def inject_u3s( # place the final layer of U3s for i in range(n): if needs_u3[i]: - gates.append(('U3', *rand(3, scale=2 * math.pi), i)) + gates.append(("U3", *rand(3, scale=2 * math.pi), i)) return gates -def gates_to_param_circuit(gates, n, parametrize='U3', **circuit_opts): +def gates_to_param_circuit(gates, n, parametrize="U3", **circuit_opts): """Turn the sequence ``gates`` into a ``Circuit`` of ``n`` qubits, with any gates that appear in ``parametrize`` being... parametrized. @@ -138,13 +135,7 @@ def gates_to_param_circuit(gates, n, parametrize='U3', **circuit_opts): return circ -def circ_ansatz_1D_zigzag( - n, - depth, - gate2='cz', - seed=None, - **circuit_opts -): +def circ_ansatz_1D_zigzag(n, depth, gate2="cz", seed=None, **circuit_opts): r"""A 1D circuit ansatz with forward and backward layers of entangling gates interleaved with U3 single qubit unitaries:: @@ -203,11 +194,7 @@ def circ_ansatz_1D_zigzag( def circ_ansatz_1D_brickwork( - n, depth, - cyclic=False, - gate2='cz', - seed=None, - **circuit_opts + n, depth, cyclic=False, gate2="cz", seed=None, **circuit_opts ): r"""A 1D circuit ansatz with odd and even layers of entangling gates interleaved with U3 single qubit unitaries:: @@ -254,7 +241,6 @@ def circ_ansatz_1D_brickwork( """ ent_gates = [] for d in range(depth): - # the even pairs layer ent_gates.extend((i, i + 1) for i in range(0, n - 1, 2)) if cyclic and (n % 2 == 1): @@ -277,9 +263,9 @@ def circ_ansatz_1D_rand( depth, seed=None, cyclic=False, - gate2='cz', + gate2="cz", avoid_doubling=True, - **circuit_opts + **circuit_opts, ): """A 1D circuit ansatz with randomly place entangling gates interleaved with U3 single qubit unitaries. @@ -322,13 +308,37 @@ def circ_ansatz_1D_rand( random.shuffle(ent_gates) # inject U3 gates! - gates = inject_u3s(ent_gates, avoid_doubling=avoid_doubling, - gate2=gate2, seed=seed) + gates = inject_u3s( + ent_gates, avoid_doubling=avoid_doubling, gate2=gate2, seed=seed + ) circ = gates_to_param_circuit(gates, n, **circuit_opts) return circ +def circ_a2a_rand( + n, + depth, + seed=None, + gate2="cz", +): + if not isinstance(seed, random.Random): + rng = random.Random(seed) + + qubits = list(range(n)) + + ent_gates = [] + for _ in range(depth): + rng.shuffle(qubits) + for i, j in zip(qubits[::2], qubits[1::2]): + ent_gates.append((i, j)) + + gates = inject_u3s(ent_gates, gate2=gate2, seed=seed) + circ = gates_to_param_circuit(gates, n) + + return circ + + def circ_qaoa( terms, depth, @@ -377,8 +387,8 @@ def circ_qaoa( """ from .circuit import Circuit - circuit_opts.setdefault('gate_opts', {}) - circuit_opts['gate_opts'].setdefault('contract', False) + circuit_opts.setdefault("gate_opts", {}) + circuit_opts["gate_opts"].setdefault("contract", False) n = max(itertools.chain.from_iterable(terms)) + 1 @@ -386,14 +396,14 @@ def circ_qaoa( # layer of hadamards to get into plus state for i in range(n): - gates.append((0, 'h', i)) + gates.append((0, "h", i)) for d in range(depth): for (i, j), wij in terms.items(): - gates.append((d, 'rzz', wij * gammas[d], i, j)) + gates.append((d, "rzz", wij * gammas[d], i, j)) for i in range(n): - gates.append((d, 'rx', -betas[d] * 2, i)) + gates.append((d, "rx", -betas[d] * 2, i)) circ = Circuit(n, **circuit_opts) circ.apply_gates(gates) diff --git a/quimb/tensor/tensor_1d.py b/quimb/tensor/tensor_1d.py index 0d3c73e4..72543c1a 100644 --- a/quimb/tensor/tensor_1d.py +++ b/quimb/tensor/tensor_1d.py @@ -548,6 +548,56 @@ def contract_structured( # contract each block of sites cumulatively return self.contract_cumulative(tags_seq, inplace=inplace, **opts) + def compute_left_environments(self, **contract_opts): + """Compute the left environments of this 1D tensor network. + + Parameters + ---------- + contract_opts + Supplied to + :meth:`~quimb.tensor.tensor_core.TensorNetwork.contract`. + + Returns + ------- + dict[int, Tensor] + Environments indexed by the site they are to the left of, so keys + run from (1, ... L - 1). + """ + left_envs = {1: self.select(0).contract(all, **contract_opts)} + for i in range(2, self.L): + tll = left_envs[i - 1] + tll.drop_tags() + tnl = self.select(i - 1) | tll + left_envs[i] = tnl.contract(all, **contract_opts) + + return left_envs + + def compute_right_environments(self, **contract_opts): + """Compute the right environments of this 1D tensor network. + + Parameters + ---------- + contract_opts + Supplied to + :meth:`~quimb.tensor.tensor_core.TensorNetwork.contract`. + + Returns + ------- + dict[int, Tensor] + Environments indexed by the site they are to the right of, so keys + run from (0, ... L - 2). + """ + right_envs = { + self.L - 2: self.select(-1).contract(all, **contract_opts) + } + for i in range(self.L - 3, -1, -1): + trr = right_envs[i + 1] + trr.drop_tags() + tnr = self.select(i + 1) | trr + right_envs[i] = tnr.contract() + + return right_envs + def _repr_info(self): info = super()._repr_info() info["L"] = self.L @@ -2431,7 +2481,9 @@ def schmidt_gap(self, i, info=None, method="svd"): return S[0] - S[1] - def partial_trace(self, keep, upper_ind_id="b{}", rescale_sites=True): + def partial_trace_to_mpo( + self, keep, upper_ind_id="b{}", rescale_sites=True + ): r"""Partially trace this matrix product state, producing a matrix product operator. @@ -2516,12 +2568,356 @@ def partial_trace(self, keep, upper_ind_id="b{}", rescale_sites=True): rho.fuse_multibonds_() return rho - def ptr(self, keep, upper_ind_id="b{}", rescale_sites=True): - """Alias of :meth:`~quimb.tensor.MatrixProductState.partial_trace`.""" - return self.partial_trace( - keep, upper_ind_id, rescale_sites=rescale_sites + def partial_trace(self, *_, **__): + raise AttributeError( + "`mps.partial_trace` has been renamed to " + "`mps.partial_trace_to_mpo`. Soon `mps.partial_trace` " + "will produce (dense) local reduced density matrices to match " + "methods elsewhere in quimb." + ) + + def ptr(self, *_, **__): + raise AttributeError( + "`mps.ptr` has been renamed " "to `mps.partial_trace_to_mpo`." ) + def partial_trace_to_dense_canonical( + self, where, normalized=True, info=None, **contract_opts + ): + """Compute the dense local reduced density matrix by canonicalizing + around the target sites and then contracting the local tensors. Note + this moves the orthogonality around inplace, and records it in `info`. + + Parameters + ---------- + where : int or tuple[int] + The site or sites to compute the reduced density matrix for. + normalized : bool, optional + Explicitly normalize the local reduced density matrix. + info : dict, optional + If supplied, will be used to infer and store various extra + information. Currently the key "cur_orthog" is used to store the + current orthogonality center. Its input value can be ``"calc"``, a + single site, or a pair of sites representing the min/max range, + inclusive. It will be updated to the actual range after. + contract_opts + Passed to `tensor_contract` when computing the reduced local + density matrix. + + Returns + ------- + array_like + """ + if self.cyclic: + raise NotImplementedError("Only supports OBC.") + + if isinstance(where, Integral): + where = (where,) + + # canonicalize around our sites + self.canonicalize_(where, info=info) + + # form the local reduced density matrix tn + kix = [self.site_ind(i) for i in where] + bix = [f"__b{i}__" for i in where] + k = self[min(where) : max(where) + 1] + b = k.reindex(dict(zip(kix, bix))).conj_() + rho_tn = k | b + + # contract down to a matrix + rho = rho_tn.to_dense(kix, bix, **contract_opts) + + if normalized: + # locally normalize, usually unnecessary for an MPS but cheap + rho = rho / do("trace", rho) + + return rho + + def local_expectation_canonical( + self, G, where, normalized=True, info=None, **contract_opts + ): + """Compute a local expectation value (via forming the reduced density + matrix). Note this moves the orthogonality around inplace, and records + it in `info`. + + Parameters + ---------- + G : array_like + The local operator to compute the expectation of. + where : int or tuple[int] + The site or sites to compute the expectation at. + normalized : bool, optional + Explicitly normalize the local reduced density matrix. + info : dict, optional + If supplied, will be used to infer and store various extra + information. Currently the key "cur_orthog" is used to store the + current orthogonality center. Its input value can be ``"calc"``, a + single site, or a pair of sites representing the min/max range, + inclusive. It will be updated to the actual range after. + contract_opts + Passed to `tensor_contract` when computing the reduced local + density matrix. + + Returns + ------- + float + """ + rho = self.partial_trace_to_dense_canonical( + where, normalized=normalized, info=info, **contract_opts + ) + return do("trace", G @ rho) + + def compute_local_expectation_canonical( + self, + terms, + normalized=True, + return_all=False, + info=None, + inplace=False, + **contract_opts, + ): + """Compute many local expectations at once, via forming the relevant + reduced density matrices via canonicalization. This moves the + orthogonality around inplace, and records it in `info`. + + Parameters + ---------- + terms : dict[int or tuple[int], array_like] + The local terms to compute values for. + normalized : bool, optional + Explicitly normalize each local reduced density matrix. + return_all : bool, optional + Whether to return each expectation in `terms` separately + or sum them all together (the default). + info : dict, optional + If supplied, will be used to infer and store various extra + information. Currently, the key "cur_orthog" is used to store the + current orthogonality center. Its input value can be ``"calc"``, a + single site, or a pair of sites representing the min/max range, + inclusive. It will be updated to the actual range after. + inplace : bool, optional + Whether to perform the required canonicalizations inplace. + contract_opts + Supplied to + :meth:`~quimb.tensor.tensor_core.TensorNetwork.contract` + when contracting the local density matrices. + + Returns + ------- + float or dict[in or tuple[int], float] + The expecetation value(s), either summed or for each term if + `return_all=True`. + + See Also + -------- + compute_local_expectation_via_envs, local_expectation_canonical + partial_trace_to_dense_canonical + """ + if info is None: + # this is used to keep track of canonical center + info = {} + + if inplace: + mps = self + else: + mps = self.copy() + info = info.copy() + + cur_orthog = info.get("cur_orthog", "calc") + if isinstance(cur_orthog, tuple): + # have a canonical center already -> start close to it + terms = sorted( + terms.items(), key=lambda kv: abs(min(kv[0]) - cur_orthog[0]) + ) + else: + # sort by the smallest site so we sweep in one direction + terms = sorted(terms.items(), key=lambda kv: min(kv[0])) + + expecs = { + where: mps.local_expectation_canonical( + G, + where, + normalized=normalized, + info=info, + **contract_opts, + ) + for where, G in terms + } + + if return_all: + return expecs + + return functools.reduce(operator.add, expecs.values()) + + def compute_local_expectation_via_envs( + self, + terms, + normalized=True, + return_all=False, + **contract_opts, + ): + """Compute many local expectations at once, via forming the relevant + local overlaps using left and right environments formed via + contraction. This does not require any canonicalization and can be + quicker if the canonical center is not already aligned. + + Parameters + ---------- + terms : dict[int or tuple[int], array_like] + The local terms to compute values for. + normalized : bool, optional + Explicitly normalize each local reduced density matrix. + return_all : bool, optional + Whether to return each expectation in `terms` separately + or sum them all together (the default). + contract_opts + Supplied to + :meth:`~quimb.tensor.tensor_core.TensorNetwork.contract` + when contracting the local overlaps. + + Returns + ------- + float or dict[int or tuple[int], float] + The expecetation value(s), either summed or for each term if + `return_all=True`. + + See Also + -------- + compute_local_expectation_canonical, compute_left_environments, + compute_right_environments + """ + norm, ket, bra = self.make_norm(return_all=True) + + left_envs = norm.compute_left_environments(**contract_opts) + right_envs = norm.compute_right_environments(**contract_opts) + + expecs = {} + + if normalized: + nfactor = (norm.select(0) | right_envs[0]).contract( + all, **contract_opts + ) + else: + nfactor = None + + for where, G in terms.items(): + sitemin = min(where) + sitemax = max(where) + tags = [ket.site_tag(i) for i in range(sitemin, sitemax + 1)] + # form: + # sitemin sitemax + # : : + # ┌─┐ ┌─┐ + # ┌──┤k├─┤k├──┐ + # │ └┬┘ └┬┘ │ + # │ │ │ │ + # ┌┴┐ ┌┴───┴┐ ┌┴┐ + # │l│ │ G │ │r│ + # └┬┘ └┬───┬┘ └┬┘ + # │ │ │ │ + # │ ┌┴┐ ┌┴┐ │ + # └──┤b├─┤b├──┘ + # └─┘ └─┘ + # (n.b. might be non-gated sites in between as well) + k = ket.select_any(tags, virtual=False) + b = bra.select_any(tags, virtual=False) + k.gate_(G, where, contract=False) + + tn_local_overlap = k | b + if sitemin in left_envs: + tn_local_overlap |= left_envs[sitemin] + if sitemax in right_envs: + tn_local_overlap |= right_envs[sitemax] + + x = tn_local_overlap.contract(all, **contract_opts) + if normalized: + x = x / nfactor + + expecs[where] = x + + if return_all: + return expecs + + return functools.reduce(operator.add, expecs.values()) + + def compute_local_expectation( + self, + terms, + normalized=True, + return_all=False, + method="canonical", + info=None, + inplace=False, + **contract_opts, + ): + """Compute many local expectations at once. + + Parameters + ---------- + terms : dict[int or tuple[int], array_like] + The local terms to compute values for. + normalized : bool, optional + Explicitly normalize each local term. + return_all : bool, optional + Whether to return each expectation in `terms` separately + or sum them all together (the default). + method : {'canonical', 'envs'}, optional + The method to use to compute the local expectations. + + - 'canonical': canonicalize around the sites of interest and + contract the local reduced density matrices, moving the canonical + center around as needed. + - 'envs': form the local overlaps using left and right environments + and contract these directly. This can be quicker if the canonical + center is not already aligned. + + info : dict, optional + If supplied, and `method=="canonical"`, will be used to infer and + store various extra information. Currently the key "cur_orthog" is + used to store the current orthogonality center. Its input value can + be ``"calc"``, a single site, or a pair of sites representing the + min/max range, inclusive. It will be updated to the actual range + after. + inplace : bool, optional + If `method=="canonical"`, whether to perform the required + canonicalizations inplace or on a copy of the state. + contract_opts + Supplied to + :meth:`~quimb.tensor.tensor_core.TensorNetwork.contract` + when contracting the local overlaps or density matrices. + + Returns + ------- + float or dict[int or tuple[int], float] + The expecetation value(s), either summed or for each term if + `return_all=True`. + + See Also + -------- + compute_local_expectation_canonical, compute_local_expectation_via_envs + """ + if method == "canonical": + return self.compute_local_expectation_canonical( + terms, + normalized=normalized, + return_all=return_all, + info=info, + inplace=inplace, + **contract_opts, + ) + elif method == "envs": + return self.compute_local_expectation_via_envs( + terms, + normalized=normalized, + return_all=return_all, + **contract_opts, + ) + else: + raise ValueError( + f"Unrecognized method: {method}, should be one of: " + "'canonical', 'envs'." + ) + @convert_cur_orthog def bipartite_schmidt_state(self, sz_a, get="ket", info=None): r"""Compute the reduced state for a bipartition of an OBC MPS, in terms @@ -3215,7 +3611,6 @@ def sample_configuration(self, seed=None, info=None): config = [] omega = 1.0 for i in range(psi.L): - # form local density matrix ki = psi[i] bi = ki.H @@ -3271,6 +3666,7 @@ def sample(self, C, seed=None, info=None): for _ in range(C): yield psi0.sample_configuration(seed=rng, info=info) + class MatrixProductOperator(TensorNetwork1DOperator, TensorNetwork1DFlat): """Initialise a matrix product operator, with auto labelling and tagging. diff --git a/quimb/tensor/tensor_core.py b/quimb/tensor/tensor_core.py index 982d7ab2..5e6615d2 100644 --- a/quimb/tensor/tensor_core.py +++ b/quimb/tensor/tensor_core.py @@ -1668,7 +1668,7 @@ def isel(self, selectors, inplace=False): T.rand_reduce_(ix) else: # index will be removed by selecting a specific index - data_loc.append(sel) + data_loc.append(int(sel)) T.modify( apply=lambda x: x[tuple(data_loc)], inds=new_inds, left_inds=None @@ -2208,12 +2208,15 @@ def vector_reduce(self, ind, v, inplace=False): """ t = self if inplace else self.copy() axis = t.inds.index(ind) - new_data = array_contract( - (t.data, v), - (tuple(range(self.ndim)), (axis,)), + + expr = array_contract_expression( + shapes=(self.shape, shape(v)), + inputs=(tuple(range(self.ndim)), (axis,)), + constants={1: v}, ) + new_inds = t.inds[:axis] + t.inds[axis + 1 :] - t.modify(data=new_data, inds=new_inds) + t.modify(apply=expr, inds=new_inds) return t vector_reduce_ = functools.partialmethod(vector_reduce, inplace=True) @@ -9645,7 +9648,7 @@ def rank_weight(ind): if equalize_norms: signs = [] for s in scalars: - signs.append(do("sign", s)) + signs.append(s / do("abs", s)) tn.exponent += do("log10", do("abs", s)) scalars = signs diff --git a/tests/test_tensor/test_circuit.py b/tests/test_tensor/test_circuit.py index 0629271d..df7085fe 100644 --- a/tests/test_tensor/test_circuit.py +++ b/tests/test_tensor/test_circuit.py @@ -466,6 +466,28 @@ def test_sample(self, group_size): assert power_divergence(f_obs, f_exp)[0] < 100 + @pytest.mark.parametrize("group_size", (1, 3)) + def test_sample_gate_by_gate(self, group_size): + import collections + from scipy.stats import power_divergence + + C = 2**10 + L = 5 + circ = random_a2a_circ(L, 3) + + psi = circ.to_dense() + p_exp = abs(psi.reshape(-1)) ** 2 + f_exp = p_exp * C + + counts = collections.Counter( + circ.sample_gate_by_gate(C, group_size=group_size) + ) + f_obs = np.zeros(2**L) + for b, c in counts.items(): + f_obs[int(b, 2)] = c + + assert power_divergence(f_obs, f_exp)[0] < 100 + def test_sample_chaotic(self): import collections from scipy.stats import power_divergence diff --git a/tests/test_tensor/test_tensor_1d.py b/tests/test_tensor/test_tensor_1d.py index 67b0fb2c..4987f3ce 100644 --- a/tests/test_tensor/test_tensor_1d.py +++ b/tests/test_tensor/test_tensor_1d.py @@ -383,7 +383,9 @@ def test_magnetization(self): def test_partial_trace(self, rescale, keep): n = 10 p = qtn.MPS_rand_state(n, 7) - r = p.ptr(keep=keep, upper_ind_id="u{}", rescale_sites=rescale) + r = p.partial_trace_to_mpo( + keep=keep, upper_ind_id="u{}", rescale_sites=rescale + ) rd = r.to_qarray() if isinstance(keep, slice): keep = p.slice2sites(keep) @@ -911,7 +913,7 @@ def test_mpo_rand_herm_trace_and_identity_like(self, cyclic): def test_partial_transpose(self): p = qtn.MPS_rand_state(8, 10) - r = p.ptr([2, 3, 4, 5, 6, 7]) + r = p.partial_trace_to_mpo([2, 3, 4, 5, 6, 7]) rd = r.to_qarray() assert qu.isherm(rd) From f911c59862961917eca62602fca32c79d77d36ed Mon Sep 17 00:00:00 2001 From: Johnnie Gray Date: Thu, 17 Oct 2024 22:17:20 -0700 Subject: [PATCH 3/5] test mps.compute_local_expectation --- tests/test_tensor/test_tensor_1d.py | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/tests/test_tensor/test_tensor_1d.py b/tests/test_tensor/test_tensor_1d.py index 4987f3ce..4b762e55 100644 --- a/tests/test_tensor/test_tensor_1d.py +++ b/tests/test_tensor/test_tensor_1d.py @@ -777,6 +777,16 @@ def test_sample_seed(self): ] assert len(set(configs)) > 1 + def test_compute_local_expectation(self): + psi = qtn.MPS_rand_state(10, 7, dtype="complex128") + terms = {(i, i + 1): qu.rand_herm(4) for i in range(9)} + + ex = psi.compute_local_expectation_exact(terms) + xa = psi.compute_local_expectation(terms, method="canonical") + assert xa == pytest.approx(ex) + xb = psi.compute_local_expectation(terms, method="envs") + assert xb == pytest.approx(ex) + class TestMatrixProductOperator: @pytest.mark.parametrize("cyclic", [False, True]) From 30375ad548dd131ca407bee46569c6b79cbedb35 Mon Sep 17 00:00:00 2001 From: Johnnie Gray Date: Fri, 18 Oct 2024 08:17:09 -0700 Subject: [PATCH 4/5] fix ptr tests --- tests/test_tensor/test_tensor_spectral_approx.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/tests/test_tensor/test_tensor_spectral_approx.py b/tests/test_tensor/test_tensor_spectral_approx.py index ccb23172..fabffb74 100644 --- a/tests/test_tensor/test_tensor_spectral_approx.py +++ b/tests/test_tensor/test_tensor_spectral_approx.py @@ -37,7 +37,7 @@ def test_realistic(self): ham = MPO_ham_heis(20) dmrg = DMRG2(ham, bond_dims=[2, 4]) dmrg.solve() - rho_ab = dmrg.state.ptr(range(6, 14)) + rho_ab = dmrg.state.partial_trace_to_mpo(range(6, 14)) xf = approx_spectral_function( rho_ab, lambda x: x, tol=0.1, verbosity=2 ) @@ -55,7 +55,7 @@ def test_realistic_ent(self): psi0 = dmrg.state.to_dense() lne = logneg_subsys(psi0, [2] * n, sysa=sysa, sysb=sysb) - rho_ab = dmrg.state.ptr(sysab, rescale_sites=True) + rho_ab = dmrg.state.partial_trace_to_mpo(sysab, rescale_sites=True) rho_ab_pt = rho_ab.partial_transpose(range(3)) lnx = log2( approx_spectral_function(rho_ab_pt, abs, tol=0.1, verbosity=2) From 71bbea9cf24cddac478f18f569ec22197968f7ce Mon Sep 17 00:00:00 2001 From: Johnnie Gray Date: Mon, 21 Oct 2024 13:16:09 -0700 Subject: [PATCH 5/5] update docs and and run squeaky on a few [skip ci] --- docs/basics.ipynb | 69 +- docs/conf.py | 2 + docs/tensor-basics.ipynb | 11304 +------- docs/tensor-circuit.ipynb | 217 +- docs/tensor-optimization.ipynb | 48000 +------------------------------ 5 files changed, 333 insertions(+), 59259 deletions(-) diff --git a/docs/basics.ipynb b/docs/basics.ipynb index 49e88da4..dd8713a3 100644 --- a/docs/basics.ipynb +++ b/docs/basics.ipynb @@ -2,6 +2,7 @@ "cells": [ { "cell_type": "markdown", + "id": "0b054e8d-d0bb-4613-bddd-81b37f3d2a8e", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -21,6 +22,7 @@ { "cell_type": "code", "execution_count": 1, + "id": "a30d59e4-ebf6-417d-9adf-16de0b1bbbe1", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -32,6 +34,7 @@ }, { "cell_type": "markdown", + "id": "1f139c32-2483-406f-8a4c-399cf1945a34", "metadata": {}, "source": [ "Kets are column vectors, i.e. with shape ``(d, 1)``:" @@ -40,6 +43,7 @@ { "cell_type": "code", "execution_count": 2, + "id": "69b02c9c-37c3-427d-99de-b480b7ea4d6d", "metadata": {}, "outputs": [ { @@ -61,6 +65,7 @@ }, { "cell_type": "markdown", + "id": "4a731dcf-13e7-4888-a7d1-e7defb06edd3", "metadata": {}, "source": [ "The ``normalized=True`` option can be used to ensure a normalized output.\n", @@ -71,6 +76,7 @@ { "cell_type": "code", "execution_count": 3, + "id": "0770dcd6-e29b-4b92-9072-2b4ade641268", "metadata": {}, "outputs": [ { @@ -90,6 +96,7 @@ }, { "cell_type": "markdown", + "id": "f2ab8914-8431-4dad-bb4b-7a6c400c60df", "metadata": {}, "source": [ "And operators are square matrices, i.e. have shape ``(d, d)``:" @@ -98,12 +105,13 @@ { "cell_type": "code", "execution_count": 4, + "id": "6a3a349c-8648-4934-8000-66d3ddf16805", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[ 1.+0.j 0.-2.j -3.+0.j]\n", + "[[ 1.+0.j 0.-2.j -3.-0.j]\n", " [ 0.+2.j 4.+0.j 0.-6.j]\n", " [-3.+0.j 0.+6.j 9.+0.j]]" ] @@ -119,6 +127,7 @@ }, { "cell_type": "markdown", + "id": "fb452078-ab1c-4ba5-81e0-799af6ef0f76", "metadata": {}, "source": [ "Which can also be sparse:" @@ -127,13 +136,14 @@ { "cell_type": "code", "execution_count": 5, + "id": "24cab7c2-7dd3-46a7-9acf-f1d3e0cbe5d3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "<3x3 sparse matrix of type ''\n", - "\twith 9 stored elements in Compressed Sparse Row format>" + "" ] }, "execution_count": 5, @@ -147,6 +157,7 @@ }, { "cell_type": "markdown", + "id": "a10ffe96-9bc3-4e4e-ace8-0098d0e29564", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -173,6 +184,7 @@ { "cell_type": "code", "execution_count": 6, + "id": "7bebe19b-bb7e-4d5d-a55c-63340574aba4", "metadata": {}, "outputs": [ { @@ -197,6 +209,7 @@ { "cell_type": "code", "execution_count": 7, + "id": "0cb44044-6832-4365-a4b0-5f6ed7b940c4", "metadata": {}, "outputs": [ { @@ -216,6 +229,7 @@ }, { "cell_type": "markdown", + "id": "9389db86-974f-47a7-94e0-729a34436be2", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -231,6 +245,7 @@ { "cell_type": "code", "execution_count": 8, + "id": "ccb3c8b1-3673-496b-9efe-d15e13e15c45", "metadata": {}, "outputs": [ { @@ -253,6 +268,7 @@ { "cell_type": "code", "execution_count": 9, + "id": "21c148d7-a55c-44cb-bbf3-8de4c9b33f41", "metadata": {}, "outputs": [ { @@ -273,6 +289,7 @@ { "cell_type": "code", "execution_count": 10, + "id": "6916a93e-bbfa-4b37-92f3-a7816d58af28", "metadata": {}, "outputs": [ { @@ -295,6 +312,7 @@ { "cell_type": "code", "execution_count": 11, + "id": "ad4186dc-309d-44b9-abed-5d6af268746a", "metadata": {}, "outputs": [ { @@ -314,6 +332,7 @@ }, { "cell_type": "markdown", + "id": "ba59088e-d798-455f-95b8-179512b0874f", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -327,12 +346,13 @@ { "cell_type": "code", "execution_count": 12, + "id": "4012d11b-f4b9-4dd5-af69-96f51299839d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "1.0" + "np.float64(1.0)" ] }, "execution_count": 12, @@ -347,12 +367,13 @@ { "cell_type": "code", "execution_count": 13, + "id": "a67c2946-6e4b-40e6-91ff-f47c17e5f0d7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0j" + "np.complex128(0j)" ] }, "execution_count": 13, @@ -366,6 +387,7 @@ }, { "cell_type": "markdown", + "id": "cd62be41-0bf5-422e-b5b5-8cb9a37174d6", "metadata": {}, "source": [ "Here's an example for a much larger (20 qubit), sparse operator expecation,\n", @@ -375,13 +397,14 @@ { "cell_type": "code", "execution_count": 14, + "id": "425bae86-798a-4d9d-a7e0-2690ea7a219b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "<1048576x1048576 sparse matrix of type ''\n", - "\twith 11534268 stored elements in Compressed Sparse Row format>" + "" ] }, "execution_count": 14, @@ -398,12 +421,13 @@ { "cell_type": "code", "execution_count": 15, + "id": "4198dbc2-d143-4514-9563-8785ef1395f4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.9998770131258168" + "np.float64(1.0004858170636874)" ] }, "execution_count": 15, @@ -418,13 +442,14 @@ { "cell_type": "code", "execution_count": 16, + "id": "bda59aa7-95c5-4dbf-9b63-95a3635f1ec9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "59 ms ± 3.85 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + "55.1 ms ± 3.82 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" ] } ], @@ -435,6 +460,7 @@ }, { "cell_type": "markdown", + "id": "e68195b9-331c-4e07-b3b2-a1276beb808e", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -464,12 +490,13 @@ ":::\n", "\n", "Often one wants to sandwich an operator with many identities,\n", - "{func}`~quimb.core.ikron` can be used for this:\n" + "{func}`~quimb.core.ikron` can be used for this:" ] }, { "cell_type": "code", "execution_count": 17, + "id": "bf597230-30d7-4d54-b876-e93967891fc7", "metadata": {}, "outputs": [ { @@ -492,6 +519,7 @@ }, { "cell_type": "markdown", + "id": "5b7a4905-ee44-4a82-89f1-6e1a612c021b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -503,6 +531,7 @@ { "cell_type": "code", "execution_count": 18, + "id": "ed53d5cc-a2e7-4acb-b867-cb1e61951d3f", "metadata": {}, "outputs": [ { @@ -532,6 +561,7 @@ }, { "cell_type": "markdown", + "id": "753aebb7-8d79-491b-8add-9b2497e6d81a", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -553,15 +583,16 @@ { "cell_type": "code", "execution_count": 19, + "id": "5c6f0168-e595-4472-b78e-e7c551089e31", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[ 0.256+0.j -0.013-0.007j 0.02 +0.008j -0.014+0.007j]\n", - " [-0.013+0.007j 0.263+0.j -0.011+0.008j 0.016+0.004j]\n", - " [ 0.02 -0.008j -0.011-0.008j 0.231+0.j 0.01 +0.008j]\n", - " [-0.014-0.007j 0.016-0.004j 0.01 -0.008j 0.25 +0.j ]]" + "[[ 0.279+0.j 0.003-0.005j 0.012+0.009j 0.018-0.009j]\n", + " [ 0.003+0.005j 0.239+0.j -0.005+0.007j -0.005-0.002j]\n", + " [ 0.012-0.009j -0.005-0.007j 0.24 +0.j -0.015-0.014j]\n", + " [ 0.018+0.009j -0.005+0.002j -0.015+0.014j 0.242+0.j ]]" ] }, "execution_count": 19, @@ -579,6 +610,7 @@ }, { "cell_type": "markdown", + "id": "5ea15f65-79d4-40a1-993a-82b011dc77e1", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -590,7 +622,7 @@ "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { - "display_name": "Python 3.10.8 ('numpy')", + "display_name": "py312", "language": "python", "name": "python3" }, @@ -604,12 +636,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.8 (main, Nov 4 2022, 13:48:29) [GCC 11.2.0]" - }, - "vscode": { - "interpreter": { - "hash": "39c10650315d977fb13868ea1402e99f3e10e9885c2c202e692ae90b8995050d" - } + "version": "3.12.6" } }, "nbformat": 4, diff --git a/docs/conf.py b/docs/conf.py index 34a9b86e..701baf1e 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -64,6 +64,8 @@ 'python': ('https://docs.python.org/3/', None), 'numpy': ('https://numpy.org/doc/stable/', None), 'scipy': ('https://docs.scipy.org/doc/scipy/', None), + 'cotengra': ('https://cotengra.readthedocs.io/en/latest/', None), + 'autoray': ('https://autoray.readthedocs.io/en/latest/', None), } # Add any paths that contain templates here, relative to this directory. diff --git a/docs/tensor-basics.ipynb b/docs/tensor-basics.ipynb index fa35b52a..2581fb05 100644 --- a/docs/tensor-basics.ipynb +++ b/docs/tensor-basics.ipynb @@ -3,6 +3,7 @@ { "attachments": {}, "cell_type": "markdown", + "id": "51f916b5-d6eb-4aad-9d56-b0f9e82f0595", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -34,6 +35,7 @@ { "cell_type": "code", "execution_count": 1, + "id": "9f2756c6-1df3-4ff4-9054-7fb7423176e4", "metadata": {}, "outputs": [], "source": [ @@ -44,6 +46,7 @@ }, { "cell_type": "markdown", + "id": "0b3e1355-f577-429e-b65e-1ca43dde5c54", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -52,8 +55,8 @@ "\n", "To create a Tensor you just need:\n", "\n", - "* `data` - a raw array, and \n", - "* `inds` - a set of 'indices' to label each dimension with. \n", + "* `data` - a raw array, and\n", + "* `inds` - a set of 'indices' to label each dimension with.\n", "\n", "Whilst naming the dimensions is useful so you don't have to remember which axis is which, the crucial point is that tensors simply sharing the same index name automatically form a 'bond' or implicit contraction when put together. Tensors can also carry an arbitrary number of identifiers - `tags` - which you can use to refer to single or groups of tensors once they are embedded in networks.\n", "\n", @@ -63,6 +66,7 @@ { "cell_type": "code", "execution_count": 2, + "id": "f8e575b2-8f76-40ca-8eb3-8a00ec3be204", "metadata": {}, "outputs": [ { @@ -92,229 +96,13 @@ { "cell_type": "code", "execution_count": 3, + "id": "2cb31903-aef9-4653-8e17-20cd092952e6", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.303768\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -332,6 +120,7 @@ }, { "cell_type": "markdown", + "id": "88d2446b-bfda-4442-a75c-4c83291f6e58", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -368,6 +157,7 @@ { "cell_type": "code", "execution_count": 4, + "id": "cee2ae1c-1c7e-442c-8c44-59baed4508b2", "metadata": {}, "outputs": [], "source": [ @@ -377,6 +167,7 @@ }, { "cell_type": "markdown", + "id": "be211a49-32b5-4512-a916-7639590f2bae", "metadata": {}, "source": [ "And finally, a random 'bra' to complete the inner product:" @@ -385,6 +176,7 @@ { "cell_type": "code", "execution_count": 5, + "id": "cbea620b-317a-4de2-9272-e4c758feb6ff", "metadata": {}, "outputs": [], "source": [ @@ -393,17 +185,19 @@ }, { "cell_type": "markdown", + "id": "db757fb1-bd13-4f65-8978-c6dd11d18303", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Note how repeating an index name is all that is required to define a contraction.\n", - "If you want to join two tensors and have the index generated automatically \n", + "If you want to join two tensors and have the index generated automatically\n", "you can use the function [`qtn.connect`](quimb.tensor.tensor_core.connect)." ] }, { "cell_type": "markdown", + "id": "e5bba4e1-7799-4dd9-b088-a31709a68712", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -416,12 +210,13 @@ "\n", "## Creating Tensor Networks\n", "\n", - "We can now combine these into a [`TensorNetwork`](quimb.tensor.tensor_core.TensorNetwork) using the `&` operator overload:\n" + "We can now combine these into a [`TensorNetwork`](quimb.tensor.tensor_core.TensorNetwork) using the `&` operator overload:" ] }, { "cell_type": "code", "execution_count": 6, + "id": "c3af54e0-0fd8-4429-90a4-767287a57475", "metadata": {}, "outputs": [ { @@ -444,6 +239,7 @@ }, { "cell_type": "markdown", + "id": "aaee6ec9-7bba-4d70-893a-7a8fd69ad75f", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -467,7 +263,7 @@ "find the names of indices connecting tensors if explicitly required.\n", ":::\n", "\n", - "Some common [`TensorNetwork`](quimb.tensor.tensor_core.TensorNetwork) methods \n", + "Some common [`TensorNetwork`](quimb.tensor.tensor_core.TensorNetwork) methods\n", "are:\n", "\n", "- [`TensorNetwork.reindex`](quimb.tensor.tensor_core.TensorNetwork.reindex)\n", @@ -491,694 +287,13 @@ { "cell_type": "code", "execution_count": 7, + "id": "16c76c97-2640-46e3-a724-7a69d595658a", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.515203\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -1196,6 +311,7 @@ }, { "cell_type": "markdown", + "id": "cdc25ee4-5a83-4241-8e25-cb761a0654f3", "metadata": {}, "source": [ "Note the tags can be used to identify both paulis at once. But they could also be uniquely identified using their ``'X'`` and ``'Y'`` tags respectively:" @@ -1203,6 +319,7 @@ }, { "cell_type": "markdown", + "id": "b48d4fc3-b7df-48c9-9d5a-4146561e60e5", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1223,770 +340,13 @@ { "cell_type": "code", "execution_count": 8, + "id": "ac74eca3-0f61-492f-8a0b-391ef1317655", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.635378\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -2017,6 +377,7 @@ }, { "cell_type": "markdown", + "id": "1f61668c-9605-496b-b1f1-d67ffe96d7b0", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2051,18 +412,19 @@ "graphs. See {ref}`tensor-network-contraction` for more details.\n", ":::\n", "\n", - "To fully contract a network we can use the `^` operator, and the `...` object:\n" + "To fully contract a network we can use the `^` operator, and the `...` object:" ] }, { "cell_type": "code", "execution_count": 9, + "id": "088405f6-6c11-4e77-8daf-dcd6f9cc8281", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(0.06766823867678032-0.8460798111575898j)" + "(0.556024406455527+0.28213663229389124j)" ] }, "execution_count": 9, @@ -2076,6 +438,7 @@ }, { "cell_type": "markdown", + "id": "03e3a18a-2f0c-4ae3-ab61-63a56e1757ad", "metadata": {}, "source": [ "Or if you only want to contract tensors with a specific set of tags, such as the two pauli operators,\n", @@ -2085,484 +448,13 @@ { "cell_type": "code", "execution_count": 10, + "id": "ea5e2905-bbb2-4f48-b801-648a174db267", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.734174\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -2593,6 +485,7 @@ }, { "cell_type": "markdown", + "id": "2aecb912-418c-49e2-afed-79c96db6ca40", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2610,13 +503,14 @@ { "cell_type": "code", "execution_count": 11, + "id": "e2aa08f9-db49-4b03-be59-28393cf5f186", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
Tensor(shape=(2, 4), inds=[a, b], tags={A, B}),backend=numpy, dtype=float64, data=array([[-1.82145456, 5.37156602, -0.6407701 , 1.73704458],\n", - " [-3.04900789, 5.68378085, -3.08717877, 4.09540662]])
" + "
Tensor(shape=(2, 4), inds=[a, b], tags={A, B}),backend=numpy, dtype=float64, data=array([[-1.07482966, 1.40801906, 0.97244287, 2.06712511],\n", + " [-1.19598176, -1.1037286 , -0.15011799, 1.1052763 ]])
" ], "text/plain": [ "Tensor(shape=(2, 4), inds=('a', 'b'), tags=oset(['A', 'B']))" @@ -2637,6 +531,7 @@ }, { "cell_type": "markdown", + "id": "b2554816-853e-4bf9-bf4e-83dc3a1d5d04", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2649,12 +544,13 @@ { "cell_type": "code", "execution_count": 12, + "id": "b136e4aa-9ad6-4bc1-af35-ba53d319f5b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "1.0" + "0.9999999999999999" ] }, "execution_count": 12, @@ -2672,6 +568,7 @@ }, { "cell_type": "markdown", + "id": "7963ae63-db42-4dab-b6fe-b2898a3a68f3", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -2688,329 +585,13 @@ { "cell_type": "code", "execution_count": 13, + "id": "227e4bfd-3b58-4879-b588-9571fe09ded4", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.785037\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -3031,347 +612,13 @@ { "cell_type": "code", "execution_count": 14, + "id": "db070ecd-d78e-4db4-ad40-4735cea49f18", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.883794\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -3391,6 +638,7 @@ }, { "cell_type": "markdown", + "id": "691cda75-a0ec-4bc8-b87e-df5db5aa931a", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -3409,535 +657,13 @@ { "cell_type": "code", "execution_count": 15, + "id": "2b21499c-40be-426a-9d3b-0226025580e5", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:50.989950\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -3957,664 +683,13 @@ { "cell_type": "code", "execution_count": 16, + "id": "af444a50-b491-4895-89fa-7f1c861b3644", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:51.107289\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -4642,6 +717,7 @@ }, { "cell_type": "markdown", + "id": "724772fe-8265-4f09-9414-eb742f14525b", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -4677,521 +753,13 @@ { "cell_type": "code", "execution_count": 17, + "id": "d0a57a78-c06b-4cdb-afd8-5fae91409189", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:51.212497\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -5214,6 +782,7 @@ }, { "cell_type": "markdown", + "id": "8b990d65-559b-47e8-bd54-282cd4e2357a", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -5239,416 +808,19 @@ "\n", "The maximum bond dimension kept is often denoted $\\chi$.\n", "The core function that handles this is\n", - "[`qtn.tensor_compress_bond`](quimb.tensor.tensor_core.tensor_compress_bond).\n" + "[`qtn.tensor_compress_bond`](quimb.tensor.tensor_core.tensor_compress_bond)." ] }, { "cell_type": "code", "execution_count": 18, + "id": "1f706cb8-37e0-4f81-b6e3-9e582afe474c", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:51.309527\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -5669,406 +841,13 @@ { "cell_type": "code", "execution_count": 19, + "id": "18180bab-1d2e-4a3f-aa0e-398c098f985f", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:51.408834\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -6090,6 +869,7 @@ }, { "cell_type": "markdown", + "id": "31e643cd-e2d9-41e0-b67d-b39a9ebd4fe4", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -6112,675 +892,19 @@ "be cast as a contraction that is usually much cheaper.\n", "\n", "Consider the following contrived TN with overall shape\n", - "`(1000, 1000, 1000, 1000)`, but which is evidently low rank:\n" + "`(1000, 1000, 1000, 1000)`, but which is evidently low rank:" ] }, { "cell_type": "code", "execution_count": 20, + "id": "a84c0de6-3dcc-4968-a354-ba96acbd62de", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:51.519428\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -6803,6 +927,7 @@ }, { "cell_type": "markdown", + "id": "96df8da5-2c83-4b40-b0f2-e4d75f87405a", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -6816,6 +941,7 @@ { "cell_type": "code", "execution_count": 21, + "id": "1a3bcae3-17e3-477a-9f9a-a3f34c4866cc", "metadata": {}, "outputs": [ { @@ -6836,6 +962,7 @@ }, { "cell_type": "markdown", + "id": "19e8585d-eb1d-4814-bb1f-599226801bc5", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -6850,12 +977,13 @@ { "cell_type": "code", "execution_count": 22, + "id": "57136381-6ed2-4135-94bb-3a49dd81cc58", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([6425.04063216+0.j])" + "array([2900.03154824+0.j])" ] }, "execution_count": 22, @@ -6869,6 +997,7 @@ }, { "cell_type": "markdown", + "id": "12c05935-a7eb-4fdb-b0e9-88343b6ee69f", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -6882,552 +1011,13 @@ { "cell_type": "code", "execution_count": 23, + "id": "49269f52-20b9-484c-87c7-bef4acd14413", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:56.825684\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -7454,6 +1044,7 @@ }, { "cell_type": "markdown", + "id": "51ae6010-83b4-4330-8217-f7eedf119351", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -7481,6 +1072,7 @@ { "cell_type": "code", "execution_count": 24, + "id": "2a60349b-1ec3-4be5-8296-a59545c29eba", "metadata": {}, "outputs": [], "source": [ @@ -7489,6 +1081,7 @@ }, { "cell_type": "markdown", + "id": "1edad091-4af5-48d6-990e-590d03312557", "metadata": {}, "source": [ "Get tensors which have **all** of the tags:" @@ -7497,647 +1090,13 @@ { "cell_type": "code", "execution_count": 25, + "id": "bb157352-624b-494c-aa97-d8fb5f4c2d0f", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:56.962082\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -8156,6 +1115,7 @@ }, { "cell_type": "markdown", + "id": "4fb3d3af-180e-4f3e-844f-9d31140a6172", "metadata": {}, "source": [ "Get tensors which *don't* have **all** of the tags:" @@ -8164,663 +1124,13 @@ { "cell_type": "code", "execution_count": 26, + "id": "9bf6efec-c02d-4af1-86f2-e657464b6a3e", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:57.091620\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -8839,6 +1149,7 @@ }, { "cell_type": "markdown", + "id": "deabe48d-218b-4197-8e92-457aff1e44ea", "metadata": {}, "source": [ "Get tensors which have **any** of the tags:" @@ -8847,663 +1158,13 @@ { "cell_type": "code", "execution_count": 27, + "id": "49c89b3a-05ee-4ffc-9bc0-a4ea39f69d8b", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:57.284905\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -9522,6 +1183,7 @@ }, { "cell_type": "markdown", + "id": "48f5f275-faf3-409b-b327-c256d40e33cc", "metadata": {}, "source": [ "Get tensors which *don't* have **any** of the tags:" @@ -9530,679 +1192,13 @@ { "cell_type": "code", "execution_count": 28, + "id": "926bf5c8-85b5-4244-90a8-74cf1de46a27", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2023-11-29T15:22:57.407596\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.1, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -10221,6 +1217,7 @@ }, { "cell_type": "markdown", + "id": "beffc29c-a696-4dd0-8123-ef3ac7245d28", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -10240,15 +1237,16 @@ { "cell_type": "code", "execution_count": 29, + "id": "6a2c5e06-36d9-479a-acc2-7673e92550e4", "metadata": {}, "outputs": [ { "data": { "text/html": [ - "
Tensor(shape=(4, 4, 4, 4), inds=[_d0324aAAABX, _d0324aAAABZ, _d0324aAAABa, _d0324aAAABR], tags={I2,3, X2, Y3, ALL, ANY}),backend=numpy, dtype=float64, data=...
" + "
Tensor(shape=(4, 4, 4, 4), inds=[_835204AAABZ, _835204AAABb, _835204AAABc, _835204AAABT], tags={I2,3, X2, Y3, ALL, ANY}),backend=numpy, dtype=float64, data=...
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" @@ -12510,23 +1444,24 @@ { "cell_type": "code", "execution_count": 35, + "id": "155c4539-7be9-48b0-a17e-44c3460a7f4a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "('_d0324aAAACH',\n", - " '_d0324aAAACI',\n", - " '_d0324aAAACJ',\n", - " '_d0324aAAACK',\n", - " '_d0324aAAACL',\n", - " '_d0324aAAACM',\n", - " '_d0324aAAACN',\n", - " '_d0324aAAACO',\n", - " '_d0324aAAACP',\n", - " '_d0324aAAACQ',\n", - " '_d0324aAAACR',\n", - " '_d0324aAAACS')" + "('_835204AAACJ',\n", + " '_835204AAACK',\n", + " '_835204AAACL',\n", + " '_835204AAACM',\n", + " '_835204AAACN',\n", + " '_835204AAACO',\n", + " '_835204AAACP',\n", + " '_835204AAACQ',\n", + " '_835204AAACR',\n", + " '_835204AAACS',\n", + " '_835204AAACT',\n", + " '_835204AAACU')" ] }, "execution_count": 35, @@ -12541,6 +1476,7 @@ }, { "cell_type": "markdown", + "id": "31fd7c7e-63e0-4984-99db-31857caf6a4b", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] @@ -12553,9 +1489,9 @@ "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { - "display_name": "Python [conda env:py311]", + "display_name": "py312", "language": "python", - "name": "conda-env-py311-py" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -12567,7 +1503,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.3" + "version": "3.12.6" } }, "nbformat": 4, diff --git a/docs/tensor-circuit.ipynb b/docs/tensor-circuit.ipynb index 37bf8db2..f90732e5 100644 --- a/docs/tensor-circuit.ipynb +++ b/docs/tensor-circuit.ipynb @@ -3,7 +3,7 @@ { "attachments": {}, "cell_type": "markdown", - "id": "0ede9831-c3b4-499e-8742-206afc229def", + "id": "31fbfeda-e02b-4029-becb-dfd8cf8a2db0", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -36,7 +36,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "a6fe930b-a519-4d59-8289-8b9c9df49b79", + "id": "e9942fcd-455d-43f7-b4d1-00d6e850469c", "metadata": {}, "outputs": [ { @@ -78,7 +78,7 @@ }, { "cell_type": "markdown", - "id": "b87c830d-8f7e-42a8-82a3-cf05a818cfdd", + "id": "bcedf1c9-7506-4006-b3e9-270c3abfb689", "metadata": {}, "source": [ "As mentioned above, various pre-processing steps need to occur (which will happen on the first run if not explicitly called). The results of these are cached such that the more you sample the more the simulation should speed up:" @@ -87,7 +87,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "d28ff774-a881-4dbf-ba62-68afa4bc3a5f", + "id": "24460891-8162-4b66-8703-88a32ef8552c", "metadata": {}, "outputs": [ { @@ -116,7 +116,7 @@ }, { "cell_type": "markdown", - "id": "9534182e-6926-4ab7-b56e-0371ee3f8650", + "id": "1586d1a4-3b3c-4d51-9eda-065f47041445", "metadata": {}, "source": [ "Collect some statistics:" @@ -125,7 +125,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "36666eef-3fdb-4d3f-a429-adcaf6c34a9f", + "id": "96770615-e231-4973-8af2-1fac694def49", "metadata": {}, "outputs": [ { @@ -158,7 +158,7 @@ }, { "cell_type": "markdown", - "id": "dbb20e23-016c-4169-b02d-710a90ce372a", + "id": "074234b6-860d-4446-b0a1-7ed4d42a1c23", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -203,7 +203,7 @@ }, { "cell_type": "markdown", - "id": "bdfbd0bc-d477-43b9-8b78-1ce0c7f067ae", + "id": "f2066f2d-cf4d-408f-92ae-1d5d07585bb2", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -227,7 +227,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "75a4e272-e3fb-44aa-9eed-fc851631869b", + "id": "5198f13a-6e4f-4b0b-8411-e1ae3fb68d37", "metadata": {}, "outputs": [ { @@ -277,7 +277,7 @@ }, { "cell_type": "markdown", - "id": "21527597-0c03-4627-bea4-26932e443e2e", + "id": "f1fa4bbc-270f-444a-8f03-c8fbf4e92f19", "metadata": {}, "source": [ "The basic tensor network representing the state is stored in the\n", @@ -287,13 +287,13 @@ { "cell_type": "code", "execution_count": 5, - "id": "06892693-b56d-46da-9341-77f57f5ea5fa", + "id": "f52d1a19-8629-4d1c-b7f0-91f4bcc9e8ed", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -311,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "80eab5ef-5c24-4fab-8991-a7f2774f5088", + "id": "039cb9b1-32c3-46f2-a5a4-a47a2b6f0c99", "metadata": {}, "source": [ "Note by default the CNOT and CZ gates have\n", @@ -324,13 +324,13 @@ { "cell_type": "code", "execution_count": 6, - "id": "d6bfd922-9821-48b4-8e21-289f1cb8b65d", + "id": "e919f266-8c89-419a-9cb5-62a15a19df75", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -348,7 +348,7 @@ }, { "cell_type": "markdown", - "id": "d67ab169-efd6-4635-a5b3-34ea07646823", + "id": "3f65f883-78d0-4132-a434-bf08b0bc3c4d", "metadata": {}, "source": [ "Or since we supplied ``gate_round`` as an keyword (which is optional), the tensors\n", @@ -358,13 +358,13 @@ { "cell_type": "code", "execution_count": 7, - "id": "a1904905-a5e1-4f95-a50e-797dd0c6d3ce", + "id": "b7041e14-1935-4af0-af18-8040c425eeec", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "1cb9fa40-f203-42d3-816d-f09f7ee042ad", + "id": "f13c177e-7e6a-42d1-a64a-1e9e82753d29", "metadata": {}, "source": [ "All of these might be helpful when addressing only certain tensors:" @@ -391,7 +391,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "f28e2b10-7455-4b2e-a2fc-5d47214f1392", + "id": "dcd9ac7c-3b83-47cf-a69f-001c69c9a20c", "metadata": {}, "outputs": [ { @@ -419,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "9160495c-c8a5-4693-9d4d-63be1213aa1b", + "id": "888c7a46-c2ca-4e11-92d4-54c584878ab3", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -435,7 +435,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "3174cadd-b595-4544-90d5-771a19ee7c30", + "id": "4ce7cc04-6be0-43d0-a0f2-e2604f613c2f", "metadata": {}, "outputs": [ { @@ -502,7 +502,7 @@ }, { "cell_type": "markdown", - "id": "6252031b-dece-40c9-bebc-595b5577fe25", + "id": "bf18f25c-8faa-4bcb-8af0-f1cf0c8c8f03", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -519,13 +519,13 @@ { "cell_type": "code", "execution_count": 10, - "id": "ef8b6097-4698-4044-bfc1-5428ad69c6eb", + "id": "dc3442d1-a015-465b-9c34-266f65051482", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "c5e2d670-03ec-4fd9-8be7-38db6a8b4fcf", + "id": "ab4bdab1-8343-4ab0-9711-1acc9f7883bc", "metadata": {}, "source": [ "We've used the ``contract=False`` option which doesn't try and split the gate tensor in any way,\n", @@ -565,7 +565,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "d087d620-f7be-4507-9fad-1bf3bd88324b", + "id": "618d5dec-fdf5-4037-84ab-1dda8c5541af", "metadata": {}, "outputs": [ { @@ -599,7 +599,7 @@ }, { "cell_type": "markdown", - "id": "fca0e3f5-ad88-4142-891a-88a5f2c8c363", + "id": "288ee59b-4914-4110-9b24-c1961b9be71d", "metadata": {}, "source": [ "For most tasks like contraction these are transparently handled like normal tensors:" @@ -608,7 +608,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "94cd7bda-556b-496b-8451-2f527f43f754", + "id": "16e2a04f-3830-4e29-a1bf-f6dea1ded19c", "metadata": {}, "outputs": [ { @@ -628,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "fc21f9a4-47ac-4654-8138-6d829e6d369b", + "id": "da59b46f-9fed-46eb-b025-1a24741b250b", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "21fc92a3-ef33-492c-864f-3680566c8af3", + "id": "88e01279-272f-4e18-bd36-54a8891afdcc", "metadata": {}, "outputs": [ { @@ -686,7 +686,7 @@ }, { "cell_type": "markdown", - "id": "6dd8eac0-d1e9-4e96-baf0-fbd541117fbd", + "id": "0630c5a7-3c86-4593-8caf-cf38342bf6e9", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -714,7 +714,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "6418b631-2e29-430c-bd4c-de92f04d820c", + "id": "65273dfe-ed10-47f1-9b7d-dfd0725f0a52", "metadata": {}, "outputs": [ { @@ -734,7 +734,7 @@ }, { "cell_type": "markdown", - "id": "d647790b-3287-48ab-bcbd-e477a67addb0", + "id": "e49efbbf-8080-4e61-9679-c7c11e152d40", "metadata": {}, "source": [ "You can compute several individual expectations on the same sites by supplying a list (they are computed in a single contraction):" @@ -743,7 +743,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "86452eee-1016-46fc-ab48-eef68cbbbdc7", + "id": "9c16ca45-3d57-44f8-87fd-468639f46ee4", "metadata": {}, "outputs": [ { @@ -770,7 +770,7 @@ }, { "cell_type": "markdown", - "id": "a111262e-4d41-4914-9ad2-3db14cbe8c05", + "id": "b6a4e492-ae83-4adb-9777-50983a1cdd92", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -800,7 +800,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "eb58f4dd-a5d9-44b4-a50a-a8fcb010b35f", + "id": "6f8b7a46-103f-4dcb-9d04-eafb995d3653", "metadata": {}, "outputs": [ { @@ -823,7 +823,7 @@ }, { "cell_type": "markdown", - "id": "e1b3bf8a-f827-40a0-b1c1-68ea845bd51d", + "id": "de9818d4-d8ea-4c2c-b5c9-3cb66ca86116", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -858,7 +858,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "d082168d-6bf3-4efc-a297-a6c1a2e676fb", + "id": "5a9db911-0e0e-4455-8178-e86c92f48a2d", "metadata": {}, "outputs": [ { @@ -881,7 +881,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "4dd589bc-976f-46d9-a65d-164ec3df1cff", + "id": "2b1fe1ba-e83f-422e-848d-b2d5abbfbd3f", "metadata": {}, "outputs": [ { @@ -901,7 +901,7 @@ }, { "cell_type": "markdown", - "id": "3e0aea44-1484-46d3-9e73-b3b7d4211678", + "id": "96df885d-510c-4052-bbcd-7a8ece61af04", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -968,7 +968,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "da48f88a-5cdb-4b5f-bc02-511ba920350b", + "id": "c4f50cba-1a87-48b6-a073-d578e3a90a45", "metadata": {}, "outputs": [ { @@ -995,7 +995,7 @@ }, { "cell_type": "markdown", - "id": "442e97aa-3316-48cc-843a-f621ba9607fc", + "id": "8c76939e-35d2-4fca-b75e-bceeaf914cc1", "metadata": {}, "source": [ "### Generate unbiased samples using the *'gate-by-gate'* method\n", @@ -1014,7 +1014,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "4c2b79b7-4be4-4a0b-bc46-a17fd5122fe5", + "id": "5bb08c38-9b0c-41b8-ab34-ff9aa24c5c97", "metadata": {}, "outputs": [ { @@ -1041,7 +1041,7 @@ }, { "cell_type": "markdown", - "id": "a2cefa76-2121-4436-ae44-760ed8371cbb", + "id": "f13d33df-62c0-41a7-93ba-82aec81ed19d", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1080,7 +1080,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "9a03b9f0-9223-44d1-8f06-6b83f29c4833", + "id": "bd141fe5-5cf4-452f-8de8-552855d86f72", "metadata": {}, "outputs": [ { @@ -1107,7 +1107,7 @@ }, { "cell_type": "markdown", - "id": "0cb43e41-62cd-4a16-99f6-7f3a48ea260b", + "id": "9f290c32-c62e-4fd7-85bd-c0b9f48ef7a0", "metadata": {}, "source": [ "Five of these qubits will now be sampled completely randomly." @@ -1115,7 +1115,7 @@ }, { "cell_type": "markdown", - "id": "42d6c608-571e-4de9-a889-f0b26024574d", + "id": "94dd7bef-873f-46f4-b262-169af327ef81", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1149,7 +1149,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "a9211ff2-99ff-4731-b0a4-d03baa0b577a", + "id": "1b4f3d41-b677-4f43-928e-a773253f708d", "metadata": {}, "outputs": [ { @@ -1175,7 +1175,7 @@ }, { "cell_type": "markdown", - "id": "f9e5e4f7-d071-48cd-af5e-8c7a37991fc6", + "id": "37b4a489-2570-49a2-8549-2f2ede26993e", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1191,6 +1191,7 @@ "- [`Circuit.partial_trace_rehearse`](quimb.tensor.circuit.Circuit.partial_trace_rehearse)\n", "- [`Circuit.compute_marginal_rehearse`](quimb.tensor.circuit.Circuit.compute_marginal_rehearse)\n", "- [`Circuit.sample_rehearse`](quimb.tensor.circuit.Circuit.sample_rehearse)\n", + "- [`Circuit.sample_gate_by_gate_rehearse`](quimb.tensor.circuit.Circuit.sample_gate_by_gate_rehearse)\n", "- [`Circuit.sample_chaotic_rehearse`](quimb.tensor.circuit.Circuit.sample_chaotic_rehearse)\n", "- [`Circuit.to_dense_rehearse`](quimb.tensor.circuit.Circuit.to_dense_rehearse)\n", "\n", @@ -1203,7 +1204,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "9407796a-c065-423c-aab9-2f7e1b8ff802", + "id": "cb933e4d-e142-4b23-945c-f7c9e4891342", "metadata": {}, "outputs": [ { @@ -1227,7 +1228,7 @@ }, { "cell_type": "markdown", - "id": "556c0538-87cf-41b5-adee-52744b27fc81", + "id": "32b9223e-b760-421f-b81b-3d0a1762a03f", "metadata": {}, "source": [ "Upper twenties is the limit for standard (~10GB) amounts of RAM." @@ -1236,7 +1237,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "7c85fdf4-e27e-413e-8baf-e9bf54f70707", + "id": "62671971-3f3e-4a61-bf44-1b26ba01ac81", "metadata": {}, "outputs": [ { @@ -1262,7 +1263,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "c250012c-4aaf-4941-955f-f061131e2f66", + "id": "58298e3d-1af0-45af-a707-0d4c693b9e7e", "metadata": {}, "outputs": [ { @@ -1283,7 +1284,7 @@ }, { "cell_type": "markdown", - "id": "3b436cc9-b5be-47f0-b313-f7d89098197b", + "id": "b011f251-aae9-4e78-93a6-0177b0dbc730", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1299,7 +1300,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "e486939e-b454-43a3-a33a-4b525136b3e6", + "id": "53c2ae2d-5282-48da-9cb7-b7d4ea77c178", "metadata": {}, "outputs": [ { @@ -1321,7 +1322,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "d00259ba-fd44-4f8b-9ee7-1cd511682fa4", + "id": "cf341e1c-38b4-4ccc-8a05-1b7432aa9b0d", "metadata": {}, "outputs": [ { @@ -1341,7 +1342,7 @@ }, { "cell_type": "markdown", - "id": "f88238f6-b8c4-4d0c-a8be-89df869ad89b", + "id": "2197b25d-9e17-452a-af25-c71ee7063a03", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1373,7 +1374,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "c88842ca-cef7-44c0-9eb3-7dd40fcee81d", + "id": "d9d6b097-35ba-4470-ba10-003fa45c2e7c", "metadata": {}, "outputs": [ { @@ -1405,13 +1406,13 @@ { "cell_type": "code", "execution_count": 29, - "id": "33ed1894-2893-45b5-8689-7ad53de24b97", + "id": "da2012fa-9fef-44fa-ad7d-eb9c9a67b3fb", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -1429,7 +1430,7 @@ }, { "cell_type": "markdown", - "id": "39da90f9-7ff8-48cf-84c7-3966938702c7", + "id": "c4190c50-a516-4b1f-ac6b-646674a796f8", "metadata": {}, "source": [ "We can plot the effect this has as selecting only these, $| \\psi \\rangle \\rightarrow | \\psi_{\\bar{q}} \\rangle$, on the norm with the following:" @@ -1438,13 +1439,13 @@ { "cell_type": "code", "execution_count": 30, - "id": "45b768b1-a628-416e-8b68-9902eeea5678", + "id": "96824aec-a768-4a0a-ba7b-ae8b5f2f547a", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -1466,7 +1467,7 @@ }, { "cell_type": "markdown", - "id": "fd51af69-d97e-4f91-96b1-860599f538d5", + "id": "3715bbcb-47a9-4c65-b701-dc5e26e25d05", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1479,7 +1480,7 @@ }, { "cell_type": "markdown", - "id": "9ddd9271-b6a3-46ed-bb54-49e580d4956e", + "id": "ff4c9f02-d48b-49b9-bbb5-8d152f78f952", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1508,13 +1509,13 @@ { "cell_type": "code", "execution_count": 31, - "id": "0c1e9d19-a569-4173-a5db-31afc4aa47ea", + "id": "86c8d9f4-b86b-4700-b0ed-009a0a568985", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -1538,7 +1539,7 @@ }, { "cell_type": "markdown", - "id": "b98b3875-32bd-425d-9abd-d9f90b456023", + "id": "1ad19a0c-6c04-4fa9-a959-923e172577e1", "metadata": {}, "source": [ "You can see that only 3+ dimensional tensors remain. Now if we turn on all the\n", @@ -1548,13 +1549,13 @@ { "cell_type": "code", "execution_count": 32, - "id": "ded99851-111e-4c92-be2d-4d051bef0673", + "id": "188da222-de38-45bc-a01d-50471de07a78", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -1578,7 +1579,7 @@ }, { "cell_type": "markdown", - "id": "9595e91f-d8fb-4c84-bc22-23d7fdec1b46", + "id": "2d668dd5-6780-4d54-bf8f-91b2ef915ebb", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -1599,7 +1600,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "12df083a-eea4-44f8-84c6-c18a66191e35", + "id": "16ae7e1c-994b-49c3-9aff-42859dfb46e9", "metadata": {}, "outputs": [ { @@ -1834,7 +1835,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "14972121-8a36-4345-b4fc-1263fc57f2c5", + "id": "899cfb2b-f7f4-41bf-b4f0-a5cd3918b951", "metadata": {}, "outputs": [ { @@ -2095,7 +2096,7 @@ }, { "cell_type": "markdown", - "id": "482fff96-b375-421b-81b7-ddbdc75ce84c", + "id": "e157ea5c-602a-4350-a4fc-5d90017ce765", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2108,7 +2109,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "87a331aa-9186-49a8-bd7d-d51ca4f78c10", + "id": "8e171bd1-0679-4879-9f75-6223c3bff6ce", "metadata": {}, "outputs": [ { @@ -2129,7 +2130,7 @@ }, { "cell_type": "markdown", - "id": "38655ea1-568c-46df-aae5-b960816b7c4d", + "id": "9fed741d-8ce0-48f3-8e6d-a5528fb55fb8", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2146,7 +2147,7 @@ "different types of values:\n", "\n", "> 1. A string, specifiying a [cotengra](https://cotengra.readthedocs.io/) registered path optimizer.\n", - "> 2. A custom `cotengra.HyperOptimizer` instance\n", + "> 2. A custom [`cotengra.HyperOptimizer`](cotengra.HyperOptimizer) instance\n", "> 2. A custom `opt_einsum.PathOptimizer` instance\n", "> 3. An explicit path - a sequence of pairs of ints - likely found from a previous rehearsal, for example.\n", "\n", @@ -2165,7 +2166,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "3c59eda8-d59f-4af4-9225-86ec3b3bdc82", + "id": "c4a292f2-14b4-40bf-be1f-81b057d529a6", "metadata": {}, "outputs": [], "source": [ @@ -2176,12 +2177,12 @@ }, { "cell_type": "markdown", - "id": "6461bb03-5a06-4f21-bee8-44d8887fbc3d", + "id": "5433605f-5aa0-42c9-9fd6-d2b3b9ee1683", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ - "### An `cotengra` preset\n", + "### A `cotengra` preset\n", "\n", "First we use the fast but low quality `'greedy'` preset:" ] @@ -2189,7 +2190,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "d078cd57-7712-4ab5-bd59-e17b3780771e", + "id": "794bf5cf-299a-4aa8-b97c-f7efdf83dd7a", "metadata": {}, "outputs": [ { @@ -2211,7 +2212,7 @@ }, { "cell_type": "markdown", - "id": "64bdd81b-6ba2-4e11-8d86-44070722b7b5", + "id": "48cc5518-5289-4921-81b3-11fa46e2e248", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2225,7 +2226,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "f902f982-3ffd-4e5d-a338-7477e85c9b8d", + "id": "bc8642ae-7627-4090-a4fb-ba556025d9fe", "metadata": {}, "outputs": [ { @@ -2243,7 +2244,7 @@ }, { "cell_type": "markdown", - "id": "72e8ad06-9e3c-4dcf-a224-c43ad707f1ca", + "id": "53caeed7-76eb-46dd-bc03-2542a38e7885", "metadata": {}, "source": [ "We can compare this to just performing the main contraction:" @@ -2252,7 +2253,7 @@ { "cell_type": "code", "execution_count": 39, - "id": "e8136022-0b6f-487d-b90d-fe2b91dd325d", + "id": "2ea2c78c-4bd0-4676-be55-70b32f8d10b2", "metadata": {}, "outputs": [ { @@ -2270,7 +2271,7 @@ }, { "cell_type": "markdown", - "id": "19c8c68c-1557-470c-a02e-b1ceb97bf2f5", + "id": "38526510-c40e-4f20-9430-3aefa6725365", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2288,7 +2289,7 @@ { "cell_type": "code", "execution_count": 40, - "id": "1a3ebbdc-43fd-4f95-a9df-5f3b4fd94603", + "id": "c355a3f1-062e-454d-be58-d8299ae9d846", "metadata": {}, "outputs": [ { @@ -2315,7 +2316,7 @@ }, { "cell_type": "markdown", - "id": "12c44773-7681-471a-a846-d12417070fdd", + "id": "04f721cb-9afe-4a62-b668-410b43044cbe", "metadata": {}, "source": [ "We see it has found a much better path than `'greedy'`, which is not so surprising.\n", @@ -2327,7 +2328,7 @@ { "cell_type": "code", "execution_count": 41, - "id": "12ec5f53-aaac-4731-b9b7-154be4ff91a6", + "id": "b490e220-012d-45a7-875e-80ef1a793c36", "metadata": {}, "outputs": [ { @@ -2348,7 +2349,7 @@ { "cell_type": "code", "execution_count": 42, - "id": "db73fe14-5df4-4fd3-b2d1-f299e6822bcd", + "id": "cb659f49-7d2b-4bdb-89ba-aa10453298a8", "metadata": {}, "outputs": [ { @@ -2366,7 +2367,7 @@ }, { "cell_type": "markdown", - "id": "192ca463-0d59-4076-a45a-ef7068f9925b", + "id": "0793283d-6a95-4310-a247-a3f749b68ce2", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2400,7 +2401,7 @@ { "cell_type": "code", "execution_count": 43, - "id": "f0ed7460-3834-4bdf-9d9e-46a652c17171", + "id": "357d665c-7248-4408-b89f-5efecd03e4a9", "metadata": {}, "outputs": [ { @@ -2440,7 +2441,7 @@ }, { "cell_type": "markdown", - "id": "d5355777-74b8-4993-8afd-9ae419c377bc", + "id": "b600436e-fc4a-49ae-a11a-aca616c361af", "metadata": {}, "source": [ "We can see even for this small contraction it has improved on the `RandomGreedy` path cost.\n", @@ -2452,7 +2453,7 @@ { "cell_type": "code", "execution_count": 44, - "id": "dd970b4e-0bfc-497c-9d57-a579776c284b", + "id": "f88f43e7-d17e-4784-ae2b-27a179144805", "metadata": {}, "outputs": [ { @@ -2470,7 +2471,7 @@ }, { "cell_type": "markdown", - "id": "dabf0797-3a9e-49ed-b86d-f95d0e03dd37", + "id": "7ef2ec50-3db8-4178-a7b5-6ec7adf86aa6", "metadata": {}, "source": [ "Again, since the main contraction is very small, we don't see any real improvement." @@ -2478,7 +2479,7 @@ }, { "cell_type": "markdown", - "id": "a10637f4-8148-4869-aa3f-eacec3b77c2c", + "id": "58b45f82-5ba8-48b5-b3c9-6dd56a7ae625", "metadata": {}, "source": [ "`cotengra` also has a `ContractionTree` object for manipulating and visualizing\n", @@ -2488,13 +2489,13 @@ { "cell_type": "code", "execution_count": 46, - "id": "a1c1fd3e-7be2-4070-91e8-790e5143b0cf", + "id": "6175b264-9abe-4112-bfff-3c4d7c01fd3d", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -2522,7 +2523,7 @@ }, { "cell_type": "markdown", - "id": "fc6cd08a-45d3-489a-b2ae-ba824fcec1fc", + "id": "617dffa5-fdd4-412a-aed6-2e55ca0b36ae", "metadata": {}, "source": [ "Here the, grey network at the bottom is the TN to be contracted, and the tree\n", @@ -2535,13 +2536,13 @@ { "cell_type": "code", "execution_count": 45, - "id": "e97ec69a-7ea5-4108-a28d-c7bd91e48e41", + "id": "6005efec-747a-4b8f-9075-16014e5f9946", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "" + "" ], "text/plain": [ "
" @@ -2569,7 +2570,7 @@ }, { "cell_type": "markdown", - "id": "457270d8-6c28-44bb-8323-bb260a701998", + "id": "a6623df9-ad8f-45be-a42a-1a328ce0da9e", "metadata": { "raw_mimetype": "text/restructuredtext" }, @@ -2583,7 +2584,7 @@ { "cell_type": "code", "execution_count": 47, - "id": "42a00fb4-5733-403b-949a-017f85618295", + "id": "37feee8f-f1ce-4823-b7a8-8ddbca0da395", "metadata": {}, "outputs": [ { @@ -2603,7 +2604,7 @@ }, { "cell_type": "markdown", - "id": "f347fa46-918a-49cd-9be8-5f8c5a51b89d", + "id": "7bcca2e3-c63e-49e9-be2f-8ea96f2299c4", "metadata": {}, "source": [ "When it comes to the actual contraction however, where large tensors will appear, it can be advantageous to\n", @@ -2621,7 +2622,7 @@ }, { "cell_type": "markdown", - "id": "d161043c-ae26-4d50-a7e4-de2f85326b6c", + "id": "ca55de97-8b0d-4ec3-9c6a-2ebba9979715", "metadata": {}, "source": [ "Sampling is an excellent candidate for GPU acceleration as the same geometry TNs\n", @@ -2632,7 +2633,7 @@ { "cell_type": "code", "execution_count": 48, - "id": "d99ed8d4-b137-4ce1-b401-6991e95d78b8", + "id": "7279cd0b-426e-4431-a866-d0ab8ce35fae", "metadata": {}, "outputs": [ { @@ -2659,7 +2660,7 @@ }, { "cell_type": "markdown", - "id": "865bc679-0bdf-4f58-8dab-ec17853093b2", + "id": "b18b3052-d369-4df1-af5e-4afc50f8a39c", "metadata": { "raw_mimetype": "text/restructuredtext" }, diff --git a/docs/tensor-optimization.ipynb b/docs/tensor-optimization.ipynb index 89f6429d..5eae6ec9 100644 --- a/docs/tensor-optimization.ipynb +++ b/docs/tensor-optimization.ipynb @@ -3,6 +3,7 @@ { "attachments": {}, "cell_type": "markdown", + "id": "c54f04b8-37a4-44bb-8969-9d8370ab98f2", "metadata": {}, "source": [ "(tensor-network-optimization)=\n", @@ -30,6 +31,7 @@ { "cell_type": "code", "execution_count": 3, + "id": "652da1b7-7dba-4a4f-8675-892474d4eb09", "metadata": {}, "outputs": [], "source": [ @@ -41,6 +43,7 @@ { "cell_type": "code", "execution_count": 4, + "id": "61708615-4fed-46b8-b9c8-b286acc3fb4b", "metadata": {}, "outputs": [], "source": [ @@ -57,6 +60,7 @@ }, { "cell_type": "markdown", + "id": "1d70582b-a30e-4457-a924-d4bfca4b94c9", "metadata": {}, "source": [ "Next we define our `norm_fn`, which here just normalizes the MPS, and our `loss_fn`, which computes the energy of the Heisenberg model by exactly contracting an MPS-MPO-MPS overlap." @@ -65,6 +69,7 @@ { "cell_type": "code", "execution_count": 5, + "id": "c57c1f96-fbad-4c47-b8e4-afec61590e9f", "metadata": {}, "outputs": [], "source": [ @@ -78,11 +83,12 @@ "def loss_fn(psi, ham):\n", " b, h, k = qtn.tensor_network_align(psi.H, ham, psi)\n", " energy_tn = b | h | k\n", - " return energy_tn ^ ...\n" + " return energy_tn ^ ..." ] }, { "cell_type": "markdown", + "id": "90ccfc56-7641-4053-8324-9f9ae791879f", "metadata": {}, "source": [ "We can check the initial loss value with:" @@ -91,6 +97,7 @@ { "cell_type": "code", "execution_count": 6, + "id": "9535c227-0f2d-42db-9cf6-e545bf03366d", "metadata": {}, "outputs": [ { @@ -110,6 +117,7 @@ }, { "cell_type": "markdown", + "id": "0f09042b-fa87-4ad9-91fc-e09ef2cf696a", "metadata": {}, "source": [ "Next we supply these to a [`TNOptimizer`](quimb.tensor.optimize.TNOptimizer) object. Since we have an extra tensor object `ham` that is needed to compute the loss, but should not be optimized, we pass it in `loss_constants`, that allows it to be converted to the correct backend etc." @@ -118,6 +126,7 @@ { "cell_type": "code", "execution_count": 7, + "id": "090eb325-5af4-418f-979b-bfb539893f4e", "metadata": {}, "outputs": [ { @@ -152,6 +161,7 @@ }, { "cell_type": "markdown", + "id": "3668f6cf-d946-4728-b325-792101d977e3", "metadata": {}, "source": [ "```{hint}\n", @@ -164,6 +174,7 @@ { "cell_type": "code", "execution_count": 8, + "id": "97f603f1-b5d7-4d38-b639-4fde48bc3e6b", "metadata": {}, "outputs": [ { @@ -180,6 +191,7 @@ }, { "cell_type": "markdown", + "id": "a24d9191-a1aa-40ff-8b2a-96aba4258d7b", "metadata": {}, "source": [ "There is a simple [`tnopt.plot`](quimb.tensor.optimize.TNOptimizer.plot) method to visualize the loss progress (note by default the first 20 points are shown on a linear plot, the rest on a log plot):" @@ -188,2558 +200,13 @@ { "cell_type": "code", "execution_count": 9, + "id": "6ac927f4-4c1a-46d6-9ab0-a255a95b8068", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - 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" @@ -2767,6 +234,7 @@ }, { "cell_type": "markdown", + "id": "23879a36-5819-43b5-b7f1-1be6c5ad3b0f", "metadata": {}, "source": [ "We can check the returned `psi_opt` optimized target indeed matches loss:" @@ -2775,6 +243,7 @@ { "cell_type": "code", "execution_count": 10, + "id": "429c3953-ee06-4ce1-9b89-b79468daf879", "metadata": {}, "outputs": [ { @@ -2794,14 +263,16 @@ }, { "cell_type": "markdown", + "id": "56d72083-c659-41a3-b8d0-554ba2a7fbf8", "metadata": {}, "source": [ - "Note this TN (which can be retrieved from [`tnopt.get_tn_opt`](quimb.tensor.optimize.tnopt.TNOptimizer.get_tn_opt)) is a copy of the original target TN, with the optimized parameters set. It has also been passed through `norm_fn` so is in normalized/projected form, and converted back to `numpy` backed arrays." + "Note this TN (which can be retrieved from [`tnopt.get_tn_opt`](quimb.tensor.optimize.TNOptimizer.get_tn_opt)) is a copy of the original target TN, with the optimized parameters set. It has also been passed through `norm_fn` so is in normalized/projected form, and converted back to `numpy` backed arrays." ] }, { "attachments": {}, "cell_type": "markdown", + "id": "f67f1e14-bf72-4424-8906-69409478a5b8", "metadata": {}, "source": [ "## Using tags to opt in, opt out or group tensors\n", @@ -2820,6 +291,7 @@ { "cell_type": "code", "execution_count": 11, + "id": "d988cc62-c9f5-43f9-89a2-e627eb581f80", "metadata": {}, "outputs": [ { @@ -2853,2474 +325,13 @@ { "cell_type": "code", "execution_count": 12, + "id": "0eba2cc5-fad6-486c-b247-af717f8b6696", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2024-05-15T11:35:50.988689\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.4, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - 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" @@ -5339,6 +350,7 @@ { "cell_type": "code", "execution_count": 13, + "id": "83427e03-ba0c-494a-98d3-169c70ae692f", "metadata": {}, "outputs": [ { @@ -5370,6 +382,7 @@ }, { "cell_type": "markdown", + "id": "b96c6021-7ce6-4724-8770-f36f5779da8c", "metadata": {}, "source": [ "You can see the dramatic reduction in the number of parameters to optimize, from 32,768 to 1,024. The optimization proceeds in the same way as before, but now the tensors A and B are constrained to be the same." @@ -5378,6 +391,7 @@ { "cell_type": "code", "execution_count": 14, + "id": "2ef1de72-8919-419d-bec4-0d80eaa86b3d", "metadata": {}, "outputs": [ { @@ -5415,2500 +429,13 @@ { "cell_type": "code", "execution_count": 15, + "id": "3575733a-5ba8-4d52-b635-84c034012191", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2024-05-15T11:36:33.317694\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.4, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - 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" @@ -42998,6 +499,7 @@ }, { "cell_type": "markdown", + "id": "b1ad5a90-1fe3-4f50-b20b-b30d80ae62fb", "metadata": {}, "source": [ "(optimizing-circuits)=\n", @@ -43009,6 +511,7 @@ { "cell_type": "code", "execution_count": 17, + "id": "cb6a603e-ba03-4857-8af5-4f5cdd67ca15", "metadata": {}, "outputs": [ { @@ -43050,6 +553,7 @@ }, { "cell_type": "markdown", + "id": "82c25e32-7692-4aeb-9835-c1c18a5f1268", "metadata": {}, "source": [ "The returned circuit now has the optimized parameters set." @@ -43058,6 +562,7 @@ { "cell_type": "code", "execution_count": 18, + "id": "cd68221f-f40e-4149-be06-eecb788c358f", "metadata": {}, "outputs": [ { @@ -43082,6 +587,7 @@ { "cell_type": "code", "execution_count": 19, + "id": "509e0fe8-8264-4c3f-8bec-32a01ec0fe52", "metadata": {}, "outputs": [ { @@ -43101,6 +607,7 @@ }, { "cell_type": "markdown", + "id": "6ddfef05-04fa-46e3-85c5-080c6a5f7095", "metadata": {}, "source": [ "But the initial state and constant gates have not been changed, and becuase the parametrized tensors are manifestly unitary, it is always normalized.\n", @@ -43114,11 +621,12 @@ }, { "cell_type": "markdown", + "id": "df7cfd7a-33d6-4e0a-ad05-9a541ed8fbee", "metadata": {}, "source": [ "## Optimizing `PTensor` objects\n", "\n", - "The circuit object paramterized gates behind the scenes use a 'paramterized' tensor object, [`PTensor`](quimb.tensor.tensor.PTensor), which holds a [`PArray`](quimb.tensor.array_opts.PArray). This is a generalization of `Tensor` whose data is defined by a function and some parameters (kind of like a local `norm_fn` that is always applied). You can use these directly for even finer control.\n", + "The circuit object paramterized gates behind the scenes use a 'paramterized' tensor object, [`PTensor`](quimb.tensor.PTensor), which holds a [`PArray`](quimb.tensor.array_ops.PArray). This is a generalization of `Tensor` whose data is defined by a function and some parameters (kind of like a local `norm_fn` that is always applied). You can use these directly for even finer control.\n", "\n", "Here we show a very roundabout way of trying to diagonalize a non-symmetric matrix using two orthogonal matrices `U` and `V`." ] @@ -43126,415 +634,13 @@ { "cell_type": "code", "execution_count": 20, + "id": "bc0fbd42-63d3-4832-8848-c80861ee36db", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2024-05-15T11:36:34.917866\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.4, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -43548,1498 +654,7 @@ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2024-05-15T11:36:34.976897\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.4, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -45093,6 +708,7 @@ { "cell_type": "code", "execution_count": 21, + "id": "33201a4e-4d04-4c9a-975f-02c42ffbc05b", "metadata": {}, "outputs": [], "source": [ @@ -45105,6 +721,7 @@ }, { "cell_type": "markdown", + "id": "469826ed-a3cc-4f6b-9665-9bc82a665b5f", "metadata": {}, "source": [ "We'll also here make use of automatic hessian-vector product computation by some backends (e.g. `jax`), which is can be used with second order optimization methods like `Newton-CG`." @@ -45113,6 +730,7 @@ { "cell_type": "code", "execution_count": 22, + "id": "7bfcc1df-0fcf-4f2f-9456-38e0617528ec", "metadata": {}, "outputs": [], "source": [ @@ -45128,6 +746,7 @@ { "cell_type": "code", "execution_count": 23, + "id": "c639c11f-f59c-467d-b40d-8559d6378ade", "metadata": {}, "outputs": [ { @@ -45145,2027 +764,13 @@ { "cell_type": "code", "execution_count": 24, + "id": "7f732bc6-e98d-42f0-b7f9-1ec208d8824e", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - 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" @@ -47194,6 +799,7 @@ { "cell_type": "code", "execution_count": 25, + "id": "c9569835-803f-4800-9a96-1e11b698041c", "metadata": {}, "outputs": [ { @@ -47238,6 +844,7 @@ { "cell_type": "code", "execution_count": 26, + "id": "30945e98-807a-4b7f-89d8-f86be0b8fff1", "metadata": {}, "outputs": [ { @@ -47259,1511 +866,13 @@ { "cell_type": "code", "execution_count": 27, + "id": "d2494938-0019-4bf9-ba68-a98aaa7d05c9", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2024-05-15T11:37:07.818372\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.8.4, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" + "" ], "text/plain": [ "
" @@ -48793,7 +902,7 @@ ], "metadata": { "kernelspec": { - "display_name": "jax", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -48807,9 +916,8 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.9" + "version": "3" }, - "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "6132c5c0a7d26b7c311caf7f55df83b87474b489906668e67e2d71a3b39ab16a"