From 5743fa5918529cc5bb41d56084a15fc31fa3ba14 Mon Sep 17 00:00:00 2001 From: Josh Izaac Date: Mon, 14 Nov 2022 20:33:23 -0500 Subject: [PATCH 01/52] Development branch --- requirements.txt | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/requirements.txt b/requirements.txt index 31a775730e..d67ec324af 100644 --- a/requirements.txt +++ b/requirements.txt @@ -17,12 +17,12 @@ cirq-core==0.14.1 cirq-pasqal==0.14.1 openfermionpyscf==0.5 # required by 2 tutorials: tutorial_quantum_chemistry and tutorial_adaptive_circuits and tutorial_diffable_shadows pennylane-lightning -pennylane==0.27.0 -pennylane-sf==0.20.1 -pennylane-cirq==0.27.0 -pennylane-qiskit==0.27.0 +git+https://github.com/PennyLaneAI/pennylane.git +git+https://github.com/PennyLaneAI/pennylane-sf.git +git+https://github.com/PennyLaneAI/pennylane-cirq.git +git+https://github.com/PennyLaneAI/pennylane-qiskit.git qulacs==0.1.10.1 -pennylane-qulacs==0.24.0 +git+https://github.com/PennyLaneAI/pennylane-qulacs.git scikit-learn==0.23.2 docutils==0.16 markupsafe==2.0.1 From a8284e3b65c67b02774a8469ad495ec16e66cd98 Mon Sep 17 00:00:00 2001 From: Rashid N H M <95639609+rashidnhm@users.noreply.github.com> Date: Mon, 19 Dec 2022 15:47:32 -0500 Subject: [PATCH 02/52] Bumped requirement package versions (#667) * Bumped jax versions * Updated neural-tangents --- requirements.txt | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/requirements.txt b/requirements.txt index ecdab7aae1..c0cf2b1ec2 100644 --- a/requirements.txt +++ b/requirements.txt @@ -42,9 +42,9 @@ matplotlib==3.5.3 noisyopt==0.2.2 Jinja2==2.11.3 pyyaml==5.4.1 -jax==0.3.15 -jaxlib==0.3.15 -neural-tangents==0.6.0 +jax==0.4.1 +jaxlib==0.4.1 +neural-tangents==0.6.1 flamingpy>=0.10.1b1 plotly>=4.5.0 kahypar==1.1.7 From ccfcf459a29f6b38d520a8f8469aef4acccf8e3b Mon Sep 17 00:00:00 2001 From: Rashid N H M <95639609+rashidnhm@users.noreply.github.com> Date: Wed, 21 Dec 2022 11:54:52 -0500 Subject: [PATCH 03/52] Merge dev in master following v0.28.0 release of PennyLane (#671) (#672) * Development branch * Bumped requirement package versions (#667) * Bumped jax versions * Updated neural-tangents * Apply suggestions from code review Co-authored-by: Josh Izaac Co-authored-by: GitHub Nightly Merge Action Co-authored-by: Rashid N H M <95639609+rashidnhm@users.noreply.github.com> Co-authored-by: Jay Soni Co-authored-by: Josh Izaac Co-authored-by: GitHub Nightly Merge Action From 13fce68c3cdf0b4c4ef22664f4047278dd9f1c57 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Thu, 26 Jan 2023 19:04:16 +0100 Subject: [PATCH 04/52] add demo, v0.1 --- demonstrations/tutorial_here_comes_the_sun.py | 369 ++++++++++++++++++ 1 file changed, 369 insertions(+) create mode 100644 demonstrations/tutorial_here_comes_the_sun.py diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py new file mode 100644 index 0000000000..61d74bcc8e --- /dev/null +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -0,0 +1,369 @@ +r""" + +Here comes the SU(N) +==================== + +.. meta:: + :property="og:description": Learn about multi-parameter gates for optimization + + :property="og:image": https://pennylane.ai/qml/_images/SpecialUnitary.png + +.. related:: + TODO + + +*Author: David Wierichs — Posted: xx.* + +If you looked at variational quantum algorithms before, maybe -- and in my experience +very likely -- you wondered why the chosen circuit ansatz looks the way it does. +In some cases there are good reasons for the choice of ansatz. For example one could +demand the circuit to be hardware compatible with respect to the used gate set and +the qubit connectivity, or one could set up a structure and parametrization that +preserves particular symmetries. Other features that impact the choice of circuit +include trainability and expressibility. +While a number of best practices for ansatz design have been developed, +a lot is still unknown about the connection between circuit structures and the +resulting features. Therefore intuition often is at play as well, and a circuit +ansatz reported in the literature might just have turned out +to work particularly well for a given problem, or might fall into a "standard" +category of circuits. +One approach to make an ansatz generic and avoid arbitrary choices in +the circuit design is to perform the most general operations locally on a few qubits +and to chose only the sets of qubits the operations are applied to. + +.. figure:: ../demonstrations/givens_rotations/lego-circuit.svg + :align: center + :width: 50% + + +In this tutorial, you will learn about a particular quantum gate which can act like +*any* gate on the corresponding qubits by chosing the parameters accordingly. +We will then look at a custom differentiation rule for this gate, construct +a simple ansatz, and use it in a toy minimization problem. + +The special unitary group SU(N) and its Lie algebra +--------------------------------------------------- + +The gate we will look at is given by a specific parametrization of the special +unitary group :math:`SU(N)`, where :math:`N=2^n` is the Hilbert space dimension of the gate +for :math:`n` qubits. Mathematically, the group can be defined as the set of operators +or matrices that can be inverted by taking their adjoint (unitarity) and that have +determinant :math:`1`. All gates acting on :math:`n` qubits are elements of :math:`SU(N)` +up to a global phase. + +The group :math:`SU(N)` is a Lie group, and its associated Lie algebra via the exponential +map is :math:`\mathfrak{su}(N)`. For our purposes it will be sufficient to look at a matrix +representation of the algebra and we may write + +.. math:: + + \mathfrak{su}(N) = \{\Omega \in \mathbb{C}^{N\times N}| \Omega^\dagger=-\Omega, \Tr{\Omega}=0\}. + +We will use so-called canonical coordinates for the algebra which are given by the coefficients +of an algebra element :math:`\Omega` in the Pauli basis (except for the identity, which does not +have trace zero, and with a prefactor :math:`i`): + +.. math:: + + \Omega &= \sum_{m=1}^d \theta_m G_m\\ + \theta_m &\in \mathbb{R}\\ + G_m &\in \mathcal{P}^{n} = i \left\{I,X,Y,Z\right\}^n \setminus \{i I^n\}. + +This yields a parametrization for the group :math:`SU(N)` as well, and the ``qml.SpecialUnitary`` gate +we will use is given by + +.. math:: + + U(\bm{\theta}) = \exp\left\{\sum_{m=1}^d \theta_m G_m \right\}. + +The number of coordinates and of Pauli words in :math:`\mathcal{P}^n` is :math:`d=4^n-1`. +Therefore, this will be the number of parameters a single ``qml.SpecialUnitary`` gate acting on +:math:`n` qubits will take. This means that it takes just ``3`` parameters for a single qubit and +a moderate number of ``15`` parameters for two qubits, but already requires ``63`` parameters for +three qubits. + +Obtaining the gradient +---------------------- + +In variational quantum algorithms, we typically use the circuit to prepare a quantum state and +then we measure some observable :math:`H`. The resulting real-valued output is considered as +cost function :math:`C` to be minimized. If we want to use gradient-based optimization for this task, +we need a method to compute the gradient :math:`\nabla C` in addition to the cost function itself. +As derived in the publication [#wiersema]_, this is possible on quantum hardware as long +as the :math:`SU(N)` gate itself can be implemented. +We will not go through the entire derivation, but note the following key points: + + #. The gradient with respect to all :math:`d` parameters of an :math:`SU(N)` gate can be computed + using :math:`2d` auxiliary circuits. Each of the circuits contains one additional operation + compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation angles + :math:`\pm\frac{\pi}{2}. + #. The computed gradient is not an approximative technique but allows for exact gradient + computation on simulators. On quantum hardware, this leads to unbiased gradient estimators. + #. With ``qml.SpecialUnitary`` and its gradient we effectively implement a so-called + Riemannian gradient flow on the respective qubits. + +The implementation in PennyLane takes care of creating the additional circuits and evaluating +them, together with adequate post-processing into the gradient :math:`\nabla C`. + + +.. figure:: ../demonstrations/givens_rotations/orbitals+states.png + :align: center + :width: 50% + +Comparing ansatz structures +--------------------------- + +We discussed above that there are many circuit architectures available and that choosing +a suitable ansatz can be difficult. Here we will compare a simple ansatz based on +the ``qml.SpecialUnitary`` gate discussed above to other approaches that fully parametrize +the special unitary group for the respective number of qubits. +In particular, we will compare ``qml.SpecialUnitary`` to standard decompositions from the +literature that parametrize :math:`SU(N)` with elementary gates, and to a sequence +of Pauli rotation gates that also allows to create any special unitary. +Let us start by defining the decompositions for one and two qubits, which are optimal in +their gate count, but not unique. For the two-qubit case we choose the decomposition +from [#vatan]_. The Pauli rotation sequence is available in PennyLane +via ``qml.ArbitraryUnitary`` and we will not need to implement it manually. + + +- explain that there are decompositions for arbitrary unitaries and introduce the generic decomposiiton for n=2 as well as the `ArbitraryUnitary` structure +- introduce one or two other ansatze with actually fewer parameters. + +Code block: code up all mentioned ansatze. + +- introduce random Hamiltonian and experiment settings + +code block: random Hamiltonian and settings + +- discuss optimization: GradientDescent? Adam? LBFGSB? + +code block: function that runs optimization + run optimization + +- announce result + +code block: energy curves + +- can we discuss anything about optimization curves? +""" + +import pennylane as qml +import numpy as np + +import time + +start = time.process_time() +def one_qubit_decomp(params, wires): + """Implement an arbitrary SU(2) gate on one qubit + using the decomposition into RZ, RY, RZ.""" + qml.Rot(*params, wires) + +def two_qubit_decomp(params, wires): + """Implement an arbitrary SU(4) gate on two qubits + using the decomposition from Theorem 5 in + https://arxiv.org/pdf/quant-ph/0308006.pdf""" + i, j = wires + # Single U(2) parameterization on qubit 1 + qml.Rot(*params[:3], wires=i) + # Single U(2) parameterization on qubit 2 + qml.Rot(*params[3:6], wires=j) + # CNOT with control on qubit 2 + qml.CNOT(wires=[j, i]) + # Rz and Ry gate + qml.RZ(params[6], wires=i) + qml.RY(params[7], wires=j) + # CNOT with control on qubit 1 + qml.CNOT(wires=[i, j]) + # Ry gate on qubit 2 + qml.RY(params[8], wires=j) + # CNOT with control on qubit 1 + qml.CNOT(wires=[j, i]) + # Single U(2) parameterization on qubit 1 + qml.Rot(*params[9:12], wires=i) + # Single U(2) parameterization on qubit 2 + qml.Rot(*params[12:15], wires=j) + +def decomp(params, wires): + """Implement an arbitrary SU(2**n) gate on n qubits.""" + if len(wires)==1: + one_qubit_decomp(params, wires) + elif len(wires)==2: + two_qubit_decomp(params, wires) + else: + raise ValueError("Not implemented for more than 2 wires") + +operations = { + "decomposition": two_qubit_decomp, + "PauliRot sequence": qml.ArbitraryUnitary, + "SU(N) gate": qml.SpecialUnitary, +} + +############################################################################## +# Now that we have the templates for the composition approach in place, we construct a toy problem to +# solve with the ansatze. We will sample a random Hamiltonian in the Pauli basis with independent +# coefficients that follow a normal distribution: +# +# .. math:: +# +# H = \sum_{m=1}^d h_m G_m, h_m\sim \mathcal{N}(0,1) +# +# We will work with 6 qubits overall. + +num_wires = 6 +wires = list(range(num_wires)) +np.random.seed(62213) + +coefficients = np.random.randn(4**num_wires - 1) +basis = qml.ops.qubit.special_unitary.pauli_basis(num_wires) # Create the Pauli basis of su(N) +H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) +E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy +print(E_min) +H = qml.Hermitian(H, wires=wires) + +############################################################################## +# Using the toy problem Hamiltonian and the three ansatze for :math:`SU(N)` operations +# from above, we create a circuit template that applies these operations in a brickwall-like +# architecture with ``num_blocks=2`` blocks and each operation acting on ``num_opwires=2`` qubits. +# For this we define a ``QNode``: + +num_blocks = 2 +num_opwires = 2 +d = num_opwires**4 - 1 # d = 15 for two-qubit operations +dev = qml.device("default.qubit", wires=num_wires) +# two blocks with two layers each. Each layer contains three operations with d parameters each +param_shape = (num_blocks, num_opwires, num_wires//num_opwires, d) + +def circuit(params, operation=None): + """Apply an operation in a brickwall-like pattern to a qubit register and measure H. + Parameters are assumed to have the dimensions number of blocks, number of + wires per operation, number of operations per layer, and number of parameters + per operation, in that order. + """ + for params_block in params: + for i, params_layer in enumerate(params_block): + for j, params_op in enumerate(params_layer): + opwires = [w%num_wires for w in range(num_opwires*j+i, num_opwires*(j+1)+i)] + operation(params_op, opwires) + return qml.expval(H) + +qnode = qml.QNode(circuit, dev, interface="jax") + +############################################################################## +# We can now proceed to preparing the optimization task using this circuit +# and an optimization routine of our choice. For simplicity, we run a vanilla gradient +# descent optimizer with fixed learning rate for 100 steps. As autodifferentiation +# interface we make use of JAX. + +import jax +jax.config.update("jax_enable_x64", True) + +learning_rate = 1e-3 +num_steps = 100 +init_params = jax.numpy.zeros(param_shape) +grad_fn = jax.jit(jax.jacobian(qnode), static_argnums=1) +qnode = jax.jit(qnode, static_argnums=1) +optimizer = qml.GradientDescentOptimizer(learning_rate) + +############################################################################## +# With this configuration, let's run the optimization! + +energies = {} +for name, operation in operations.items(): + params = init_params.copy() + energy = [] + for step in range(num_steps): + params, cost = optimizer.step_and_cost(qnode, params, grad_fn=grad_fn, operation=operation) + energy.append(cost) # Store energy value + if step%10==0: # Report current energy + print(cost) + + energy.append(qnode(params, operation)) # Final energy value + energies[name] = energy + +############################################################################## +# So, did it work? Judging from the intermediate energy values it seems that the optimization +# outcomes differ notably. But let's take a look at the relative error in energy across the +# optimization process. + +import matplotlib.pyplot as plt + +fig, ax = plt.subplots(1, 1) +for name in operations.keys(): + error = (energies[name] - E_min) / abs(E_min) + ax.plot(list(range(num_steps+1)), error, label=name) + +ax.set( + xlabel="Iteration", + ylabel="Relative error", + yscale="log", +) +ax.legend() +#plt.show() + +############################################################################## +# We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` +# than for the other two general unitaries, while using the same number of parameters. This +# means that we found a particularly well-trainable parametrization of the unitaries that +# allows to reduce the energy of the prepared quantum state more easily. +# +# Finally, let's look at the optimization behaviour with a shot-based device. After all, +# PennyLane supports the differentiation of all three two-qubit operations using the +# parameter-shift rule, enabling training on quantum hardware and shot-based simulators. + +dev_shots = qml.device("default.qubit", wires=num_wires, shots=2000) +qnode_shots = qml.QNode(circuit, dev_shots, interface="jax") +grad_fn = jax.jacobian(qnode_shots) +optimizer = qml.GradientDescentOptimizer(learning_rate) + +energies_shots = {} +for name, operation in operations.items(): + params = init_params.copy() + energy = [] + for step in range(num_steps): + params, cost = optimizer.step_and_cost(qnode_shots, params, grad_fn=grad_fn, operation=operation) + energy.append(cost) # Store energy value + if step%10==0: # Report current energy + print(cost) + + energy.append(qnode_shots(params, operation)) # Final energy value + energies_shots[name] = energy + +end = time.process_time() +print(end-start) +fig, ax = plt.subplots(1, 1) +for name in operations.keys(): + error = (energies[name] - E_min) / abs(E_min) + ax.plot(list(range(num_steps+1)), error, label=name) + +ax.set( + xlabel="Iteration", + ylabel="Relative error", + yscale="log", +) +ax.legend() +plt.show() + +# +# References +# ---------- +# +# .. [#vatan] +# +# Farrokh Vatan and Colin Williams, +# "Optimal Quantum Circuits for General Two-Qubit Gates", arXiv:quant-ph/0308006, (2003). +# +# .. [#barkoutsos] +# +# P. KL. Barkoutsos, Panagiotis, et al., "Quantum algorithms for electronic structure +# calculations: Particle-hole Hamiltonian and optimized wave-function expansions", Physical +# Review A 98(2), 022322, (2018). +# +# .. [#arrazola] +# +# J. M. Arrazola, O. Di Matteo, N. Quesada, S. Jahangiri, A. Delgado, N. Killoran, "Universal +# quantum circuits for quantum chemistry", arXiv:2106.13839, (2021) +# +# +# About the author +# ---------------- +# .. include:: ../_static/authors/david_wierichs.txt From 6cfaa34d75b6481cd67d0ec327db60089d52341d Mon Sep 17 00:00:00 2001 From: dwierichs Date: Fri, 27 Jan 2023 17:41:52 +0100 Subject: [PATCH 05/52] update demo with shots optimization --- demonstrations/tutorial_here_comes_the_sun.py | 74 +++++++++++++------ 1 file changed, 50 insertions(+), 24 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index 61d74bcc8e..f2346ba726 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -153,11 +153,14 @@ import time start = time.process_time() + + def one_qubit_decomp(params, wires): """Implement an arbitrary SU(2) gate on one qubit using the decomposition into RZ, RY, RZ.""" qml.Rot(*params, wires) + def two_qubit_decomp(params, wires): """Implement an arbitrary SU(4) gate on two qubits using the decomposition from Theorem 5 in @@ -183,15 +186,17 @@ def two_qubit_decomp(params, wires): # Single U(2) parameterization on qubit 2 qml.Rot(*params[12:15], wires=j) + def decomp(params, wires): """Implement an arbitrary SU(2**n) gate on n qubits.""" - if len(wires)==1: + if len(wires) == 1: one_qubit_decomp(params, wires) - elif len(wires)==2: + elif len(wires) == 2: two_qubit_decomp(params, wires) else: raise ValueError("Not implemented for more than 2 wires") + operations = { "decomposition": two_qubit_decomp, "PauliRot sequence": qml.ArbitraryUnitary, @@ -206,7 +211,7 @@ def decomp(params, wires): # .. math:: # # H = \sum_{m=1}^d h_m G_m, h_m\sim \mathcal{N}(0,1) -# +# # We will work with 6 qubits overall. num_wires = 6 @@ -214,9 +219,9 @@ def decomp(params, wires): np.random.seed(62213) coefficients = np.random.randn(4**num_wires - 1) -basis = qml.ops.qubit.special_unitary.pauli_basis(num_wires) # Create the Pauli basis of su(N) +basis = qml.ops.qubit.special_unitary.pauli_basis(num_wires) # Create the Pauli basis of su(N) H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) -E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy +E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy print(E_min) H = qml.Hermitian(H, wires=wires) @@ -228,10 +233,11 @@ def decomp(params, wires): num_blocks = 2 num_opwires = 2 -d = num_opwires**4 - 1 # d = 15 for two-qubit operations +d = num_opwires**4 - 1 # d = 15 for two-qubit operations dev = qml.device("default.qubit", wires=num_wires) # two blocks with two layers each. Each layer contains three operations with d parameters each -param_shape = (num_blocks, num_opwires, num_wires//num_opwires, d) +param_shape = (num_blocks, num_opwires, num_wires // num_opwires, d) + def circuit(params, operation=None): """Apply an operation in a brickwall-like pattern to a qubit register and measure H. @@ -242,19 +248,23 @@ def circuit(params, operation=None): for params_block in params: for i, params_layer in enumerate(params_block): for j, params_op in enumerate(params_layer): - opwires = [w%num_wires for w in range(num_opwires*j+i, num_opwires*(j+1)+i)] + opwires = [ + w % num_wires for w in range(num_opwires * j + i, num_opwires * (j + 1) + i) + ] operation(params_op, opwires) return qml.expval(H) + qnode = qml.QNode(circuit, dev, interface="jax") ############################################################################## # We can now proceed to preparing the optimization task using this circuit # and an optimization routine of our choice. For simplicity, we run a vanilla gradient -# descent optimizer with fixed learning rate for 100 steps. As autodifferentiation +# descent optimizer with fixed learning rate for 100 steps. As autodifferentiation # interface we make use of JAX. import jax + jax.config.update("jax_enable_x64", True) learning_rate = 1e-3 @@ -271,13 +281,13 @@ def circuit(params, operation=None): for name, operation in operations.items(): params = init_params.copy() energy = [] - for step in range(num_steps): + for step in range(1): params, cost = optimizer.step_and_cost(qnode, params, grad_fn=grad_fn, operation=operation) - energy.append(cost) # Store energy value - if step%10==0: # Report current energy + energy.append(cost) # Store energy value + if step % 10 == 0: # Report current energy print(cost) - energy.append(qnode(params, operation)) # Final energy value + energy.append(qnode(params, operation)) # Final energy value energies[name] = energy ############################################################################## @@ -290,7 +300,7 @@ def circuit(params, operation=None): fig, ax = plt.subplots(1, 1) for name in operations.keys(): error = (energies[name] - E_min) / abs(E_min) - ax.plot(list(range(num_steps+1)), error, label=name) + ax.plot(list(range(len(error))), error, label=name) ax.set( xlabel="Iteration", @@ -298,17 +308,31 @@ def circuit(params, operation=None): yscale="log", ) ax.legend() -#plt.show() +# plt.show() ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` -# than for the other two general unitaries, while using the same number of parameters. This +# than for the other two general unitaries, while using the same number of parameters. This # means that we found a particularly well-trainable parametrization of the unitaries that # allows to reduce the energy of the prepared quantum state more easily. # # Finally, let's look at the optimization behaviour with a shot-based device. After all, -# PennyLane supports the differentiation of all three two-qubit operations using the +# PennyLane supports the differentiation of all three two-qubit operations using the # parameter-shift rule, enabling training on quantum hardware and shot-based simulators. +# +# TODO: REVERT num_wires reduction once we can JIT the decomposition of SpecialUnitary? + +num_wires = 2 +wires = list(range(num_wires)) +np.random.seed(62213) + +coefficients = np.random.randn(4**num_wires - 1) +basis = qml.ops.qubit.special_unitary.pauli_basis(num_wires) # Create the Pauli basis of su(N) +H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) +E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy +H = qml.Hermitian(H, wires=wires) +param_shape = (num_blocks, num_opwires, num_wires // num_opwires, d) +init_params = jax.numpy.zeros(param_shape) dev_shots = qml.device("default.qubit", wires=num_wires, shots=2000) qnode_shots = qml.QNode(circuit, dev_shots, interface="jax") @@ -320,20 +344,22 @@ def circuit(params, operation=None): params = init_params.copy() energy = [] for step in range(num_steps): - params, cost = optimizer.step_and_cost(qnode_shots, params, grad_fn=grad_fn, operation=operation) - energy.append(cost) # Store energy value - if step%10==0: # Report current energy + params, cost = optimizer.step_and_cost( + qnode_shots, params, grad_fn=grad_fn, operation=operation + ) + energy.append(cost) # Store energy value + if step % 10 == 0: # Report current energy print(cost) - energy.append(qnode_shots(params, operation)) # Final energy value + energy.append(qnode_shots(params, operation)) # Final energy value energies_shots[name] = energy end = time.process_time() -print(end-start) +print(end - start) fig, ax = plt.subplots(1, 1) for name in operations.keys(): - error = (energies[name] - E_min) / abs(E_min) - ax.plot(list(range(num_steps+1)), error, label=name) + error = (energies_shots[name] - E_min) / abs(E_min) + ax.plot(list(range(len(error))), error, label=name) ax.set( xlabel="Iteration", From ea82b2fe85a4d6d564111b07207ca9ab5db16278 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 31 Jan 2023 18:10:55 +0100 Subject: [PATCH 06/52] improvements to text, remove notes, draw circuit. --- demonstrations/tutorial_here_comes_the_sun.py | 208 ++++++++---------- 1 file changed, 96 insertions(+), 112 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index f2346ba726..eec8a99113 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -1,10 +1,10 @@ r""" -Here comes the SU(N) -==================== +Here comes the SU(N): multivariate quantum gates and gradients +============================================================== .. meta:: - :property="og:description": Learn about multi-parameter gates for optimization + :property="og:description": Learn about multivariate quantum gates for optimization :property="og:image": https://pennylane.ai/qml/_images/SpecialUnitary.png @@ -14,32 +14,40 @@ *Author: David Wierichs — Posted: xx.* -If you looked at variational quantum algorithms before, maybe -- and in my experience -very likely -- you wondered why the chosen circuit ansatz looks the way it does. -In some cases there are good reasons for the choice of ansatz. For example one could -demand the circuit to be hardware compatible with respect to the used gate set and -the qubit connectivity, or one could set up a structure and parametrization that -preserves particular symmetries. Other features that impact the choice of circuit -include trainability and expressibility. +Variational quantum algorithms have been promoted to be useful for many applications. +When designing such an algorithm, a central task is to choose the quantum circuit ansatz, +which provides a parametrization of quantum states. In the course of the algorithm, +the corresponding parameters are then optimized in order to reduce some cost function. +The ansatz can have a big impact on the quantum states that can be found (expressivity) +within the algorithm and on the optimization behaviour. It also strongly affects the +cost of executing the algorithm on quantum hardware, and the strength of the noise +which enters the computation. Finally, the application itself often influences, or +even fixes, the choice of ansatz. + +.. figure:: ../demonstrations/here_comes_the_sun/pennylane_guy_scratching_head.png + :align: center + :width: 50% + While a number of best practices for ansatz design have been developed, a lot is still unknown about the connection between circuit structures and the -resulting features. Therefore intuition often is at play as well, and a circuit -ansatz reported in the literature might just have turned out +resulting properties. Therefore circuit design often is based on intuition or heuristics +as well, and an ansatz reported in the literature might just have turned out to work particularly well for a given problem, or might fall into a "standard" category of circuits. One approach to make an ansatz generic and avoid arbitrary choices in -the circuit design is to perform the most general operations locally on a few qubits -and to chose only the sets of qubits the operations are applied to. +the circuit design is to perform the most general operations *locally* on a few qubits +and to reduce the design question to choosing the sets of qubits such operations are +applied to and their order. -.. figure:: ../demonstrations/givens_rotations/lego-circuit.svg +.. figure:: ../demonstrations/here_comes_the_sun/sun_fabric.png :align: center :width: 50% - In this tutorial, you will learn about a particular quantum gate which can act like *any* gate on the corresponding qubits by chosing the parameters accordingly. We will then look at a custom differentiation rule for this gate, construct a simple ansatz, and use it in a toy minimization problem. +Let's start with a brief math intro (no really, just a little bit). The special unitary group SU(N) and its Lie algebra --------------------------------------------------- @@ -47,66 +55,71 @@ The gate we will look at is given by a specific parametrization of the special unitary group :math:`SU(N)`, where :math:`N=2^n` is the Hilbert space dimension of the gate for :math:`n` qubits. Mathematically, the group can be defined as the set of operators -or matrices that can be inverted by taking their adjoint (unitarity) and that have +(or matrices) that can be inverted by taking their adjoint and that have determinant :math:`1`. All gates acting on :math:`n` qubits are elements of :math:`SU(N)` up to a global phase. -The group :math:`SU(N)` is a Lie group, and its associated Lie algebra via the exponential -map is :math:`\mathfrak{su}(N)`. For our purposes it will be sufficient to look at a matrix -representation of the algebra and we may write +The group :math:`SU(N)` is a Lie group, and its associated Lie algebra +is :math:`\mathfrak{su}(N)`. For our purposes it will be sufficient to look at a matrix +representation of the algebra and we may define it as .. math:: \mathfrak{su}(N) = \{\Omega \in \mathbb{C}^{N\times N}| \Omega^\dagger=-\Omega, \Tr{\Omega}=0\}. -We will use so-called canonical coordinates for the algebra which are given by the coefficients -of an algebra element :math:`\Omega` in the Pauli basis (except for the identity, which does not -have trace zero, and with a prefactor :math:`i`): +We will use so-called canonical coordinates for the algebra which are simply the coefficients +of an algebra element :math:`\Omega` in the Pauli basis: .. math:: \Omega &= \sum_{m=1}^d \theta_m G_m\\ \theta_m &\in \mathbb{R}\\ - G_m &\in \mathcal{P}^{n} = i \left\{I,X,Y,Z\right\}^n \setminus \{i I^n\}. + G_m &\in \mathcal{P}^{(n)} = i \left\{I,X,Y,Z\right\}^n \setminus \{i I^n\}. -This yields a parametrization for the group :math:`SU(N)` as well, and the ``qml.SpecialUnitary`` gate -we will use is given by +As you can see, we actually use the Pauli basis words with a prefactor :math:`i`, and +we skip the identity, because it does not have a vanishing trace. +We can use the canonical coordinates of the algebra to express a group element +:math:`SU(N)` as well and the ``qml.SpecialUnitary`` gate we will use is defined as .. math:: U(\bm{\theta}) = \exp\left\{\sum_{m=1}^d \theta_m G_m \right\}. -The number of coordinates and of Pauli words in :math:`\mathcal{P}^n` is :math:`d=4^n-1`. +The number of coordinates and of Pauli words in :math:`\mathcal{P}^{(n)}` is :math:`d=4^n-1`. Therefore, this will be the number of parameters a single ``qml.SpecialUnitary`` gate acting on -:math:`n` qubits will take. This means that it takes just ``3`` parameters for a single qubit and -a moderate number of ``15`` parameters for two qubits, but already requires ``63`` parameters for +:math:`n` qubits will take. For example, it takes just three parameters for a single qubit and +a moderate number of 15 parameters for two qubits, but already requires 63 parameters for three qubits. Obtaining the gradient ---------------------- In variational quantum algorithms, we typically use the circuit to prepare a quantum state and -then we measure some observable :math:`H`. The resulting real-valued output is considered as -cost function :math:`C` to be minimized. If we want to use gradient-based optimization for this task, -we need a method to compute the gradient :math:`\nabla C` in addition to the cost function itself. -As derived in the publication [#wiersema]_, this is possible on quantum hardware as long -as the :math:`SU(N)` gate itself can be implemented. +then we measure some observable :math:`H`. The resulting real-valued output is considered to be the +cost function :math:`C` that should be minimized. If we want to use gradient-based optimization for +this task, we need a method to compute the gradient :math:`\nabla C` in addition to the cost +function itself. As derived in the publication [#wiersema]_, this is possible on quantum hardware +as long as the :math:`SU(N)` gate itself can be implemented. We will not go through the entire derivation, but note the following key points: - #. The gradient with respect to all :math:`d` parameters of an :math:`SU(N)` gate can be computed - using :math:`2d` auxiliary circuits. Each of the circuits contains one additional operation - compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation angles - :math:`\pm\frac{\pi}{2}. - #. The computed gradient is not an approximative technique but allows for exact gradient - computation on simulators. On quantum hardware, this leads to unbiased gradient estimators. + #. The gradient with respect to all :math:`d` parameters of an :math:`SU(N)` gate can be + computed using :math:`2d` auxiliary circuits. Each of the circuits contains one additional + operation compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation + angles :math:`\pm\frac{\pi}{2}. Not that these Pauli rotations act on up to :math:`n` + qubits. + #. This differentiation uses automatic differentiation during compilation and postprocessing, + which becomes expensive for large :math:`n`, but the differentiation is quantum + hardware-compatible. + #. The computed gradient is not an approximative technique but allows for an exact computation + of the gradient on simulators. On quantum hardware, this leads to unbiased gradient + estimators. #. With ``qml.SpecialUnitary`` and its gradient we effectively implement a so-called - Riemannian gradient flow on the respective qubits. + Riemannian gradient flow on the qubits the gate acts on. The implementation in PennyLane takes care of creating the additional circuits and evaluating them, together with adequate post-processing into the gradient :math:`\nabla C`. - -.. figure:: ../demonstrations/givens_rotations/orbitals+states.png +.. figure:: ../demonstrations/here_comes_the_sun/mathy_riemannian_flow_pic.png :align: center :width: 50% @@ -114,37 +127,19 @@ --------------------------- We discussed above that there are many circuit architectures available and that choosing -a suitable ansatz can be difficult. Here we will compare a simple ansatz based on -the ``qml.SpecialUnitary`` gate discussed above to other approaches that fully parametrize -the special unitary group for the respective number of qubits. +a suitable ansatz is important but can be difficult. Here we will compare a simple ansatz +based on the ``qml.SpecialUnitary`` gate discussed above to other approaches that fully +parametrize the special unitary group for the respective number of qubits. In particular, we will compare ``qml.SpecialUnitary`` to standard decompositions from the -literature that parametrize :math:`SU(N)` with elementary gates, and to a sequence +literature that parametrize :math:`SU(N)` with elementary gates, as well as to a sequence of Pauli rotation gates that also allows to create any special unitary. -Let us start by defining the decompositions for one and two qubits, which are optimal in -their gate count, but not unique. For the two-qubit case we choose the decomposition -from [#vatan]_. The Pauli rotation sequence is available in PennyLane -via ``qml.ArbitraryUnitary`` and we will not need to implement it manually. - +Let us start by defining the decomposition of a two-qubit unitary. +We choose the decomposition, which is optimal but not unique, from [#vatan]_. +The Pauli rotation sequence is available in PennyLane +via ``qml.ArbitraryUnitary`` and we will not need to implement it ourselves. -- explain that there are decompositions for arbitrary unitaries and introduce the generic decomposiiton for n=2 as well as the `ArbitraryUnitary` structure - introduce one or two other ansatze with actually fewer parameters. -Code block: code up all mentioned ansatze. - -- introduce random Hamiltonian and experiment settings - -code block: random Hamiltonian and settings - -- discuss optimization: GradientDescent? Adam? LBFGSB? - -code block: function that runs optimization - run optimization - -- announce result - -code block: energy curves - -- can we discuss anything about optimization curves? """ import pennylane as qml @@ -154,13 +149,6 @@ start = time.process_time() - -def one_qubit_decomp(params, wires): - """Implement an arbitrary SU(2) gate on one qubit - using the decomposition into RZ, RY, RZ.""" - qml.Rot(*params, wires) - - def two_qubit_decomp(params, wires): """Implement an arbitrary SU(4) gate on two qubits using the decomposition from Theorem 5 in @@ -186,7 +174,6 @@ def two_qubit_decomp(params, wires): # Single U(2) parameterization on qubit 2 qml.Rot(*params[12:15], wires=j) - def decomp(params, wires): """Implement an arbitrary SU(2**n) gate on n qubits.""" if len(wires) == 1: @@ -196,30 +183,30 @@ def decomp(params, wires): else: raise ValueError("Not implemented for more than 2 wires") - operations = { - "decomposition": two_qubit_decomp, + "Decomposition": two_qubit_decomp, "PauliRot sequence": qml.ArbitraryUnitary, "SU(N) gate": qml.SpecialUnitary, } ############################################################################## -# Now that we have the templates for the composition approach in place, we construct a toy problem to -# solve with the ansatze. We will sample a random Hamiltonian in the Pauli basis with independent -# coefficients that follow a normal distribution: +# Now that we have the templates for the composition approach in place, we construct a toy +# problem to solve using the ansatze. We will sample a random Hamiltonian in the Pauli basis +# (this time without the prefactor :math:`i`) +# with independent coefficients that follow a normal distribution: # # .. math:: # -# H = \sum_{m=1}^d h_m G_m, h_m\sim \mathcal{N}(0,1) +# H = \sum_{m=1}^d h_m G_m,\quad h_m\sim \mathcal{N}(0,1) # -# We will work with 6 qubits overall. +# We will work with six qubits. num_wires = 6 wires = list(range(num_wires)) np.random.seed(62213) coefficients = np.random.randn(4**num_wires - 1) -basis = qml.ops.qubit.special_unitary.pauli_basis(num_wires) # Create the Pauli basis of su(N) +basis = qml.ops.qubit.special_unitary.pauli_basis_matrices(num_wires) # Create the Pauli basis H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy print(E_min) @@ -228,40 +215,42 @@ def decomp(params, wires): ############################################################################## # Using the toy problem Hamiltonian and the three ansatze for :math:`SU(N)` operations # from above, we create a circuit template that applies these operations in a brickwall-like -# architecture with ``num_blocks=2`` blocks and each operation acting on ``num_opwires=2`` qubits. +# architecture with ``num_blocks=2`` blocks and each operation acting on ``num_wires_op=2`` qubits. # For this we define a ``QNode``: num_blocks = 2 -num_opwires = 2 -d = num_opwires**4 - 1 # d = 15 for two-qubit operations +num_wires_op = 2 +d = num_wires_op**4 - 1 # d = 15 for two-qubit operations dev = qml.device("default.qubit", wires=num_wires) # two blocks with two layers each. Each layer contains three operations with d parameters each -param_shape = (num_blocks, num_opwires, num_wires // num_opwires, d) +param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) +init_params = np.zeros(param_shape) def circuit(params, operation=None): """Apply an operation in a brickwall-like pattern to a qubit register and measure H. - Parameters are assumed to have the dimensions number of blocks, number of + Parameters are assumed to have the dimensions (number of blocks, number of wires per operation, number of operations per layer, and number of parameters - per operation, in that order. + per operation), in that order. """ for params_block in params: for i, params_layer in enumerate(params_block): for j, params_op in enumerate(params_layer): - opwires = [ - w % num_wires for w in range(num_opwires * j + i, num_opwires * (j + 1) + i) + wires_op = [ + w % num_wires for w in range(num_wires_op * j + i, num_wires_op * (j + 1) + i) ] - operation(params_op, opwires) + operation(params_op, wires_op) return qml.expval(H) qnode = qml.QNode(circuit, dev, interface="jax") +print(qml.draw(qnode)(init_params, qml.SpecialUnitary)) ############################################################################## # We can now proceed to preparing the optimization task using this circuit # and an optimization routine of our choice. For simplicity, we run a vanilla gradient -# descent optimizer with fixed learning rate for 100 steps. As autodifferentiation -# interface we make use of JAX. +# descent optimizer with fixed learning rate for 100 steps. For auto-differentiation +# we make use of JAX. import jax @@ -269,7 +258,7 @@ def circuit(params, operation=None): learning_rate = 1e-3 num_steps = 100 -init_params = jax.numpy.zeros(param_shape) +init_params = jax.numpy.array(init_params) grad_fn = jax.jit(jax.jacobian(qnode), static_argnums=1) qnode = jax.jit(qnode, static_argnums=1) optimizer = qml.GradientDescentOptimizer(learning_rate) @@ -281,7 +270,7 @@ def circuit(params, operation=None): for name, operation in operations.items(): params = init_params.copy() energy = [] - for step in range(1): + for step in range(num_steps): params, cost = optimizer.step_and_cost(qnode, params, grad_fn=grad_fn, operation=operation) energy.append(cost) # Store energy value if step % 10 == 0: # Report current energy @@ -308,7 +297,7 @@ def circuit(params, operation=None): yscale="log", ) ax.legend() -# plt.show() +plt.show() ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` @@ -317,8 +306,9 @@ def circuit(params, operation=None): # allows to reduce the energy of the prepared quantum state more easily. # # Finally, let's look at the optimization behaviour with a shot-based device. After all, -# PennyLane supports the differentiation of all three two-qubit operations using the -# parameter-shift rule, enabling training on quantum hardware and shot-based simulators. +# PennyLane supports the differentiation of all three two-qubit operations we are using +# by applying the parameter-shift rule, enabling training on quantum hardware +# and shot-based simulators. # # TODO: REVERT num_wires reduction once we can JIT the decomposition of SpecialUnitary? @@ -327,11 +317,11 @@ def circuit(params, operation=None): np.random.seed(62213) coefficients = np.random.randn(4**num_wires - 1) -basis = qml.ops.qubit.special_unitary.pauli_basis(num_wires) # Create the Pauli basis of su(N) +basis = qml.ops.qubit.special_unitary.pauli_basis_matrices(num_wires) # Create the Pauli basis H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy H = qml.Hermitian(H, wires=wires) -param_shape = (num_blocks, num_opwires, num_wires // num_opwires, d) +param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) init_params = jax.numpy.zeros(param_shape) dev_shots = qml.device("default.qubit", wires=num_wires, shots=2000) @@ -378,16 +368,10 @@ def circuit(params, operation=None): # Farrokh Vatan and Colin Williams, # "Optimal Quantum Circuits for General Two-Qubit Gates", arXiv:quant-ph/0308006, (2003). # -# .. [#barkoutsos] -# -# P. KL. Barkoutsos, Panagiotis, et al., "Quantum algorithms for electronic structure -# calculations: Particle-hole Hamiltonian and optimized wave-function expansions", Physical -# Review A 98(2), 022322, (2018). -# -# .. [#arrazola] +# .. [#wiersema] # -# J. M. Arrazola, O. Di Matteo, N. Quesada, S. Jahangiri, A. Delgado, N. Killoran, "Universal -# quantum circuits for quantum chemistry", arXiv:2106.13839, (2021) +# R. Wiersema, D. Lewis, J. F. Carrasquilla, and N. Killoran, +# in preparation, arXiv:23xx.xxxxx, (2023) # # # About the author From 303ea0b1677211bb00ffaa60149859f30683985b Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 31 Jan 2023 18:11:10 +0100 Subject: [PATCH 07/52] black --- demonstrations/tutorial_here_comes_the_sun.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index eec8a99113..dd29f0a334 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -149,6 +149,7 @@ start = time.process_time() + def two_qubit_decomp(params, wires): """Implement an arbitrary SU(4) gate on two qubits using the decomposition from Theorem 5 in @@ -174,6 +175,7 @@ def two_qubit_decomp(params, wires): # Single U(2) parameterization on qubit 2 qml.Rot(*params[12:15], wires=j) + def decomp(params, wires): """Implement an arbitrary SU(2**n) gate on n qubits.""" if len(wires) == 1: @@ -183,6 +185,7 @@ def decomp(params, wires): else: raise ValueError("Not implemented for more than 2 wires") + operations = { "Decomposition": two_qubit_decomp, "PauliRot sequence": qml.ArbitraryUnitary, From 254788cb2f2f4f7047da44d6a9e4fde2a2eb81c3 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Thu, 2 Feb 2023 12:41:53 +0100 Subject: [PATCH 08/52] remove qml.optimize dependency --- demonstrations/tutorial_here_comes_the_sun.py | 16 +++++++--------- 1 file changed, 7 insertions(+), 9 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index dd29f0a334..6ddbdd2705 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -252,19 +252,18 @@ def circuit(params, operation=None): ############################################################################## # We can now proceed to preparing the optimization task using this circuit # and an optimization routine of our choice. For simplicity, we run a vanilla gradient -# descent optimizer with fixed learning rate for 100 steps. For auto-differentiation +# descent optimization with fixed learning rate for 200 steps. For auto-differentiation # we make use of JAX. import jax jax.config.update("jax_enable_x64", True) -learning_rate = 1e-3 -num_steps = 100 +learning_rate = 5e-4 +num_steps = 200 init_params = jax.numpy.array(init_params) grad_fn = jax.jit(jax.jacobian(qnode), static_argnums=1) qnode = jax.jit(qnode, static_argnums=1) -optimizer = qml.GradientDescentOptimizer(learning_rate) ############################################################################## # With this configuration, let's run the optimization! @@ -274,7 +273,8 @@ def circuit(params, operation=None): params = init_params.copy() energy = [] for step in range(num_steps): - params, cost = optimizer.step_and_cost(qnode, params, grad_fn=grad_fn, operation=operation) + cost = qnode(params, operation) + params = params - learning_rate * grad_fn(params, operation) energy.append(cost) # Store energy value if step % 10 == 0: # Report current energy print(cost) @@ -330,16 +330,14 @@ def circuit(params, operation=None): dev_shots = qml.device("default.qubit", wires=num_wires, shots=2000) qnode_shots = qml.QNode(circuit, dev_shots, interface="jax") grad_fn = jax.jacobian(qnode_shots) -optimizer = qml.GradientDescentOptimizer(learning_rate) energies_shots = {} for name, operation in operations.items(): params = init_params.copy() energy = [] for step in range(num_steps): - params, cost = optimizer.step_and_cost( - qnode_shots, params, grad_fn=grad_fn, operation=operation - ) + cost = qnode(params, operation) + params = params - learning_rate * grad_fn(params, operation) energy.append(cost) # Store energy value if step % 10 == 0: # Report current energy print(cost) From bb9f4ac3ee89c73f82b9b9e6d0348b2e54bb3c72 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Fri, 17 Feb 2023 11:26:29 +0100 Subject: [PATCH 09/52] update, improve code --- demonstrations/tutorial_here_comes_the_sun.py | 132 +++++++++--------- demos_optimization.rst | 10 +- 2 files changed, 77 insertions(+), 65 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index 6ddbdd2705..b65be42584 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -9,35 +9,42 @@ :property="og:image": https://pennylane.ai/qml/_images/SpecialUnitary.png .. related:: - TODO + tutorial_vqe A brief overview of VQE + tutorial_general_parshift General parameter-shift rules for quantum gradients + tutorial_unitary_designs Unitary designs and their uses in quantum computing -*Author: David Wierichs — Posted: xx.* + +*Author: David Wierichs — Posted: xx March 2023.* Variational quantum algorithms have been promoted to be useful for many applications. When designing such an algorithm, a central task is to choose the quantum circuit ansatz, -which provides a parametrization of quantum states. In the course of the algorithm, -the corresponding parameters are then optimized in order to reduce some cost function. -The ansatz can have a big impact on the quantum states that can be found (expressivity) -within the algorithm and on the optimization behaviour. It also strongly affects the +which provides a parametrization of quantum states. In the course of the variational algorithm, +the circuit parameters are then optimized in order to minimize some cost function. +The choice of the ansatz can have a big impact on the quantum states that can be found +by the algorithm (expressivity), and on the optimization behaviour (trainability). +It also typically affects the cost of executing the algorithm on quantum hardware, and the strength of the noise -which enters the computation. Finally, the application itself often influences, or -even fixes, the choice of ansatz. +that enters the computation. Finally, the application itself often influences, or +even fixes, the choice of ansatz, leading to constraints in the ansatz design. -.. figure:: ../demonstrations/here_comes_the_sun/pennylane_guy_scratching_head.png +.. figure:: ../demonstrations/here_comes_the_sun/pennylane_guy_scratching_head_in_front_of_circuits.png :align: center :width: 50% While a number of best practices for ansatz design have been developed, a lot is still unknown about the connection between circuit structures and the -resulting properties. Therefore circuit design often is based on intuition or heuristics -as well, and an ansatz reported in the literature might just have turned out +resulting properties. Therefore, circuit design often also is based on intuition or heuristics, +and an ansatz reported in the literature might just have turned out to work particularly well for a given problem, or might fall into a "standard" category of circuits. -One approach to make an ansatz generic and avoid arbitrary choices in -the circuit design is to perform the most general operations *locally* on a few qubits -and to reduce the design question to choosing the sets of qubits such operations are -applied to and their order. + +It is therefore interesting to construct circuit ansätze that are rather generic and +avoid arbitrary choices in the design that bias the optimization landscape. +On such approach is to perform the most general operations *locally* on a few qubits +and to reduce the design question to choosing the sets of qubits these operations are +applied to (as well as their order). In particular, we consider a general local operation +that comes without any preferred optimization direction. .. figure:: ../demonstrations/here_comes_the_sun/sun_fabric.png :align: center @@ -47,19 +54,20 @@ *any* gate on the corresponding qubits by chosing the parameters accordingly. We will then look at a custom differentiation rule for this gate, construct a simple ansatz, and use it in a toy minimization problem. + Let's start with a brief math intro (no really, just a little bit). The special unitary group SU(N) and its Lie algebra --------------------------------------------------- The gate we will look at is given by a specific parametrization of the special -unitary group :math:`SU(N)`, where :math:`N=2^n` is the Hilbert space dimension of the gate +unitary group :math:`\mathrm{SU}(N)`, where :math:`N=2^n` is the Hilbert space dimension of the gate for :math:`n` qubits. Mathematically, the group can be defined as the set of operators (or matrices) that can be inverted by taking their adjoint and that have -determinant :math:`1`. All gates acting on :math:`n` qubits are elements of :math:`SU(N)` +determinant :math:`1`. All gates acting on :math:`n` qubits are elements of :math:`\mathrm{SU}(N)` up to a global phase. -The group :math:`SU(N)` is a Lie group, and its associated Lie algebra +The group :math:`\mathrm{SU}(N)` is a Lie group, and its associated Lie algebra is :math:`\mathfrak{su}(N)`. For our purposes it will be sufficient to look at a matrix representation of the algebra and we may define it as @@ -79,7 +87,7 @@ As you can see, we actually use the Pauli basis words with a prefactor :math:`i`, and we skip the identity, because it does not have a vanishing trace. We can use the canonical coordinates of the algebra to express a group element -:math:`SU(N)` as well and the ``qml.SpecialUnitary`` gate we will use is defined as +:math:`\mathrm{SU}(N)` as well and the ``qml.SpecialUnitary`` gate we will use is defined as .. math:: @@ -99,10 +107,10 @@ cost function :math:`C` that should be minimized. If we want to use gradient-based optimization for this task, we need a method to compute the gradient :math:`\nabla C` in addition to the cost function itself. As derived in the publication [#wiersema]_, this is possible on quantum hardware -as long as the :math:`SU(N)` gate itself can be implemented. +as long as the :math:`\mathrm{SU}(N)` gate itself can be implemented. We will not go through the entire derivation, but note the following key points: - #. The gradient with respect to all :math:`d` parameters of an :math:`SU(N)` gate can be + #. The gradient with respect to all :math:`d` parameters of an :math:`\mathrm{SU}(N)` gate can be computed using :math:`2d` auxiliary circuits. Each of the circuits contains one additional operation compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation angles :math:`\pm\frac{\pi}{2}. Not that these Pauli rotations act on up to :math:`n` @@ -131,20 +139,21 @@ based on the ``qml.SpecialUnitary`` gate discussed above to other approaches that fully parametrize the special unitary group for the respective number of qubits. In particular, we will compare ``qml.SpecialUnitary`` to standard decompositions from the -literature that parametrize :math:`SU(N)` with elementary gates, as well as to a sequence +literature that parametrize :math:`\mathrm{SU}(N)` with elementary gates, as well as to a sequence of Pauli rotation gates that also allows to create any special unitary. Let us start by defining the decomposition of a two-qubit unitary. We choose the decomposition, which is optimal but not unique, from [#vatan]_. The Pauli rotation sequence is available in PennyLane via ``qml.ArbitraryUnitary`` and we will not need to implement it ourselves. -- introduce one or two other ansatze with actually fewer parameters. +- introduce one or two other ansätze with actually fewer parameters. """ import pennylane as qml import numpy as np +# TODO: remove import and timing import time start = time.process_time() @@ -155,47 +164,31 @@ def two_qubit_decomp(params, wires): using the decomposition from Theorem 5 in https://arxiv.org/pdf/quant-ph/0308006.pdf""" i, j = wires - # Single U(2) parameterization on qubit 1 + # Single U(2) parameterization on both qubits separately qml.Rot(*params[:3], wires=i) - # Single U(2) parameterization on qubit 2 qml.Rot(*params[3:6], wires=j) - # CNOT with control on qubit 2 - qml.CNOT(wires=[j, i]) - # Rz and Ry gate + qml.CNOT(wires=[j, i]) # First CNOT qml.RZ(params[6], wires=i) qml.RY(params[7], wires=j) - # CNOT with control on qubit 1 - qml.CNOT(wires=[i, j]) - # Ry gate on qubit 2 + qml.CNOT(wires=[i, j]) # Second CNOT qml.RY(params[8], wires=j) - # CNOT with control on qubit 1 - qml.CNOT(wires=[j, i]) - # Single U(2) parameterization on qubit 1 + qml.CNOT(wires=[j, i]) # Third CNOT + # Single U(2) parameterization on both qubits separately qml.Rot(*params[9:12], wires=i) - # Single U(2) parameterization on qubit 2 qml.Rot(*params[12:15], wires=j) -def decomp(params, wires): - """Implement an arbitrary SU(2**n) gate on n qubits.""" - if len(wires) == 1: - one_qubit_decomp(params, wires) - elif len(wires) == 2: - two_qubit_decomp(params, wires) - else: - raise ValueError("Not implemented for more than 2 wires") - - +# The three building blocks on two qubits we will compare: operations = { "Decomposition": two_qubit_decomp, "PauliRot sequence": qml.ArbitraryUnitary, - "SU(N) gate": qml.SpecialUnitary, + "\mathrm{SU}(N) gate": qml.SpecialUnitary, } ############################################################################## -# Now that we have the templates for the composition approach in place, we construct a toy -# problem to solve using the ansatze. We will sample a random Hamiltonian in the Pauli basis -# (this time without the prefactor :math:`i`) +# Now that we have the template for the composition approach in place, we construct a toy +# problem to solve using the ansätze. We will sample a random Hamiltonian in the Pauli basis +# (this time without the prefactor :math:`i`, as we want to construct a Hermitian operator) # with independent coefficients that follow a normal distribution: # # .. math:: @@ -209,24 +202,30 @@ def decomp(params, wires): np.random.seed(62213) coefficients = np.random.randn(4**num_wires - 1) -basis = qml.ops.qubit.special_unitary.pauli_basis_matrices(num_wires) # Create the Pauli basis +# Create the matrices for the entire Pauli basis +basis = qml.ops.qubit.special_unitary.pauli_basis_matrices(num_wires) +# Construct the Hamiltonian from the normal random coefficients and the basis H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) -E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy +# Compute the ground state energy +E_min = np.linalg.eigvalsh(H).min() print(E_min) H = qml.Hermitian(H, wires=wires) ############################################################################## -# Using the toy problem Hamiltonian and the three ansatze for :math:`SU(N)` operations -# from above, we create a circuit template that applies these operations in a brickwall-like -# architecture with ``num_blocks=2`` blocks and each operation acting on ``num_wires_op=2`` qubits. +# Using the toy problem Hamiltonian and the three ansätze for :math:`\mathrm{SU}(N)` operations +# from above, we create a circuit template that applies these operations in a brick-layer +# architecture with two blocks and each operation acting on ``num_wires_op=2`` qubits. # For this we define a ``QNode``: +# TODO: Remove num_blocks = 2 num_wires_op = 2 d = num_wires_op**4 - 1 # d = 15 for two-qubit operations dev = qml.device("default.qubit", wires=num_wires) -# two blocks with two layers each. Each layer contains three operations with d parameters each +# TODO: Remove the following line param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) +# two blocks with two layers each. Each layer contains three operations with d parameters each +param_shape = (2, 2, 3, d) init_params = np.zeros(param_shape) @@ -290,8 +289,8 @@ def circuit(params, operation=None): import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) -for name in operations.keys(): - error = (energies[name] - E_min) / abs(E_min) +for name, energy in energies.items(): + error = (energy - E_min) / abs(E_min) ax.plot(list(range(len(error))), error, label=name) ax.set( @@ -305,7 +304,7 @@ def circuit(params, operation=None): ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` # than for the other two general unitaries, while using the same number of parameters. This -# means that we found a particularly well-trainable parametrization of the unitaries that +# means that we found a particularly well-trainable parametrization of the local unitaries which # allows to reduce the energy of the prepared quantum state more easily. # # Finally, let's look at the optimization behaviour with a shot-based device. After all, @@ -313,21 +312,26 @@ def circuit(params, operation=None): # by applying the parameter-shift rule, enabling training on quantum hardware # and shot-based simulators. # -# TODO: REVERT num_wires reduction once we can JIT the decomposition of SpecialUnitary? +# TODO: REVERT num_wires reduction once we can JIT the decomposition of SpecialUnitary? or: +# As this simulation is more costly, we reduce the number of qubits to four. Therefore, we +# require a new toy Hamiltonian and initial parameters, which we initialize together with +# the shot-based device. -num_wires = 2 +num_wires = 4 wires = list(range(num_wires)) np.random.seed(62213) coefficients = np.random.randn(4**num_wires - 1) basis = qml.ops.qubit.special_unitary.pauli_basis_matrices(num_wires) # Create the Pauli basis H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) -E_min = np.linalg.eigvalsh(H).min() # Compute the ground state energy +E_min = np.linalg.eigvalsh(H).min() H = qml.Hermitian(H, wires=wires) -param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) +# TODO: Decide between the following lines +# param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) +param_shape = (2, 2, num_wires // 2, d) init_params = jax.numpy.zeros(param_shape) -dev_shots = qml.device("default.qubit", wires=num_wires, shots=2000) +dev_shots = qml.device("default.qubit", wires=num_wires, shots=1000) qnode_shots = qml.QNode(circuit, dev_shots, interface="jax") grad_fn = jax.jacobian(qnode_shots) @@ -371,7 +375,7 @@ def circuit(params, operation=None): # # .. [#wiersema] # -# R. Wiersema, D. Lewis, J. F. Carrasquilla, and N. Killoran, +# R. Wiersema, D. Lewis, D. Wierichs, J. F. Carrasquilla, and N. Killoran, # in preparation, arXiv:23xx.xxxxx, (2023) # # diff --git a/demos_optimization.rst b/demos_optimization.rst index 846590e1f2..6ed8c6e0e8 100644 --- a/demos_optimization.rst +++ b/demos_optimization.rst @@ -163,6 +163,12 @@ in quantum neural networks. :description: :doc:`demos/tutorial_barren_gadgets` :tags: optimization barren plateaus +.. gallery-item:: + :tooltip: Construct and optimize circuits with generic quantum gates + :figure: demonstrations/here_comes_the_sun/thumbnail_tutorial_here_comes_the_sun.jpg + :description: :doc:`demos/tutorial_here_comes_the_sun` + :tags: quantumcomputing circuitdesign + :html:`
` @@ -175,7 +181,7 @@ in quantum neural networks. demos/tutorial_vqe_qng demos/tutorial_barren_plateaus demos/tutorial_local_cost_functions - demos/spsa + demos/tutorial_spsa demos/tutorial_general_parshift demos/tutorial_doubly_stochastic demos/tutorial_stochastic_parameter_shift @@ -194,3 +200,5 @@ in quantum neural networks. demos/tutorial_diffable-mitigation demos/tutorial_implicit_diff_susceptibility demos/tutorial_barren_gadgets + demos/tutorial_here_comes_the_sun + From 8356ccaea7c2485bc3cad5da0fc2e57c0ed32f42 Mon Sep 17 00:00:00 2001 From: soranjh <40344468+soranjh@users.noreply.github.com> Date: Tue, 21 Feb 2023 16:51:18 -0500 Subject: [PATCH 10/52] Update chemical reactions demo to use pyscf for openshell H3 (#704) * use pyscf for openshell H3 * change date and fix interface warning --- demonstrations/tutorial_chemical_reactions.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/demonstrations/tutorial_chemical_reactions.py b/demonstrations/tutorial_chemical_reactions.py index ce29d79acd..e6c048aa04 100644 --- a/demonstrations/tutorial_chemical_reactions.py +++ b/demonstrations/tutorial_chemical_reactions.py @@ -10,7 +10,7 @@ tutorial_quantum_chemistry Building molecular Hamiltonians tutorial_vqe A brief overview of VQE -*Authors: Varun Rishi and Juan Miguel Arrazola — Posted: 23 July 2021. Last updated: 23 July 2021.* +*Authors: Varun Rishi and Juan Miguel Arrazola — Posted: 23 July 2021. Last updated: 21 February 2023.* The term "chemical reaction" is another name for the transformation of molecules -- the breaking and forming of bonds. They are characterized by an energy barrier that determines @@ -129,13 +129,13 @@ coordinates = np.array([0.0, 0.0, 0.0, 0.0, 0.0, r]) # Obtain the qubit Hamiltonian - H, qubits = qchem.molecular_hamiltonian(symbols, coordinates) + H, qubits = qchem.molecular_hamiltonian(symbols, coordinates, method='pyscf') # define the device, optimizer and circuit dev = qml.device("default.qubit", wires=qubits) opt = qml.GradientDescentOptimizer(stepsize=0.4) - @qml.qnode(dev) + @qml.qnode(dev, interface='autograd') def circuit(parameters): # Prepare the HF state: |1100> qml.BasisState(hf, wires=range(qubits)) @@ -283,12 +283,12 @@ def circuit(parameters): coordinates = np.array([0.0, 0.0, 0.0, 0.0, 0.0, r, 0.0, 0.0, 4.0]) # We now specify the multiplicity - H, qubits = qchem.molecular_hamiltonian(symbols, coordinates, mult=multiplicity) + H, qubits = qchem.molecular_hamiltonian(symbols, coordinates, mult=multiplicity, method='pyscf') dev = qml.device("default.qubit", wires=qubits) opt = qml.GradientDescentOptimizer(stepsize=1.5) - @qml.qnode(dev) + @qml.qnode(dev, interface='autograd') def circuit(parameters): AllSinglesDoubles(parameters, range(qubits), hf, singles, doubles) return qml.expval(H) # we are interested in minimizing this expectation value From 10d6d86def924de3f453e3b2f4682d00d96e1f55 Mon Sep 17 00:00:00 2001 From: Romain Moyard Date: Wed, 22 Feb 2023 13:14:13 -0500 Subject: [PATCH 11/52] Change ibm device in Quantum volume (#703) * Ibm oslo * Update to new hardware * Change to Lima * Typo * Replace * One below --- demonstrations/quantum_volume.py | 148 +- .../quantum_volume/{ourense.svg => lima.svg} | 0 .../lima_heavy_output_distributions.svg | 2241 +++++++++++++++++ .../ourense_heavy_output_distributions.svg | 2127 ---------------- 4 files changed, 2314 insertions(+), 2202 deletions(-) rename demonstrations/quantum_volume/{ourense.svg => lima.svg} (100%) create mode 100644 demonstrations/quantum_volume/lima_heavy_output_distributions.svg delete mode 100644 demonstrations/quantum_volume/ourense_heavy_output_distributions.svg diff --git a/demonstrations/quantum_volume.py b/demonstrations/quantum_volume.py index f3c33be50d..87f7ec93b7 100644 --- a/demonstrations/quantum_volume.py +++ b/demonstrations/quantum_volume.py @@ -397,38 +397,38 @@ def qv_circuit_layer(num_qubits): # # .. code-block:: none # -# 0: ─╭SWAP─╭U(M0)─╭U(M1)─╭SWAP───────╭U(M2)─┤ -# 1: ─╰SWAP─╰U(M0)─╰U(M1)─│─────╭SWAP─╰U(M2)─┤ -# 2: ─────────────────────╰SWAP─╰SWAP────────┤ -# 3: ────────────────────────────────────────┤ -# 4: ────────────────────────────────────────┤ -# M0 = -# [[-0.17514647+0.00759447j 0.11975927+0.16007614j -0.41793925+0.49643728j -# 0.62304058-0.34640531j] -# [-0.73367896-0.58079555j -0.11348577+0.00751965j -0.02640159-0.15592112j -# -0.19507153-0.21998821j] -# [ 0.02988983+0.09364586j -0.74053162+0.55032455j 0.31350059-0.01305651j -# 0.16283233-0.11885036j] -# [-0.13103809-0.25850305j 0.18298996+0.2497364j 0.34879438+0.57771772j -# -0.02385446+0.60346274j]] -# M1 = -# [[ 0.14296171+0.28087257j -0.5985737 -0.27489922j -0.43838149+0.10344812j -# 0.04022491+0.51216658j] -# [-0.21538853+0.02728431j -0.24776721-0.57146257j 0.60975755+0.36241573j -# 0.21787038-0.11953391j] -# [-0.24405375+0.05780278j -0.11688629-0.17397518j -0.51628349-0.11381455j -# 0.44143429-0.64714776j] -# [-0.750841 -0.47630904j -0.28666068+0.22820556j -0.09459735+0.07429451j -# -0.17243398+0.17582253j]] -# M2 = -# [[-0.63733359+1.91519046e-01j -0.49615702+9.79920998e-05j -# 0.06949634+4.54968771e-01j 0.21112196-2.33571716e-01j] -# [ 0.4774216 +5.19692450e-02j -0.2741782 -3.71778068e-01j -# 0.09817361+6.01972062e-01j -0.39517581+1.66741872e-01j] -# [ 0.14401687-1.53582182e-01j 0.51636466-1.58216631e-01j -# 0.43804144+3.62586089e-01j 0.4473567 -3.74872915e-01j] -# [ 0.51670588+1.23210608e-01j -0.48982566-9.40288988e-02j -# -0.19210465-2.36457367e-01j 0.53202679-3.05278186e-01j]] +# 0: ─╭SWAP───────╭U(M0)─╭SWAP───────╭U(M1)─╭U(M2)─┤ +# 1: ─│─────╭SWAP─╰U(M0)─╰SWAP─╭SWAP─╰U(M1)─╰U(M2)─┤ +# 2: ─╰SWAP─╰SWAP──────────────╰SWAP───────────────┤ +# 3: ──────────────────────────────────────────────┤ +# 4: ──────────────────────────────────────────────┤ +# M0 = +# [[ 0.22234537+0.12795769j 0.24613682-0.34470179j 0.58179809-0.36478045j +# -0.16337007-0.50650086j] +# [-0.08840637-0.42456216j -0.01961572+0.35189839j 0.4214659 +0.31514336j +# -0.63733039+0.06764003j] +# [ 0.28919627-0.23577761j -0.11249786-0.67687982j 0.22914826+0.37205064j +# 0.12755164+0.42749545j] +# [ 0.59999195+0.49689511j -0.29294024+0.37382355j 0.23724315-0.06544043j +# -0.039832 +0.3246437j ]] +# M1 = +# [[ 0.11583153-0.3628563j 0.55797708+0.48315028j -0.22400838-0.264741j +# -0.34856401+0.26149824j] +# [-0.04549494-0.25884483j 0.00258749-0.20351027j -0.26326583-0.70408962j +# 0.33442905-0.46109931j] +# [-0.46824254-0.14274112j -0.00491681+0.61278881j -0.02506472+0.26582603j +# 0.54135395-0.14312156j] +# [ 0.73672445-0.05881259j 0.19534118+0.01057264j -0.29145879+0.398047j +# 0.33955583-0.23837031j]] +# M2 = +# [[-0.33352575+0.21982221j -0.29128941-0.51347253j 0.63543764-0.11913356j +# 0.27186717+0.00704727j] +# [-0.22330473+0.02289549j 0.1997405 -0.47316218j -0.23040621-0.14078015j +# -0.47922028-0.61909121j] +# [-0.00705247+0.82724695j 0.52220719+0.02527864j -0.05490671-0.04899343j +# 0.03167901+0.18935341j] +# [ 0.23396138-0.22566431j 0.32400589+0.09694607j 0.54666955-0.45261179j +# -0.48177768+0.2101061j ]] ############################################################################## @@ -510,19 +510,19 @@ def heavy_output_set(m, probs): # # .. code-block:: none # -# State Probability -# 000 0.0157 -# 001 0.0200 -# 010 0.0026 -# 011 0.2765 -# 100 0.0175 -# 101 0.4266 -# 110 0.0045 -# 111 0.2365 +# State Probability +# 000 0.0559 +# 001 0.3687 +# 010 0.0326 +# 011 0.0179 +# 100 0.0550 +# 101 0.3590 +# 110 0.1103 +# 111 0.0005 # -# Median is 0.0188 -# Probability of a heavy output is 0.9596 -# Heavy outputs are ['001', '111', '011', '101'] +# Median is 0.0554 +# Probability of a heavy output is 0.8939 +# Heavy outputs are ['000', '110', '101', '001'] # ############################################################################## @@ -531,7 +531,7 @@ def heavy_output_set(m, probs): # ~~~~~~~~~~~~~~~~~~~~~~~~ # # Now it's time to run the protocol. First, let's set up our hardware -# device. We'll use a simulated version of the 5-qubit IBM Ourense as an example +# device. We'll use a simulated version of the 5-qubit IBM Lima as an example # --- the reported quantum volume according to IBM is :math:`V_Q=8`, so we # endeavour to reproduce that here. This means that we should be able to run our # square circuits reliably on up to :math:`\log_2 V_Q =3` qubits. @@ -551,13 +551,10 @@ def heavy_output_set(m, probs): # # .. note:: # -# In the time since the original release of this demo, the Ourense device is -# no longer available from IBM Q. However, we leave the original results for -# expository purposes, and note that the methods are applicable in general. # Users can get a list of available IBM Q backends by importing IBM Q, # specifying their provider and then calling: ``provider.backends()`` # -dev_ourense = qml.device("qiskit.ibmq", wires=5, backend="ibmq_bogota") +dev_lima = qml.device("qiskit.ibmq", wires=5, backend="ibmq_lima") ############################################################################## # @@ -567,18 +564,18 @@ def heavy_output_set(m, probs): import matplotlib.pyplot as plt import networkx as nx -ourense_hardware_graph = nx.Graph(dev_ourense.backend.configuration().coupling_map) +lima_hardware_graph = nx.Graph(dev_lima.backend.configuration().coupling_map) nx.draw_networkx( - ourense_hardware_graph, + lima_hardware_graph, node_color="cyan", - labels={x: x for x in range(dev_ourense.num_wires)}, + labels={x: x for x in range(dev_lima.num_wires)}, ) ############################################################################## # -# .. figure:: ../demonstrations/quantum_volume/ourense.svg +# .. figure:: ../demonstrations/quantum_volume/lima.svg # :align: center # :width: 75% # @@ -589,16 +586,16 @@ def heavy_output_set(m, probs): # to make some adjustments when non-connected qubits need to interact. # # To actually perform the simulations, we'll need to access a copy of the -# Ourense noise model. Again, we won't be running on Ourense directly --- +# Lima noise model. Again, we won't be running on Lima directly --- # we'll set up a local device to simulate its behaviour. # from qiskit.providers.aer import noise -noise_model = noise.NoiseModel.from_backend(dev_ourense.backend) +noise_model = noise.NoiseModel.from_backend(dev_lima.backend) dev_noisy = qml.device( - "qiskit.aer", wires=dev_ourense.num_wires, shots=1000, noise_model=noise_model + "qiskit.aer", wires=dev_lima.num_wires, shots=1000, noise_model=noise_model ) ############################################################################## @@ -609,7 +606,7 @@ def heavy_output_set(m, probs): # qubit placement and routing techniques [#sabre]_ in order to fit the circuits # on the hardware graph in the best way possible. -coupling_map = dev_ourense.backend.configuration().to_dict()["coupling_map"] +coupling_map = dev_lima.backend.configuration().to_dict()["coupling_map"] dev_noisy.set_transpile_args( **{ @@ -697,24 +694,24 @@ def heavy_output_set(m, probs): # .. code-block:: none # # Ideal mean probabilities: -# m = 2: 0.797979 above threshold. -# m = 3: 0.844052 above threshold. -# m = 4: 0.841203 above threshold. -# m = 5: 0.856904 above threshold. +# m = 2: 0.801480 above threshold. +# m = 3: 0.853320 above threshold. +# m = 4: 0.832995 above threshold. +# m = 5: 0.858370 above threshold. # # Device mean probabilities: -# m = 2: 0.773760 above threshold. -# m = 3: 0.794875 above threshold. -# m = 4: 0.722860 above threshold. -# m = 5: 0.692935 above threshold. +# m = 2: 0.765920 above threshold. +# m = 3: 0.773985 above threshold. +# m = 4: 0.674380 above threshold. +# m = 5: 0.639500 below threshold. ############################################################################## # # We see that the ideal probabilities are well over 2/3. In fact, they're quite # close to the expected value of :math:`(1 + \ln 2)/2`, which we recall from # above is :math:`\approx 0.85`. For this experiment, we see that the device -# probabilities are also above the threshold. But it isn't enough that just the -# mean of the heavy output probabilities is greater than 2/3. Since we're +# probabilities are also above the threshold (except one). But it isn't enough +# that just the mean of the heavy output probabilities is greater than 2/3. Since we're # dealing with randomness, we also want to ensure these results were not just a # fluke! To be confident, we also want to be above 2/3 within 2 standard # deviations :math:`(\sigma)` of the mean. This is referred to as a 97.5% @@ -766,13 +763,14 @@ def heavy_output_set(m, probs): label="2σ", ) -fig.suptitle("Heavy output distributions for (simulated) Ourense QPU", fontsize=18) +fig.suptitle("Heavy output distributions for (simulated) Lima QPU", fontsize=18) plt.legend(fontsize=14) plt.tight_layout() + ############################################################################## # -# .. figure:: ../demonstrations/quantum_volume/ourense_heavy_output_distributions.svg +# .. figure:: ../demonstrations/quantum_volume/lima_heavy_output_distributions.svg # :align: center # :width: 90% # @@ -795,16 +793,16 @@ def heavy_output_set(m, probs): # # .. code-block:: none # -# m = 2: 0.714590 above threshold. -# m = 3: 0.737770 above threshold. -# m = 4: 0.659562 below threshold. -# m = 5: 0.627701 below threshold. +# m = 2: 0.706039 above threshold. +# m = 3: 0.714836 above threshold. +# m = 4: 0.608109 below threshold. +# m = 5: 0.571597 below threshold. # ############################################################################## # # We see that we are :math:`2\sigma` above the threshold only for :math:`m=2`, -# and :math:`m=3`. Thus, we find that the quantum volume of our simulated Ourense is +# and :math:`m=3`. Thus, we find that the quantum volume of our simulated Lima is # :math:`\log_2 V_Q = 3`, or :math:`V_Q = 8`, as expected. # # This framework and code will allow you to calculate the quantum volume of many @@ -831,7 +829,7 @@ def heavy_output_set(m, probs): # number of qubits continues to increase and error rates are getting lower, # both of which imply that our square circuits will be growing in both width and # depth as time goes on. Eventually they will reach a point where they are no -# longer classical simulable and we will have to design new benchmarks. +# longer classical simulable, and we will have to design new benchmarks. # # Another limitation is that the protocol only looks at one type of circuit, # i.e., square circuits. It might be the case that a processor has very few diff --git a/demonstrations/quantum_volume/ourense.svg b/demonstrations/quantum_volume/lima.svg similarity index 100% rename from demonstrations/quantum_volume/ourense.svg rename to demonstrations/quantum_volume/lima.svg diff --git a/demonstrations/quantum_volume/lima_heavy_output_distributions.svg b/demonstrations/quantum_volume/lima_heavy_output_distributions.svg new file mode 100644 index 0000000000..0a12856aef --- /dev/null +++ b/demonstrations/quantum_volume/lima_heavy_output_distributions.svg @@ -0,0 +1,2241 @@ + + + + + + + + 2023-02-21T16:23:37.357171 + image/svg+xml + + + Matplotlib v3.6.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/demonstrations/quantum_volume/ourense_heavy_output_distributions.svg b/demonstrations/quantum_volume/ourense_heavy_output_distributions.svg deleted file mode 100644 index 759fcfbdc2..0000000000 --- a/demonstrations/quantum_volume/ourense_heavy_output_distributions.svg +++ /dev/null @@ -1,2127 +0,0 @@ - - - - - - - - - 2021-01-24T11:24:04.152682 - image/svg+xml - - - Matplotlib v3.3.1, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - From ab34e2aa5ed66240b7fef111f3486a558e8d1871 Mon Sep 17 00:00:00 2001 From: Mudit Pandey Date: Wed, 22 Feb 2023 16:17:50 -0500 Subject: [PATCH 12/52] Update demos to remove warnings (#705) * Added interface, removed deprecated functionality * Addressing PR comments --------- Co-authored-by: Romain Moyard --- demonstrations/tutorial_adaptive_circuits.py | 10 +-- demonstrations/tutorial_backprop.py | 14 ++-- demonstrations/tutorial_barren_plateaus.py | 4 +- demonstrations/tutorial_classical_kernels.py | 2 +- .../tutorial_classically_boosted_vqe.py | 4 +- demonstrations/tutorial_coherent_vqls.py | 6 +- .../tutorial_data_reuploading_classifier.py | 2 +- demonstrations/tutorial_diffable_shadows.py | 22 +++--- demonstrations/tutorial_differentiable_HF.py | 2 +- demonstrations/tutorial_doubly_stochastic.py | 6 +- .../tutorial_expressivity_fourier_series.py | 8 +- demonstrations/tutorial_falqon.py | 8 +- demonstrations/tutorial_givens_rotations.py | 10 +-- .../tutorial_kernel_based_training.py | 2 +- demonstrations/tutorial_kernels_module.py | 2 +- .../tutorial_local_cost_functions.py | 16 ++-- demonstrations/tutorial_mbqc.py | 16 ++-- .../tutorial_measurement_optimize.py | 14 ++-- demonstrations/tutorial_mol_geo_opt.py | 2 +- .../tutorial_noisy_circuit_optimization.py | 77 ++++++++++--------- demonstrations/tutorial_plugins_hybrid.py | 2 +- demonstrations/tutorial_qgrnn.py | 2 +- .../tutorial_quantum_natural_gradient.py | 14 ++-- demonstrations/tutorial_quanvolution.py | 2 +- demonstrations/tutorial_qubit_rotation.py | 4 +- demonstrations/tutorial_qubit_tapering.py | 14 ++-- demonstrations/tutorial_rosalin.py | 10 +-- demonstrations/tutorial_sc_qubits.py | 16 ++-- demonstrations/tutorial_testing_symmetry.py | 2 +- demonstrations/tutorial_tn_circuits.py | 10 +-- demonstrations/tutorial_trapped_ions.py | 14 ++-- .../tutorial_variational_classifier.py | 6 +- demonstrations/tutorial_vqe.py | 2 +- demonstrations/tutorial_vqe_qng.py | 4 +- demonstrations/tutorial_vqe_spin_sectors.py | 8 +- demonstrations/tutorial_vqls.py | 4 +- demonstrations/tutorial_vqt.py | 2 +- 37 files changed, 174 insertions(+), 169 deletions(-) diff --git a/demonstrations/tutorial_adaptive_circuits.py b/demonstrations/tutorial_adaptive_circuits.py index b40804500d..13e4649ff3 100644 --- a/demonstrations/tutorial_adaptive_circuits.py +++ b/demonstrations/tutorial_adaptive_circuits.py @@ -123,7 +123,7 @@ def circuit_1(params, excitations): # with respect to the Hartree-Fock state. dev = qml.device("default.qubit", wires=qubits) -cost_fn = qml.QNode(circuit_1, dev) +cost_fn = qml.QNode(circuit_1, dev, interface="autograd") circuit_gradient = qml.grad(cost_fn, argnum=0) @@ -181,7 +181,7 @@ def circuit_2(params, excitations, gates_select, params_select): ############################################################################## # We now compute the gradients for the single excitation gates. -cost_fn = qml.QNode(circuit_2, dev) +cost_fn = qml.QNode(circuit_2, dev, interface="autograd") circuit_gradient = qml.grad(cost_fn, argnum=0) params = [0.0] * len(singles) @@ -213,7 +213,7 @@ def circuit_2(params, excitations, gates_select, params_select): # We perform one final step of optimization to get the ground-state energy. The resulting energy # should match the exact energy of the ground electronic state of LiH which is -7.8825378193 Ha. -cost_fn = qml.QNode(circuit_1, dev) +cost_fn = qml.QNode(circuit_1, dev, interface="autograd") params = np.zeros(len(doubles_select + singles_select), requires_grad=True) @@ -239,7 +239,7 @@ def circuit_2(params, excitations, gates_select, params_select): # PennyLane function :func:`~.pennylane.utils.sparse_hamiltonian`. This function # returns the matrix in the SciPy `sparse coordinate `_ format. -H_sparse = qml.utils.sparse_hamiltonian(H) +H_sparse = H.sparse_matrix() H_sparse ############################################################################## @@ -264,7 +264,7 @@ def circuit_2(params, excitations, gates_select, params_select): params = np.zeros(len(excitations), requires_grad=True) -@qml.qnode(dev, diff_method="parameter-shift") +@qml.qnode(dev, diff_method="parameter-shift", interface="autograd") def circuit(params): qml.BasisState(hf_state, wires=range(qubits)) diff --git a/demonstrations/tutorial_backprop.py b/demonstrations/tutorial_backprop.py index 285df1d23e..2198861a50 100644 --- a/demonstrations/tutorial_backprop.py +++ b/demonstrations/tutorial_backprop.py @@ -64,7 +64,7 @@ # create a device to execute the circuit on dev = qml.device("default.qubit", wires=3) -@qml.qnode(dev, diff_method="parameter-shift") +@qml.qnode(dev, diff_method="parameter-shift", interface="autograd") def circuit(params): qml.RX(params[0], wires=0) qml.RY(params[1], wires=1) @@ -167,7 +167,7 @@ def parameter_shift(qnode, params): dev = qml.device("default.qubit", wires=4) -@qml.qnode(dev, diff_method="parameter-shift") +@qml.qnode(dev, diff_method="parameter-shift", interface="autograd") def circuit(params): qml.StronglyEntanglingLayers(params, wires=[0, 1, 2, 3]) return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1) @ qml.PauliZ(2) @ qml.PauliZ(3)) @@ -264,7 +264,7 @@ def circuit(params): # mode* for the ``default.qubit`` device. -@qml.qnode(dev, diff_method="backprop") +@qml.qnode(dev, diff_method="backprop", interface="autograd") def circuit(params): qml.StronglyEntanglingLayers(params, wires=[0, 1, 2, 3]) return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1) @ qml.PauliZ(2) @ qml.PauliZ(3)) @@ -336,8 +336,8 @@ def circuit(params): # forward pass timing # =================== - qnode_shift = qml.QNode(circuit, dev, diff_method="parameter-shift") - qnode_backprop = qml.QNode(circuit, dev, diff_method="backprop") + qnode_shift = qml.QNode(circuit, dev, diff_method="parameter-shift", interface="autograd") + qnode_backprop = qml.QNode(circuit, dev, diff_method="backprop", interface="autograd") # parameter-shift t = timeit.repeat("qnode_shift(params)", globals=globals(), number=num, repeat=reps) @@ -353,8 +353,8 @@ def circuit(params): # Gradient timing # =============== - qnode_shift = qml.QNode(circuit, dev, diff_method="parameter-shift") - qnode_backprop = qml.QNode(circuit, dev, diff_method="backprop") + qnode_shift = qml.QNode(circuit, dev, diff_method="parameter-shift", interface="autograd") + qnode_backprop = qml.QNode(circuit, dev, diff_method="backprop", interface="autograd") # parameter-shift t = timeit.repeat("qml.grad(qnode_shift)(params)", globals=globals(), number=num, repeat=reps) diff --git a/demonstrations/tutorial_barren_plateaus.py b/demonstrations/tutorial_barren_plateaus.py index f5209dd09e..876e18dfff 100644 --- a/demonstrations/tutorial_barren_plateaus.py +++ b/demonstrations/tutorial_barren_plateaus.py @@ -132,7 +132,7 @@ def rand_circuit(params, random_gate_sequence=None, num_qubits=None): for i in range(num_samples): gate_sequence = {i: np.random.choice(gate_set) for i in range(num_qubits)} - qcircuit = qml.QNode(rand_circuit, dev) + qcircuit = qml.QNode(rand_circuit, dev, interface="autograd") grad = qml.grad(qcircuit, argnum=0) params = np.random.uniform(0, 2 * np.pi, size=num_qubits) gradient = grad(params, random_gate_sequence=gate_sequence, num_qubits=num_qubits) @@ -161,7 +161,7 @@ def rand_circuit(params, random_gate_sequence=None, num_qubits=None): grad_vals = [] for i in range(num_samples): dev = qml.device("default.qubit", wires=num_qubits) - qcircuit = qml.QNode(rand_circuit, dev) + qcircuit = qml.QNode(rand_circuit, dev, interface="autograd") grad = qml.grad(qcircuit, argnum=0) gate_set = [qml.RX, qml.RY, qml.RZ] diff --git a/demonstrations/tutorial_classical_kernels.py b/demonstrations/tutorial_classical_kernels.py index 7b73263966..cecc229c68 100644 --- a/demonstrations/tutorial_classical_kernels.py +++ b/demonstrations/tutorial_classical_kernels.py @@ -416,7 +416,7 @@ def ansatz(x1, x2, thetas, amplitudes, wires): ############################################################################### # Next, we construct the quantum node: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def QK_circuit(x1, x2, thetas, amplitudes): ansatz(x1, x2, thetas, amplitudes, wires = range(n_wires)) return qml.probs(wires = range(n_wires)) diff --git a/demonstrations/tutorial_classically_boosted_vqe.py b/demonstrations/tutorial_classically_boosted_vqe.py index 0621a66170..0bd1707812 100644 --- a/demonstrations/tutorial_classically_boosted_vqe.py +++ b/demonstrations/tutorial_classically_boosted_vqe.py @@ -154,7 +154,7 @@ def circuit_VQE(theta, wires): # dev = qml.device('default.qubit', wires=qubits) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_fn(theta): circuit_VQE(theta,range(qubits)) return qml.expval(H) @@ -424,7 +424,7 @@ def cost_fn(theta): wires = range(qubits + 1) dev = qml.device("default.qubit", wires=wires) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def hadamard_test(Uq, Ucl, component='real'): if component == 'imag': diff --git a/demonstrations/tutorial_coherent_vqls.py b/demonstrations/tutorial_coherent_vqls.py index 83f4d9672f..2001971d0f 100644 --- a/demonstrations/tutorial_coherent_vqls.py +++ b/demonstrations/tutorial_coherent_vqls.py @@ -361,7 +361,7 @@ def full_circuit(weights): dev = qml.device("default.qubit", wires=tot_qubits) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def global_ground(weights): # Circuit gates full_circuit(weights) @@ -370,7 +370,7 @@ def global_ground(weights): P[0, 0] = 1.0 return qml.expval(qml.Hermitian(P, wires=range(tot_qubits))) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def ancilla_ground(weights): # Circuit gates full_circuit(weights) @@ -489,7 +489,7 @@ def cost(weights): dev_x = qml.device("default.qubit", wires=n_qubits, shots=n_shots) -@qml.qnode(dev_x) +@qml.qnode(dev_x, interface="autograd") def prepare_and_sample(weights): # Variational circuit generating a guess for the solution vector |x> diff --git a/demonstrations/tutorial_data_reuploading_classifier.py b/demonstrations/tutorial_data_reuploading_classifier.py index 3e5b9a4357..7d1ae371cc 100644 --- a/demonstrations/tutorial_data_reuploading_classifier.py +++ b/demonstrations/tutorial_data_reuploading_classifier.py @@ -262,7 +262,7 @@ def density_matrix(state): # Install any pennylane-plugin to run on some particular backend -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def qcircuit(params, x, y): """A variational quantum circuit representing the Universal classifier. diff --git a/demonstrations/tutorial_diffable_shadows.py b/demonstrations/tutorial_diffable_shadows.py index 9653b19f8b..28861db562 100644 --- a/demonstrations/tutorial_diffable_shadows.py +++ b/demonstrations/tutorial_diffable_shadows.py @@ -105,7 +105,7 @@ H = qml.Hamiltonian([1., 1.], [qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliX(0) @ qml.PauliX(1)]) dev = qml.device("default.qubit", wires=range(2), shots=10000) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def qnode(x, H): qml.Hadamard(0) qml.CNOT((0,1)) @@ -132,7 +132,7 @@ def qnode(x, H): # class methods. dev = qml.device("default.qubit", wires=range(2), shots=1000) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def qnode(x): qml.Hadamard(0) qml.CNOT((0,1)) @@ -196,7 +196,7 @@ def circuit(): obs = qml.PauliX(0) @ qml.PauliZ(3) @ qml.PauliX(6) @ qml.PauliZ(7) dev_ideal = qml.device("default.qubit", wires=range(n_wires), shots=None) -@qml.qnode(dev_ideal) +@qml.qnode(dev_ideal, interface="autograd") def qnode_ideal(): circuit() return qml.expval(obs) @@ -214,12 +214,12 @@ def qnode_ideal(): # repeating experiment 10 times to obtain averages and standard deviations dev = qml.device("default.qubit", wires=range(10), shots=shots) - @qml.qnode(dev) + @qml.qnode(dev, interface="autograd") def qnode_finite(): circuit() return qml.expval(obs) - @qml.qnode(dev) + @qml.qnode(dev, interface="autograd") def qnode_shadow(): circuit() return qml.shadow_expval(obs) @@ -297,7 +297,7 @@ def circuit(): for i in range(n): qml.CNOT((i, (i+1)%n)) -@qml.qnode(dev_ideal) +@qml.qnode(dev_ideal, interface="autograd") def qnode_ideal(): circuit() return qml.expval(H) @@ -311,7 +311,7 @@ def qnode_ideal(): coeffs = np.random.rand(len(all_observables)) H = qml.Hamiltonian(coeffs, all_observables, grouping_type="qwc") - @qml.qnode(dev_ideal) + @qml.qnode(dev_ideal, interface="autograd") def qnode_ideal(): circuit() return qml.expval(H) @@ -321,13 +321,13 @@ def qnode_ideal(): for _ in range(10): dev = qml.device("default.qubit", wires=range(5), shots=shots) - @qml.qnode(dev) + @qml.qnode(dev, interface="autograd") def qnode_finite(): circuit() return qml.expval(H) dev = qml.device("default.qubit", wires=range(5), shots=shots*n_groups) - @qml.qnode(dev) + @qml.qnode(dev, interface="autograd") def qnode_shadow(): circuit() return qml.shadow_expval(H) @@ -421,7 +421,7 @@ def circuit(): # execute qwc measurements dev_finite = qml.device("default.qubit", wires=range(n_wires), shots=int(shots)) - @qml.qnode(dev_finite) + @qml.qnode(dev_finite, interface="autograd") def qnode_finite(H): circuit() return qml.expval(H) @@ -431,7 +431,7 @@ def qnode_finite(H): # execute shadows measurements dev_shadow = qml.device("default.qubit", wires=range(n_wires), shots=int(shots)*n_groups) - @qml.qnode(dev_shadow) + @qml.qnode(dev_shadow, interface="autograd") def qnode(): circuit() return classical_shadow(wires=range(n_wires)) diff --git a/demonstrations/tutorial_differentiable_HF.py b/demonstrations/tutorial_differentiable_HF.py index 512a4f82c7..fc147f43b4 100644 --- a/demonstrations/tutorial_differentiable_HF.py +++ b/demonstrations/tutorial_differentiable_HF.py @@ -267,7 +267,7 @@ dev = qml.device("default.qubit", wires=4) def energy(mol): - @qml.qnode(dev) + @qml.qnode(dev, interface="autograd") def circuit(*args): qml.BasisState(np.array([1, 1, 0, 0]), wires=range(4)) qml.DoubleExcitation(*args[0][0], wires=[0, 1, 2, 3]) diff --git a/demonstrations/tutorial_doubly_stochastic.py b/demonstrations/tutorial_doubly_stochastic.py index 3153900461..df31247a34 100644 --- a/demonstrations/tutorial_doubly_stochastic.py +++ b/demonstrations/tutorial_doubly_stochastic.py @@ -151,8 +151,8 @@ def circuit(params): # Now, we create three QNodes, each corresponding to a device above, # and optimize them using gradient descent via the parameter-shift rule. -qnode_analytic = qml.QNode(circuit, dev_analytic) -qnode_stochastic = qml.QNode(circuit, dev_stochastic) +qnode_analytic = qml.QNode(circuit, dev_analytic, interface="autograd") +qnode_stochastic = qml.QNode(circuit, dev_stochastic, interface="autograd") param_shape = StronglyEntanglingLayers.shape(n_layers=num_layers, n_wires=num_wires) init_params = np.random.uniform(low=0, high=2*np.pi, size=param_shape, requires_grad=True) @@ -293,7 +293,7 @@ def circuit(params): ) -@qml.qnode(dev_stochastic) +@qml.qnode(dev_stochastic, interface="autograd") def circuit(params, n=None): StronglyEntanglingLayers(weights=params, wires=[0, 1]) idx = np.random.choice(np.arange(5), size=n, replace=False) diff --git a/demonstrations/tutorial_expressivity_fourier_series.py b/demonstrations/tutorial_expressivity_fourier_series.py index 4614bff616..be09145d18 100644 --- a/demonstrations/tutorial_expressivity_fourier_series.py +++ b/demonstrations/tutorial_expressivity_fourier_series.py @@ -284,7 +284,7 @@ def W(theta): qml.Rot(theta[0], theta[1], theta[2], wires=0) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def serial_quantum_model(weights, x): for theta in weights[:-1]: @@ -489,7 +489,7 @@ def cost(weights, x, y): dev = qml.device('default.qubit', wires=4) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def ansatz(weights): StronglyEntanglingLayers(weights, wires=range(n_qubits)) return qml.expval(qml.Identity(wires=0)) @@ -517,7 +517,7 @@ def W(theta): StronglyEntanglingLayers(theta, wires=range(r)) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def parallel_quantum_model(weights, x): W(weights[0]) @@ -675,7 +675,7 @@ def W(theta): BasicEntanglerLayers(theta, wires=range(n_qubits)) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def quantum_model(weights, x): W(weights[0]) diff --git a/demonstrations/tutorial_falqon.py b/demonstrations/tutorial_falqon.py index 6962dcb415..b913530f8e 100644 --- a/demonstrations/tutorial_falqon.py +++ b/demonstrations/tutorial_falqon.py @@ -250,7 +250,7 @@ def expval_circuit(beta, measurement_h): def max_clique_falqon(graph, n, beta_1, delta_t, dev): comm_h = build_hamiltonian(graph) # Builds the commutator cost_h, driver_h = qaoa.max_clique(graph, constrained=False) # Builds H_c and H_d - cost_fn = qml.QNode(expval_circuit, dev) # The ansatz + measurement circuit is executable + cost_fn = qml.QNode(expval_circuit, dev, interface="autograd") # The ansatz + measurement circuit is executable beta = [beta_1] # Records each value of beta_k energies = [] # Records the value of the cost function at each step @@ -296,7 +296,7 @@ def max_clique_falqon(graph, n, beta_1, delta_t, dev): # we can create a graph showing the probability of measuring each possible bit string. # We define the following circuit, feeding in the optimal values of :math:`\beta_k`: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def prob_circuit(): ansatz = build_maxclique_ansatz(cost_h, driver_h, delta_t) ansatz(res_beta) @@ -418,7 +418,7 @@ def qaoa_circuit(params, **kwargs): qml.layer(qaoa_layer, depth, params[0], params[1]) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def qaoa_expval(params): qaoa_circuit(params) return qml.expval(cost_h) @@ -450,7 +450,7 @@ def qaoa_expval(params): # define a circuit which outputs the probabilities of measuring each bit string, and # create a bar graph: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def prob_circuit(params): qaoa_circuit(params) return qml.probs(wires=dev.wires) diff --git a/demonstrations/tutorial_givens_rotations.py b/demonstrations/tutorial_givens_rotations.py index 5c1ce99a83..948964e036 100644 --- a/demonstrations/tutorial_givens_rotations.py +++ b/demonstrations/tutorial_givens_rotations.py @@ -189,7 +189,7 @@ dev = qml.device('default.qubit', wires=3) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(x, y): # prepares the reference state |100> qml.BasisState(np.array([1, 0, 0]), wires=[0, 1, 2]) @@ -260,7 +260,7 @@ def circuit(x, y): dev2 = qml.device('default.qubit', wires=6) -@qml.qnode(dev2) +@qml.qnode(dev2, interface="autograd") def circuit2(x, y): # prepares reference state qml.BasisState(np.array([1, 1, 1, 0, 0, 0]), wires=[0, 1, 2, 3, 4, 5]) @@ -356,7 +356,7 @@ def circuit2(x, y): dev = qml.device('default.qubit', wires=6) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit3(x, y, z): qml.BasisState(np.array([1, 1, 0, 0, 0, 0]), wires=[i for i in range(6)]) qml.DoubleExcitation(x, wires=[0, 1, 2, 3]) @@ -380,7 +380,7 @@ def circuit3(x, y, z): # above, this time controlling on the state of the first qubit and verify that we can prepare the # desired state. To perform the control, we use the :func:`~.pennylane.ctrl` transform: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit4(x, y, z): qml.BasisState(np.array([1, 1, 0, 0, 0, 0]), wires=[i for i in range(6)]) qml.DoubleExcitation(x, wires=[0, 1, 2, 3]) @@ -438,7 +438,7 @@ def circuit4(x, y, z): dev = qml.device('default.qubit', wires=4) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def state_preparation(params): qml.BasisState(np.array([1, 1, 0, 0]), wires=[0, 1, 2, 3]) qml.SingleExcitation(params[0], wires=[1, 2]) diff --git a/demonstrations/tutorial_kernel_based_training.py b/demonstrations/tutorial_kernel_based_training.py index 2a786fe4e2..0c8126c61c 100644 --- a/demonstrations/tutorial_kernel_based_training.py +++ b/demonstrations/tutorial_kernel_based_training.py @@ -254,7 +254,7 @@ projector = np.zeros((2**n_qubits, 2**n_qubits)) projector[0, 0] = 1 -@qml.qnode(dev_kernel) +@qml.qnode(dev_kernel, interface="autograd") def kernel(x1, x2): """The quantum kernel.""" AngleEmbedding(x1, wires=range(n_qubits)) diff --git a/demonstrations/tutorial_kernels_module.py b/demonstrations/tutorial_kernels_module.py index c7d226fc8d..0b90f5c9f7 100644 --- a/demonstrations/tutorial_kernels_module.py +++ b/demonstrations/tutorial_kernels_module.py @@ -292,7 +292,7 @@ def random_params(num_wires, num_layers): # finally extract the probabilities of observing each basis state. -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def kernel_circuit(x1, x2, params): ansatz(x1, params, wires=wires) adjoint_ansatz(x2, params, wires=wires) diff --git a/demonstrations/tutorial_local_cost_functions.py b/demonstrations/tutorial_local_cost_functions.py index 75ade6e3d5..580d64a851 100644 --- a/demonstrations/tutorial_local_cost_functions.py +++ b/demonstrations/tutorial_local_cost_functions.py @@ -124,9 +124,9 @@ def local_cost_simple(rotations): qml.RY(rotations[1][i], wires=i) return [qml.probs(wires=i) for i in range(wires)] -global_circuit = qml.QNode(global_cost_simple, dev) +global_circuit = qml.QNode(global_cost_simple, dev, interface="autograd") -local_circuit = qml.QNode(local_cost_simple, dev) +local_circuit = qml.QNode(local_cost_simple, dev, interface="autograd") def cost_local(rotations): return 1 - np.sum(local_circuit(rotations)[:,0])/wires @@ -252,9 +252,9 @@ def local_cost_simple(rotations): qml.broadcast(qml.CNOT, wires=range(wires), pattern="chain") return qml.probs(wires=[0]) -global_circuit = qml.QNode(global_cost_simple, dev) +global_circuit = qml.QNode(global_cost_simple, dev, interface="autograd") -local_circuit = qml.QNode(local_cost_simple, dev) +local_circuit = qml.QNode(local_cost_simple, dev, interface="autograd") def cost_local(rotations): return 1 - local_circuit(rotations)[0] @@ -344,7 +344,7 @@ def cost_global(rotations): # dev.shots = None -global_circuit = qml.QNode(global_cost_simple, dev) +global_circuit = qml.QNode(global_cost_simple, dev, interface="autograd") print( "Current cost: " + str(cost_global(params_local)) @@ -378,7 +378,7 @@ def cost_tunable(rotations): return 1 - tunable_circuit(rotations)[0] dev.shots = 10000 -tunable_circuit = qml.QNode(tunable_cost_simple, dev) +tunable_circuit = qml.QNode(tunable_cost_simple, dev, interface="autograd") locality = 2 params_tunable = params_local fig, ax = qml.draw_mpl(tunable_circuit, decimals=2)(params_tunable) @@ -441,7 +441,7 @@ def cost_tunable(rotations): wires = 8 dev = qml.device("default.qubit", wires=wires, shots=10000) -global_circuit = qml.QNode(global_cost_simple, dev) +global_circuit = qml.QNode(global_cost_simple, dev, interface="autograd") for runs in range(samples): print("--- New run! ---") @@ -474,7 +474,7 @@ def cost_tunable(rotations): wires = 8 dev = qml.device("default.qubit", wires=wires, shots=10000) -tunable_circuit = qml.QNode(tunable_cost_simple, dev) +tunable_circuit = qml.QNode(tunable_cost_simple, dev, interface="autograd") for runs in range(samples): locality = 1 diff --git a/demonstrations/tutorial_mbqc.py b/demonstrations/tutorial_mbqc.py index b59366e35b..d23e4ca68b 100644 --- a/demonstrations/tutorial_mbqc.py +++ b/demonstrations/tutorial_mbqc.py @@ -97,7 +97,7 @@ dev = qml.device("default.qubit", wires=qubits) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cluster_state(): for node in qubits: qml.Hadamard(wires=[node]) @@ -159,7 +159,7 @@ def cluster_state(): dev = qml.device("default.qubit", wires=2) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def one_bit_teleportation(input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=0) @@ -302,7 +302,7 @@ def generate_random_state(n=1): dev = qml.device("default.qubit", wires=1) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def RZ(theta, input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=0) @@ -323,7 +323,7 @@ def RZ(theta, input_state): mbqc_dev = qml.device("default.qubit", wires=2) -@qml.qnode(mbqc_dev) +@qml.qnode(mbqc_dev, interface="autograd") def RZ_MBQC(theta, input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=0) @@ -364,7 +364,7 @@ def RZ_MBQC(theta, input_state): dev = qml.device("default.qubit", wires=1) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def RX(theta, input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=0) @@ -379,7 +379,7 @@ def RX(theta, input_state): mbqc_dev = qml.device("default.qubit", wires=3) -@qml.qnode(mbqc_dev) +@qml.qnode(mbqc_dev, interface="autograd") def RX_MBQC(theta, input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=0) @@ -444,7 +444,7 @@ def RX_MBQC(theta, input_state): dev = qml.device("default.qubit", wires=2) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def CNOT(input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=[0, 1]) @@ -456,7 +456,7 @@ def CNOT(input_state): mbqc_dev = qml.device("default.qubit", wires=4) -@qml.qnode(mbqc_dev) +@qml.qnode(mbqc_dev, interface="autograd") def CNOT_MBQC(input_state): # Prepare the input state qml.QubitStateVector(input_state, wires=[0, 1]) diff --git a/demonstrations/tutorial_measurement_optimize.py b/demonstrations/tutorial_measurement_optimize.py index cd6310bc29..d5d3f4c0f7 100644 --- a/demonstrations/tutorial_measurement_optimize.py +++ b/demonstrations/tutorial_measurement_optimize.py @@ -141,7 +141,7 @@ ) # generate the cost function -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_circuit(params): ansatz(params, wires=dev.wires) return qml.expval(H) @@ -386,13 +386,13 @@ def cost_circuit(params): dev = qml.device("default.qubit", wires=3) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit1(weights): qml.StronglyEntanglingLayers(weights, wires=range(3)) return qml.expval(obs[0]) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit2(weights): qml.StronglyEntanglingLayers(weights, wires=range(3)) return qml.expval(obs[1]) @@ -407,7 +407,7 @@ def circuit2(weights): # Now, let's use our QWC approach to reduce this down to a *single* measurement # of the probabilities in the shared eigenbasis of both QWC observables: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit_qwc(weights): qml.StronglyEntanglingLayers(weights, wires=range(3)) @@ -453,7 +453,7 @@ def circuit_qwc(weights): # Luckily, PennyLane automatically performs this QWC grouping under the hood. We simply # return the two QWC Pauli terms from the QNode: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(weights): qml.StronglyEntanglingLayers(weights, wires=range(3)) return [ @@ -704,7 +704,7 @@ def format_pauli_word(term): dev = qml.device("default.qubit", wires=4) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(weights, group=None, **kwargs): qml.StronglyEntanglingLayers(weights, wires=range(4)) return [qml.expval(o) for o in group] @@ -729,7 +729,7 @@ def circuit(weights, group=None, **kwargs): # automatically optimize the measurements. H = qml.Hamiltonian(coeffs=np.ones(len(terms)), observables=terms, grouping_type="qwc") -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_fn(weights): qml.StronglyEntanglingLayers(weights, wires=range(4)) return qml.expval(H) diff --git a/demonstrations/tutorial_mol_geo_opt.py b/demonstrations/tutorial_mol_geo_opt.py index 76b43f617c..108604dfd7 100644 --- a/demonstrations/tutorial_mol_geo_opt.py +++ b/demonstrations/tutorial_mol_geo_opt.py @@ -195,7 +195,7 @@ def H(x): dev = qml.device("default.qubit", wires=num_wires) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(params, obs, wires): qml.BasisState(hf, wires=wires) qml.DoubleExcitation(params[0], wires=[0, 1, 2, 3]) diff --git a/demonstrations/tutorial_noisy_circuit_optimization.py b/demonstrations/tutorial_noisy_circuit_optimization.py index 879b4967e3..8a8f73cb3b 100644 --- a/demonstrations/tutorial_noisy_circuit_optimization.py +++ b/demonstrations/tutorial_noisy_circuit_optimization.py @@ -94,39 +94,40 @@ B2 = qml.Hermitian(np.array([[1, -1], [-1, -1]]) / np.sqrt(2), wires=1) CHSH_observables = [A1 @ B1, A1 @ B2, A2 @ B1, A2 @ B2] + # subcircuit for creating an entangled pair of qubits def bell_pair(): qml.Hadamard(wires=0) qml.CNOT(wires=[0, 1]) + # circuits for measuring each distinct observable @qml.qnode(dev) def measure_A1B1(): bell_pair() return qml.expval(A1 @ B1) + @qml.qnode(dev) def measure_A1B2(): bell_pair() return qml.expval(A1 @ B2) + @qml.qnode(dev) def measure_A2B1(): bell_pair() return qml.expval(A2 @ B1) + @qml.qnode(dev) def measure_A2B2(): bell_pair() return qml.expval(A2 @ B2) -circuits = qml.QNodeCollection([measure_A1B1, - measure_A1B2, - measure_A2B1, - measure_A2B2]) # now we measure each circuit and construct the CHSH inequality -expvals = circuits() +expvals = [measure_A1B1(), measure_A1B2(), measure_A2B1(), measure_A2B2()] # The CHSH operator is A1 @ B1 + A1 @ B2 + A2 @ B1 - A2 @ B2 CHSH_expval = np.sum(expvals[:3]) - expvals[3] @@ -152,10 +153,11 @@ def measure_A2B2(): # circuit declarations. from pennylane_cirq import ops as cirq_ops + # Note that the 'Operation' op is a generic base class # from PennyLane core. # All other ops are provided by Cirq. -available_ops = [op for op in dir(cirq_ops) if not op.startswith('_')] +available_ops = [op for op in dir(cirq_ops) if not op.startswith("_")] print("\n".join(available_ops)) ############################################################################## @@ -181,23 +183,20 @@ def bell_pair(): qml.CNOT(wires=[0, 1]) cirq_ops.BitFlip(p, wires=0) cirq_ops.BitFlip(p, wires=1) + # measuring the circuits will now use the new noisy bell_pair() function - expvals = circuits() + expvals = [measure_A1B1(), measure_A1B2(), measure_A2B1(), measure_A2B2()] noisy_expvals.append(expvals) noisy_expvals = np.array(noisy_expvals) -CHSH_expvals = np.sum(noisy_expvals[:,:3], axis=1) - noisy_expvals[:,3] +CHSH_expvals = np.sum(noisy_expvals[:, :3], axis=1) - noisy_expvals[:, 3] # Plot the individual observables -plt.plot(noise_vals, noisy_expvals[:, 0], 'D', - label = r"$\hat{A1}\otimes \hat{B1}$", markersize=5) -plt.plot(noise_vals, noisy_expvals[:, 1], 'x', - label = r"$\hat{A1}\otimes \hat{B2}$", markersize=12) -plt.plot(noise_vals, noisy_expvals[:, 2], '+', - label = r"$\hat{A2}\otimes \hat{B1}$", markersize=10) -plt.plot(noise_vals, noisy_expvals[:, 3], 'v', - label = r"$\hat{A2}\otimes \hat{B2}$", markersize=10) -plt.xlabel('Noise parameter') -plt.ylabel(r'Expectation value $\langle \hat{A}_i\otimes\hat{B}_j\rangle$') +plt.plot(noise_vals, noisy_expvals[:, 0], "D", label=r"$\hat{A1}\otimes \hat{B1}$", markersize=5) +plt.plot(noise_vals, noisy_expvals[:, 1], "x", label=r"$\hat{A1}\otimes \hat{B2}$", markersize=12) +plt.plot(noise_vals, noisy_expvals[:, 2], "+", label=r"$\hat{A2}\otimes \hat{B1}$", markersize=10) +plt.plot(noise_vals, noisy_expvals[:, 3], "v", label=r"$\hat{A2}\otimes \hat{B2}$", markersize=10) +plt.xlabel("Noise parameter") +plt.ylabel(r"Expectation value $\langle \hat{A}_i\otimes\hat{B}_j\rangle$") plt.legend() plt.show() @@ -223,10 +222,9 @@ def bell_pair(): # values greater than 2 can safely be considered "quantum". plt.plot(noise_vals, CHSH_expvals, label="CHSH") -plt.plot(noise_vals, 2 * np.ones_like(noise_vals), - label="Quantum-classical boundary") -plt.xlabel('Noise parameter') -plt.ylabel('CHSH Expectation value') +plt.plot(noise_vals, 2 * np.ones_like(noise_vals), label="Quantum-classical boundary") +plt.xlabel("Noise parameter") +plt.ylabel("CHSH Expectation value") plt.legend() plt.show() @@ -260,6 +258,7 @@ def bell_pair(): # technique for modelling noise, but may not be appropriate for all # situations. + @qml.qnode(dev) def circuit(gate_params, noise_param=0.0): qml.RX(gate_params[0], wires=0) @@ -267,6 +266,7 @@ def circuit(gate_params, noise_param=0.0): cirq_ops.Depolarize(noise_param, wires=0) return qml.expval(qml.PauliZ(0)) + gate_pars = [0.54, 0.12] print("Expectation value:", circuit(gate_pars)) @@ -284,12 +284,12 @@ def circuit(gate_params, noise_param=0.0): # :class:`~pennylane.ops.PauliZ` expectation value changes as # a function of the noise strength. -noise_vals = np.linspace(0., 1., 20) +noise_vals = np.linspace(0.0, 1.0, 20) expvals = [circuit(gate_pars, noise_param=p) for p in noise_vals] plt.plot(noise_vals, expvals, label="Expectation value") -plt.plot(noise_vals, np.ones_like(noise_vals), '--', label="Highest possible") -plt.plot(noise_vals, -np.ones_like(noise_vals), '--', label="Lowest possible") +plt.plot(noise_vals, np.ones_like(noise_vals), "--", label="Highest possible") +plt.plot(noise_vals, -np.ones_like(noise_vals), "--", label="Lowest possible") plt.ylabel(r"Expectation value $\langle \hat{Z} \rangle$") plt.xlabel(r"Noise strength $p$") plt.legend() @@ -302,13 +302,16 @@ def circuit(gate_params, noise_param=0.0): # i.e., to tune the qubit state until it has a ``PauliZ`` expectation value # of :math:`-1` (the lowest possible). + # declare the cost functions to be optimized def cost(x): return circuit(x, noise_param=0.0) + def noisy_cost(x): return circuit(x, noise_param=0.3) + # initialize the optimizer opt = qml.GradientDescentOptimizer(stepsize=0.4) @@ -326,10 +329,11 @@ def noisy_cost(x): noisy_circuit_params = opt.step(noisy_cost, noisy_circuit_params) if (i + 1) % 5 == 0: - print("Step {:5d}. Cost: {: .7f}; Noisy Cost: {: .7f}". - format(i + 1, - cost(params), - noisy_cost(noisy_circuit_params))) + print( + "Step {:5d}. Cost: {: .7f}; Noisy Cost: {: .7f}".format( + i + 1, cost(params), noisy_cost(noisy_circuit_params) + ) + ) print("\nOptimized rotation angles (noise-free case):") print("({: .7f}, {: .7f})".format(*params)) @@ -452,17 +456,18 @@ def noisy_cost(x): angles = np.linspace(0, 2 * np.pi, 50) theta2 = np.pi / 4 + def param_shift(theta1): - return 0.5 * (noisy_cost([theta1 + np.pi / 2, theta2]) - \ - noisy_cost([theta1 - np.pi / 2, theta2])) + return 0.5 * ( + noisy_cost([theta1 + np.pi / 2, theta2]) - noisy_cost([theta1 - np.pi / 2, theta2]) + ) + noisy_expvals = [noisy_cost([theta1, theta2]) for theta1 in angles] noisy_param_shift = [param_shift(theta1) for theta1 in angles] -plt.plot(angles, noisy_expvals, - label="Expectation value") # looks like 0.4 * cos(phi) -plt.plot(angles, noisy_param_shift, - label="Parameter-shift value") # looks like -0.4 * sin(phi) +plt.plot(angles, noisy_expvals, label="Expectation value") # looks like 0.4 * cos(phi) +plt.plot(angles, noisy_param_shift, label="Parameter-shift value") # looks like -0.4 * sin(phi) plt.ylabel(r"Expectation value $\langle \hat{Z} \rangle$") plt.xlabel(r"Angle $\theta_1$") plt.legend() @@ -538,4 +543,4 @@ def param_shift(theta1): # # About the author # ---------------- -# .. include:: ../_static/authors/nathan_killoran.txt \ No newline at end of file +# .. include:: ../_static/authors/nathan_killoran.txt diff --git a/demonstrations/tutorial_plugins_hybrid.py b/demonstrations/tutorial_plugins_hybrid.py index f7a24efffa..8ebc31d08f 100644 --- a/demonstrations/tutorial_plugins_hybrid.py +++ b/demonstrations/tutorial_plugins_hybrid.py @@ -260,7 +260,7 @@ def cost(params): dev_fock = qml.device("strawberryfields.fock", wires=2, cutoff_dim=10) -@qml.qnode(dev_qubit) +@qml.qnode(dev_qubit, interface="autograd") def qubit_rotation(phi1, phi2): """Qubit rotation QNode""" qml.RX(phi1, wires=0) diff --git a/demonstrations/tutorial_qgrnn.py b/demonstrations/tutorial_qgrnn.py index 695ff344af..a88df5799d 100644 --- a/demonstrations/tutorial_qgrnn.py +++ b/demonstrations/tutorial_qgrnn.py @@ -557,7 +557,7 @@ def cost_function(weight_params, bias_params): qgrnn_dev = qml.device("default.qubit", wires=2 * qubit_number + 1) # Defines the new QNode -qgrnn_qnode = qml.QNode(qgrnn, qgrnn_dev) +qgrnn_qnode = qml.QNode(qgrnn, qgrnn_dev, interface="autograd") steps = 300 diff --git a/demonstrations/tutorial_quantum_natural_gradient.py b/demonstrations/tutorial_quantum_natural_gradient.py index 2e7e6f053c..22f8b7fd21 100644 --- a/demonstrations/tutorial_quantum_natural_gradient.py +++ b/demonstrations/tutorial_quantum_natural_gradient.py @@ -192,7 +192,7 @@ dev = qml.device("default.qubit", wires=3) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(params): # |psi_0>: state preparation qml.RY(np.pi / 4, wires=0) @@ -273,7 +273,7 @@ def layer0_subcircuit(params): # We can see that the diagonal terms are simply given by the variance: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def layer0_diag(params): layer0_subcircuit(params) return qml.var(qml.PauliZ(0)), qml.var(qml.PauliZ(1)) @@ -289,13 +289,13 @@ def layer0_diag(params): # off-diagonal covariance terms of :math:`g^{(0)}`: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def layer0_off_diag_single(params): layer0_subcircuit(params) return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1)) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def layer0_off_diag_double(params): layer0_subcircuit(params) ZZ = np.kron(np.diag([1, -1]), np.diag([1, -1])) @@ -350,7 +350,7 @@ def layer1_subcircuit(params): # :target: javascript:void(0) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def layer1_diag(params): layer1_subcircuit(params) return qml.var(qml.PauliY(1)), qml.var(qml.PauliX(2)) @@ -369,13 +369,13 @@ def layer1_diag(params): # observables to be computed. -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def layer1_off_diag_single(params): layer1_subcircuit(params) return qml.expval(qml.PauliY(1)), qml.expval(qml.PauliX(2)) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def layer1_off_diag_double(params): layer1_subcircuit(params) X = np.array([[0, 1], [1, 0]]) diff --git a/demonstrations/tutorial_quanvolution.py b/demonstrations/tutorial_quanvolution.py index 465d261a78..43a3ea9c11 100644 --- a/demonstrations/tutorial_quanvolution.py +++ b/demonstrations/tutorial_quanvolution.py @@ -145,7 +145,7 @@ # Random circuit parameters rand_params = np.random.uniform(high=2 * np.pi, size=(n_layers, 4)) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(phi): # Encoding of 4 classical input values for j in range(4): diff --git a/demonstrations/tutorial_qubit_rotation.py b/demonstrations/tutorial_qubit_rotation.py index b8de2d943d..acc9ab0b19 100644 --- a/demonstrations/tutorial_qubit_rotation.py +++ b/demonstrations/tutorial_qubit_rotation.py @@ -214,7 +214,7 @@ def circuit(params): # **directly above** the function definition: -@qml.qnode(dev1) +@qml.qnode(dev1, interface="autograd") def circuit(params): qml.RX(params[0], wires=0) qml.RY(params[1], wires=0) @@ -266,7 +266,7 @@ def circuit(params): # two positional arguments, instead of one array argument: -@qml.qnode(dev1) +@qml.qnode(dev1, interface="autograd") def circuit2(phi1, phi2): qml.RX(phi1, wires=0) qml.RY(phi2, wires=0) diff --git a/demonstrations/tutorial_qubit_tapering.py b/demonstrations/tutorial_qubit_tapering.py index 1036c75866..5a77fe3458 100644 --- a/demonstrations/tutorial_qubit_tapering.py +++ b/demonstrations/tutorial_qubit_tapering.py @@ -177,8 +177,8 @@ # representation of Hamiltonians. This allows us to directly diagonalize them to obtain exact values # of the ground-state energies. -H_sparse = qml.SparseHamiltonian(qml.utils.sparse_hamiltonian(H), wires=H.wires) -H_tapered_sparse = qml.SparseHamiltonian(qml.utils.sparse_hamiltonian(H_tapered), wires=H_tapered.wires) +H_sparse = qml.SparseHamiltonian(H.sparse_matrix(), wires=H.wires) +H_tapered_sparse = qml.SparseHamiltonian(H_tapered.sparse_matrix(), wires=H_tapered.wires) print("Eigenvalues of H:\n", qml.eigvals(H_sparse, k=16)) print("\nEigenvalues of H_tapered:\n", qml.eigvals(H_tapered_sparse, k=4)) @@ -202,23 +202,23 @@ # Hartree-Fock energies for each Hamiltonian. dev = qml.device("default.qubit", wires=H.wires) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(): qml.BasisState(np.array([1, 1, 0, 0]), wires=H.wires) return qml.state() qubit_state = circuit() -HF_energy = qubit_state.T @ qml.utils.sparse_hamiltonian(H).toarray() @ qubit_state +HF_energy = qubit_state.T @ H.sparse_matrix().toarray() @ qubit_state print(f"HF energy: {np.real(HF_energy):.8f} Ha") dev = qml.device("default.qubit", wires=H_tapered.wires) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(): qml.BasisState(np.array([1, 1]), wires=H_tapered.wires) return qml.state() qubit_state = circuit() -HF_energy = qubit_state.T @ qml.utils.sparse_hamiltonian(H_tapered).toarray() @ qubit_state +HF_energy = qubit_state.T @ H_tapered.sparse_matrix().toarray() @ qubit_state print(f"HF energy (tapered): {np.real(HF_energy):.8f} Ha") ############################################################################## @@ -245,7 +245,7 @@ def circuit(): ] dev = qml.device("default.qubit", wires=H_tapered.wires) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def tapered_circuit(params): qml.BasisState(state_tapered, wires=H_tapered.wires) for idx, tapered_op in enumerate(tapered_doubles + tapered_singles): diff --git a/demonstrations/tutorial_rosalin.py b/demonstrations/tutorial_rosalin.py index 57a0d94e18..13368b6626 100644 --- a/demonstrations/tutorial_rosalin.py +++ b/demonstrations/tutorial_rosalin.py @@ -186,7 +186,7 @@ from pennylane.templates.layers import StronglyEntanglingLayers -@qml.qnode(non_analytic_dev, diff_method="parameter-shift") +@qml.qnode(non_analytic_dev, diff_method="parameter-shift", interface="autograd") def qnode(weights, observable): StronglyEntanglingLayers(weights, wires=non_analytic_dev.wires) return qml.expval(observable) @@ -235,7 +235,7 @@ def cost(params): # Here, we will split the 8000 total shots evenly across all Hamiltonian terms, # also known as *uniform deterministic sampling*. -@qml.qnode(non_analytic_dev, diff_method="parameter-shift") +@qml.qnode(non_analytic_dev, diff_method="parameter-shift", interface="autograd") def qnode(weights, obs): StronglyEntanglingLayers(weights, wires=non_analytic_dev.wires) return qml.expval(obs) @@ -448,7 +448,7 @@ def estimate_hamiltonian(self, params, shots): results = [] - @qml.qnode(rosalin_device, diff_method="parameter-shift") + @qml.qnode(rosalin_device, diff_method="parameter-shift", interface="autograd") def qnode(weights, observable): StronglyEntanglingLayers(weights, wires=rosalin_device.wires) return qml.sample(observable) @@ -555,7 +555,7 @@ def step(self, params): # also create a separate cost function using an 'exact' quantum device, so that we can keep track of the # *exact* cost function value at each iteration. -@qml.qnode(analytic_dev) +@qml.qnode(analytic_dev, interface="autograd") def cost_analytic(weights): StronglyEntanglingLayers(weights, wires=analytic_dev.wires) return qml.expval(qml.Hamiltonian(coeffs, obs)) @@ -593,7 +593,7 @@ def cost_analytic(weights): non_analytic_dev.shots = adam_shots_per_eval -@qml.qnode(non_analytic_dev, diff_method="parameter-shift") +@qml.qnode(non_analytic_dev, diff_method="parameter-shift", interface="autograd") def cost(weights): StronglyEntanglingLayers(weights, wires=non_analytic_dev.wires) return qml.expval(qml.Hamiltonian(coeffs, obs)) diff --git a/demonstrations/tutorial_sc_qubits.py b/demonstrations/tutorial_sc_qubits.py index 65b11d26d5..973fc1aa67 100644 --- a/demonstrations/tutorial_sc_qubits.py +++ b/demonstrations/tutorial_sc_qubits.py @@ -416,14 +416,14 @@ # Implement displacement and rotation and measure both X and P observables -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def measure_P_shots(time, state): qml.Displacement(epsilon * time, 0, wires=0) qml.Rotation((-1) ** state * chi * time, wires=0) return qml.sample(qml.P(0)) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def measure_X_shots(time, state): qml.Displacement(epsilon * time, 0, wires=0) qml.Rotation((-1) ** state * chi * time, wires=0) @@ -499,7 +499,7 @@ def measure_X_shots(time, state): dev2 = qml.device("default.qubit", wires=1) # Implement Hamiltonian evolution given phase phi and time t, from a given initial state -@qml.qnode(dev2) +@qml.qnode(dev2, interface="autograd") def H_evolve(state, phi, time): if state == 1: @@ -513,7 +513,7 @@ def H_evolve(state, phi, time): # Implement X rotation exactly -@qml.qnode(dev2) +@qml.qnode(dev2, interface="autograd") def Sc_X_rot(state, phi): if state == 1: @@ -524,7 +524,7 @@ def Sc_X_rot(state, phi): # Implement Y rotation exactly -@qml.qnode(dev2) +@qml.qnode(dev2, interface="autograd") def Sc_Y_rot(state, phi): if state == 1: @@ -617,7 +617,7 @@ def Sc_Y_rot(state, phi): Two_qubit_H = qml.Hamiltonian(coeffs, ops) # Implement Hamiltonian evolution for time t and some initial computational basis state -@qml.qnode(dev3) +@qml.qnode(dev3, interface="autograd") def Sc_ISWAP(basis_state, time): qml.templates.BasisStatePreparation(basis_state, wires=range(2)) ApproxTimeEvolution(Two_qubit_H, time, 1) @@ -625,7 +625,7 @@ def Sc_ISWAP(basis_state, time): # Implement ISWAP exactly -@qml.qnode(dev3) +@qml.qnode(dev3, interface="autograd") def iswap(basis_state): qml.templates.BasisStatePreparation(basis_state, wires=range(2)) qml.ISWAP(wires=[0, 1]) @@ -732,7 +732,7 @@ def cnot_with_iswap(): # the evolution under this Hamiltonian for a time :math:`t=\tfrac{\pi}{4\Omega}` with :math:`R_x` and :math:`R_y` rotations # and a ``qml.Hadamard`` gate: # -@qml.qnode(dev3) +@qml.qnode(dev3, interface="autograd") def H_evolve(state, phi, time): # Prepare initial state qml.templates.BasisStatePreparation(state, wires=range(2)) diff --git a/demonstrations/tutorial_testing_symmetry.py b/demonstrations/tutorial_testing_symmetry.py index a1bf46471b..9c858dd0e3 100644 --- a/demonstrations/tutorial_testing_symmetry.py +++ b/demonstrations/tutorial_testing_symmetry.py @@ -322,7 +322,7 @@ def CU_cpy(): # # Circuit for average symmetry -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def avg_symm(hamiltonian, time): # Use Choi-Jamiołkowski isomorphism diff --git a/demonstrations/tutorial_tn_circuits.py b/demonstrations/tutorial_tn_circuits.py index 3bb5e7c3b1..f91b2999f4 100644 --- a/demonstrations/tutorial_tn_circuits.py +++ b/demonstrations/tutorial_tn_circuits.py @@ -138,7 +138,7 @@ def block(weights, wires): dev = qml.device("default.qubit", wires=4) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(template_weights): qml.MPS( wires=range(4), @@ -173,7 +173,7 @@ def deep_block(weights, wires): dev = qml.device("default.qubit", wires=4) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(template_weights): qml.MPS( wires=range(4), @@ -222,7 +222,7 @@ def wide_block(weights, wires): dev = qml.device("default.qubit", wires=8) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(template_weights): qml.MPS( wires=range(8), @@ -253,7 +253,7 @@ def block(weights, wires): dev = qml.device("default.qubit", wires=8) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(template_weights): qml.TTN( wires=range(8), @@ -330,7 +330,7 @@ def block(weights, wires): dev = qml.device("default.qubit", wires=4) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(image, template_weights): qml.BasisStatePreparation(image, wires=range(4)) qml.TTN( diff --git a/demonstrations/tutorial_trapped_ions.py b/demonstrations/tutorial_trapped_ions.py index fd990fadcf..ee95f54799 100644 --- a/demonstrations/tutorial_trapped_ions.py +++ b/demonstrations/tutorial_trapped_ions.py @@ -422,7 +422,7 @@ def evolution(phi, t): dev = qml.device("default.qubit", wires=1) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def ion_hadamard(state): if state == 1: @@ -440,7 +440,7 @@ def ion_hadamard(state): return qml.state() #For comparison, we use the Hadamard built into PennyLane -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def hadamard(state): if state == 1: @@ -459,7 +459,7 @@ def hadamard(state): # A similar exercise can be done for the :math:`T` gate: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def ion_Tgate(state): if state == 1: @@ -472,7 +472,7 @@ def ion_Tgate(state): return qml.state() -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def tgate(state): if state == 1: @@ -504,7 +504,7 @@ def tgate(state): import matplotlib.pyplot as plt -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def evolution_prob(t): qml.QubitUnitary(evolution(0, t / Omega), wires=0) @@ -811,7 +811,7 @@ def Molmer_Sorensen(t): dev2 = qml.device("default.qubit",wires=2) -@qml.qnode(dev2) +@qml.qnode(dev2, interface="autograd") def ion_cnot(basis_state): #Prepare the two-qubit basis states from the input @@ -827,7 +827,7 @@ def ion_cnot(basis_state): return qml.state() #Compare with built-in CNOT -@qml.qnode(dev2) +@qml.qnode(dev2, interface="autograd") def cnot_gate(basis_state): qml.templates.BasisStatePreparation(basis_state, wires=range(2)) diff --git a/demonstrations/tutorial_variational_classifier.py b/demonstrations/tutorial_variational_classifier.py index c4a7ff1059..411a8bcc0f 100644 --- a/demonstrations/tutorial_variational_classifier.py +++ b/demonstrations/tutorial_variational_classifier.py @@ -113,7 +113,7 @@ def statepreparation(x): # we call the parameters ``weights``. -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(weights, x): statepreparation(x) @@ -318,7 +318,7 @@ def statepreparation(a): ang = get_angles(x) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def test(angles): statepreparation(angles) @@ -355,7 +355,7 @@ def layer(W): # layer functions. -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def circuit(weights, angles): statepreparation(angles) diff --git a/demonstrations/tutorial_vqe.py b/demonstrations/tutorial_vqe.py index e8ebad0245..f5065bc8da 100644 --- a/demonstrations/tutorial_vqe.py +++ b/demonstrations/tutorial_vqe.py @@ -146,7 +146,7 @@ def circuit(param, wires): # run the cost function as an executable QNode with the gate parameter :math:`\theta`: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_fn(param): circuit(param, wires=range(qubits)) return qml.expval(H) diff --git a/demonstrations/tutorial_vqe_qng.py b/demonstrations/tutorial_vqe_qng.py index 4eecfdbccb..806a490372 100644 --- a/demonstrations/tutorial_vqe_qng.py +++ b/demonstrations/tutorial_vqe_qng.py @@ -64,7 +64,7 @@ def circuit(params, wires=0): H = qml.Hamiltonian(coeffs, obs) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_fn(params): circuit(params) return qml.expval(H) @@ -297,7 +297,7 @@ def ansatz(params, wires=[0, 1, 2, 3]): # the Hartree-Fock state of the hydrogen molecule described in the minimal basis. # Again, we define the cost function to be the following QNode that measures ``expval(H)``: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost(params): ansatz(params) return qml.expval(hamiltonian) diff --git a/demonstrations/tutorial_vqe_spin_sectors.py b/demonstrations/tutorial_vqe_spin_sectors.py index 04f03f2fc1..9596a81271 100644 --- a/demonstrations/tutorial_vqe_spin_sectors.py +++ b/demonstrations/tutorial_vqe_spin_sectors.py @@ -191,7 +191,7 @@ def circuit(params, wires): # a cost function that can be evaluated with the circuit parameters: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_fn(params): circuit(params, wires=range(qubits)) return qml.expval(H) @@ -202,7 +202,7 @@ def cost_fn(params): # we can now define a function to compute its expectation value: -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def S2_exp_value(params): circuit(params, wires=range(qubits)) return qml.expval(S2) @@ -304,13 +304,13 @@ def circuit(params, wires): # and the total spin operator for the new circuit. -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def cost_fn(params): circuit(params, wires=range(qubits)) return qml.expval(H) -@qml.qnode(dev) +@qml.qnode(dev, interface="autograd") def S2_exp_value(params): circuit(params, wires=range(qubits)) return qml.expval(S2) diff --git a/demonstrations/tutorial_vqls.py b/demonstrations/tutorial_vqls.py index 64d7db0792..d4c3ac1746 100644 --- a/demonstrations/tutorial_vqls.py +++ b/demonstrations/tutorial_vqls.py @@ -280,7 +280,7 @@ def variational_block(weights): dev_mu = qml.device("default.qubit", wires=tot_qubits) -@qml.qnode(dev_mu) +@qml.qnode(dev_mu, interface="autograd") def local_hadamard_test(weights, l=None, lp=None, j=None, part=None): # First Hadamard gate applied to the ancillary qubit. @@ -467,7 +467,7 @@ def cost_loc(weights): dev_x = qml.device("default.qubit", wires=n_qubits, shots=n_shots) -@qml.qnode(dev_x) +@qml.qnode(dev_x, interface="autograd") def prepare_and_sample(weights): # Variational circuit generating a guess for the solution vector |x> diff --git a/demonstrations/tutorial_vqt.py b/demonstrations/tutorial_vqt.py index c6138d962e..d5543fa344 100644 --- a/demonstrations/tutorial_vqt.py +++ b/demonstrations/tutorial_vqt.py @@ -274,7 +274,7 @@ def quantum_circuit(rotation_params, coupling_params, sample=None): # Constructs the QNode -qnode = qml.QNode(quantum_circuit, dev) +qnode = qml.QNode(quantum_circuit, dev, interface="autograd") ###################################################################### From 382178ec09772b68ccc27c4757db15d035a60329 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Wed, 22 Feb 2023 23:49:48 +0100 Subject: [PATCH 13/52] tmp --- demonstrations/tutorial_here_comes_the_sun.py | 47 ++++++++++++------- 1 file changed, 29 insertions(+), 18 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index b65be42584..eef90518db 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -157,6 +157,7 @@ import time start = time.process_time() +qml.enable_return() def two_qubit_decomp(params, wires): @@ -259,7 +260,7 @@ def circuit(params, operation=None): jax.config.update("jax_enable_x64", True) learning_rate = 5e-4 -num_steps = 200 +num_steps = 500 init_params = jax.numpy.array(init_params) grad_fn = jax.jit(jax.jacobian(qnode), static_argnums=1) qnode = jax.jit(qnode, static_argnums=1) @@ -267,6 +268,7 @@ def circuit(params, operation=None): ############################################################################## # With this configuration, let's run the optimization! +""" energies = {} for name, operation in operations.items(): params = init_params.copy() @@ -293,13 +295,10 @@ def circuit(params, operation=None): error = (energy - E_min) / abs(E_min) ax.plot(list(range(len(error))), error, label=name) -ax.set( - xlabel="Iteration", - ylabel="Relative error", - yscale="log", -) +ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() +""" ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` @@ -331,22 +330,38 @@ def circuit(params, operation=None): param_shape = (2, 2, num_wires // 2, d) init_params = jax.numpy.zeros(param_shape) -dev_shots = qml.device("default.qubit", wires=num_wires, shots=1000) -qnode_shots = qml.QNode(circuit, dev_shots, interface="jax") -grad_fn = jax.jacobian(qnode_shots) +dev_shots = qml.device("lightning.qubit", wires=num_wires, shots=100) + +def qnode_shots(params, operation, key): + dev = qml.device("default.qubit.jax", wires=4, shots=100, prng_key=key) + _qnode = qml.QNode(circuit, dev, interface="jax", diff_method="parameter-shift") + return _qnode(params, operation) + +#grad_fn = jax.jit(jax.grad(qnode_shots), static_argnums=1) +#qnode_shots = jax.jit(qnode_shots, static_argnums=1) +grad_fn = jax.grad(qnode_shots) + +num_steps = 200 + +# TODO: remove +from tqdm import tqdm energies_shots = {} for name, operation in operations.items(): + key = jax.random.PRNGKey(821321) params = init_params.copy() energy = [] - for step in range(num_steps): - cost = qnode(params, operation) - params = params - learning_rate * grad_fn(params, operation) + for step in tqdm(range(num_steps)): + key, use_key = jax.random.split(key) + cost = qnode_shots(params, operation, use_key) + key, use_key = jax.random.split(key) + params = params - learning_rate * grad_fn(params, operation, use_key) energy.append(cost) # Store energy value if step % 10 == 0: # Report current energy print(cost) - energy.append(qnode_shots(params, operation)) # Final energy value + key, use_key = jax.random.split(key) + energy.append(qnode_shots(params, operation, key)) # Final energy value energies_shots[name] = energy end = time.process_time() @@ -356,11 +371,7 @@ def circuit(params, operation=None): error = (energies_shots[name] - E_min) / abs(E_min) ax.plot(list(range(len(error))), error, label=name) -ax.set( - xlabel="Iteration", - ylabel="Relative error", - yscale="log", -) +ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() From e8811cdfe6d93b63335f6fe06ebbb02e491f48c1 Mon Sep 17 00:00:00 2001 From: Romain Moyard Date: Thu, 23 Feb 2023 16:32:33 -0500 Subject: [PATCH 14/52] Update classical shadows (#708) * More * typo * Trigger CI * lightning req no depth * Trigger CI --- demonstrations/tutorial_classical_shadows.py | 26 ++++++++++++-------- requirements.txt | 1 - requirements_no_deps.txt | 1 + 3 files changed, 17 insertions(+), 11 deletions(-) diff --git a/demonstrations/tutorial_classical_shadows.py b/demonstrations/tutorial_classical_shadows.py index b82544f943..80b7b87d3d 100644 --- a/demonstrations/tutorial_classical_shadows.py +++ b/demonstrations/tutorial_classical_shadows.py @@ -198,6 +198,7 @@ def calculate_classical_shadow(circuit_template, params, shadow_size, num_qubits # set up a two-qubit device with shots = 1 to ensure that we only get a single measurement dev = qml.device("default.qubit", wires=num_qubits, shots=1) + # simple circuit to prepare rho @qml.qnode(dev) def local_qubit_rotation_circuit(params, **kwargs): @@ -352,6 +353,7 @@ def shadow_state_reconstruction(shadow): dev = qml.device("default.qubit", wires=num_qubits, shots=1) + # circuit to create a Bell state and measure it in # the bases specified by the 'observable' keyword argument. @qml.qnode(dev) @@ -387,6 +389,7 @@ def bell_state_circuit(params, **kwargs): bell_state = np.array([[0.5, 0, 0, 0.5], [0, 0, 0, 0], [0, 0, 0, 0], [0.5, 0, 0, 0.5]]) + ############################################################################## # To measure the closeness we can use the operator norm. @@ -435,6 +438,7 @@ def operator_2_norm(R): plt.ylabel("Distance") plt.show() + ############################################################################## # As expected, when the number of snapshots increases, the state reconstruction # becomes closer to the ideal state. @@ -520,8 +524,8 @@ def estimate_shadow_obervable(shadow, observable, k=10): # assign the splits temporarily b_lists_k, obs_lists_k = ( - b_lists[i : i + shadow_size // k], - obs_lists[i : i + shadow_size // k], + b_lists[i: i + shadow_size // k], + obs_lists[i: i + shadow_size // k], ) # find the exact matches for the observable of interest at the specified locations @@ -581,8 +585,7 @@ def shadow_bound(error, observables, failure_rate=0.01): dev = qml.device("default.qubit", wires=num_qubits, shots=1) -@qml.qnode(dev) -def circuit(params, **kwargs): +def circuit_base(params, **kwargs): observables = kwargs.pop("observable") for w in range(num_qubits): qml.Hadamard(wires=w) @@ -594,6 +597,8 @@ def circuit(params, **kwargs): return [qml.expval(o) for o in observables] +circuit = qml.QNode(circuit_base, dev) + params = np.random.randn(2 * num_qubits) ############################################################################## @@ -604,9 +609,9 @@ def circuit(params, **kwargs): # O = \sum_{i=0}^{n-1} X_i X_{i+1} + Y_i Y_{i+1} + Z_i Z_{i+1}. list_of_observables = ( - [qml.PauliX(i) @ qml.PauliX(i + 1) for i in range(num_qubits - 1)] - + [qml.PauliY(i) @ qml.PauliY(i + 1) for i in range(num_qubits - 1)] - + [qml.PauliZ(i) @ qml.PauliZ(i + 1) for i in range(num_qubits - 1)] + [qml.PauliX(i) @ qml.PauliX(i + 1) for i in range(num_qubits - 1)] + + [qml.PauliY(i) @ qml.PauliY(i + 1) for i in range(num_qubits - 1)] + + [qml.PauliZ(i) @ qml.PauliZ(i + 1) for i in range(num_qubits - 1)] ) ############################################################################## @@ -652,9 +657,10 @@ def circuit(params, **kwargs): dev_exact = qml.device("default.qubit", wires=num_qubits) # change the simulator to be the exact one. -circuit.device = dev_exact +circuit = qml.QNode(circuit_base, dev_exact) + expval_exact = [ - circuit(params, wires=dev_exact.wires, observable=[o]) for o in list_of_observables + circuit(params, observable=[o]) for o in list_of_observables ] ############################################################################## @@ -691,7 +697,7 @@ def circuit(params, **kwargs): # calculate entanglement witnesses, and even find a way to approximate the von Neumann entropy. # These applications illustrate the potential power # of classical shadows for the characterization of quantum systems. - + ############################################################################## # References diff --git a/requirements.txt b/requirements.txt index cb793fce5c..3fb1c53526 100644 --- a/requirements.txt +++ b/requirements.txt @@ -16,7 +16,6 @@ pyscf==2.1.1 cirq-core==0.14.1 cirq-pasqal==0.14.1 openfermionpyscf==0.5 # required by 2 tutorials: tutorial_quantum_chemistry and tutorial_adaptive_circuits and tutorial_diffable_shadows -pennylane-lightning git+https://github.com/PennyLaneAI/pennylane.git git+https://github.com/PennyLaneAI/pennylane-sf.git git+https://github.com/PennyLaneAI/pennylane-cirq.git diff --git a/requirements_no_deps.txt b/requirements_no_deps.txt index fd5d3d3aa6..2cbcb376ed 100644 --- a/requirements_no_deps.txt +++ b/requirements_no_deps.txt @@ -1,2 +1,3 @@ mitiq==0.13.0 pyquil==2.21 +pennylane-lightning \ No newline at end of file From 942cbb57e9373dc0630d19e3a1a94b1071553146 Mon Sep 17 00:00:00 2001 From: David Wierichs Date: Fri, 24 Feb 2023 17:15:46 +0100 Subject: [PATCH 15/52] Update SPSA demo to count circuit executions manually. (#706) * new version of SPSA demo * Update demonstrations/spsa.py Co-authored-by: Josh Izaac * simplify code, update outputs and figures * Apply suggestions from code review Co-authored-by: Romain Moyard * review and tweaking * make spsa an executing tutorial * move file * fix links * fix some more links * author bio * line breaks, undo link change, fixing them actually * links... * links again... bio * update to count executions manually * reword device executions -> circuit executions. avoid recreating device and qnode * print executions --------- Co-authored-by: Josh Izaac Co-authored-by: Romain Moyard --- demonstrations/tutorial_spsa.py | 106 +++++++++++++++----------------- 1 file changed, 49 insertions(+), 57 deletions(-) diff --git a/demonstrations/tutorial_spsa.py b/demonstrations/tutorial_spsa.py index d4dcd6dee3..3c313a49df 100644 --- a/demonstrations/tutorial_spsa.py +++ b/demonstrations/tutorial_spsa.py @@ -14,7 +14,7 @@ tutorial_vqe_qng Accelerating VQEs with quantum natural gradient qnspsa Quantum natural SPSA optimizer -*Authors: Antal Szava & David Wierichs — Posted: 19 March 2021. Last updated: 10 February 2023.* +*Authors: Antal Szava & David Wierichs — Posted: 19 March 2021. Last updated: 23 February 2023.* In this tutorial, we investigate using a stochastic optimizer called the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm to optimize quantum @@ -29,7 +29,7 @@ 2. The variational quantum eigensolver on a simulated hardware device. Throughout the demo, we show results obtained with SPSA and with gradient -descent and also compare the number of device executions required to complete +descent and also compare the number of executed circuits required to complete each optimization. Background @@ -147,7 +147,7 @@ .. note:: - Just as with other PennyLane device, the number of samples taken for a device + Just as with other PennyLane device, the number of samples taken for a circuit execution can be specified using the ``shots`` keyword argument of the device. @@ -191,51 +191,44 @@ def circuit(param): ############################################################################## # We will execute a few optimizations in this demo, so let's prepare a convenience -# function that runs an optimizer instance and records the cost values and the -# number of device executions along the way. The latter will be an interesting -# quantity to evaluate the optimization cost on hardware! +# function that runs an optimizer instance and records the cost values +# along the way. Together with the number of executed circuits, this will be an +# interesting quantity to evaluate the optimization cost on hardware! -def run_optimizer(optimizer, cost_function, init_param, num_steps, interval): +def run_optimizer(opt, cost_function, init_param, num_steps, interval, execs_per_step): # Copy the initial parameters to make sure they are never overwritten param = init_param.copy() # Obtain the device used in the cost function dev = cost_function.device - # Initialize the memory for cost values and device executions during the optimization + # Initialize the memory for cost values during the optimization cost_history = [] - exec_history = [0] # Monitor the initial cost value cost_history.append(cost_function(param)) - execs_per_cost_eval = dev.num_executions + exec_history = [0] - print( - f"\nRunning the {optimizer.__class__.__name__} optimizer for {num_steps} iterations." - ) + print(f"\nRunning the {opt.__class__.__name__} optimizer for {num_steps} iterations.") for step in range(num_steps): - # Perform an update step - param = optimizer.step(cost_function, param) - - # Monitor the device executions, deducting the executions for cost monitoring - exec_history.append(dev.num_executions - (step + 1) * execs_per_cost_eval) - - # Monitor the cost value - cost_history.append(cost_function(param)) - # Print out the status of the optimization if step % interval == 0: print( - f"Iteration = {step:3d}, " - f"Device executions = {exec_history[step]:4d}, " + f"Step {step:3d}: Circuit executions: {exec_history[step]:4d}, " f"Cost = {cost_history[step]}" ) + # Perform an update step + param = opt.step(cost_function, param) + + # Monitor the cost value + cost_history.append(cost_function(param)) + exec_history.append((step + 1) * execs_per_step) + print( - f"Iteration = {num_steps:3d}, Device executions = {exec_history[-1]:4d}, " + f"Step {num_steps:3d}: Circuit executions: {exec_history[-1]:4d}, " f"Cost = {cost_history[-1]}" ) - return cost_history, exec_history @@ -269,32 +262,30 @@ def run_optimizer(optimizer, cost_function, init_param, num_steps, interval): num_steps_spsa = 200 opt = qml.SPSAOptimizer(maxiter=num_steps_spsa, c=0.15, a=0.2) +# We spend 2 circuit evaluations per step: +execs_per_step = 2 cost_history_spsa, exec_history_spsa = run_optimizer( - opt, cost_function, init_param, num_steps_spsa, 20 + opt, cost_function, init_param, num_steps_spsa, 20, execs_per_step ) ############################################################################## # Now let's perform the same optimization using gradient descent. We set the # step size according to a favourable value found after grid search for fast -# convergence. Note that we also create a new device in order to reset the -# execution count to 0. With the new device, we recreate the cost function as well. - -# Create a new device and a qnode as cost function -device = qml.device("qiskit.aer", wires=num_wires, shots=1000) -cost_function = qml.QNode(circuit, device) +# convergence. num_steps_grad = 15 opt = qml.GradientDescentOptimizer(stepsize=0.3) +# We spend 2 circuit evaluations per parameter per step: +execs_per_step = 2 * np.prod(param_shape) cost_history_grad, exec_history_grad = run_optimizer( - opt, cost_function, init_param, num_steps_grad, 3 + opt, cost_function, init_param, num_steps_grad, 3, execs_per_step ) ############################################################################## # SPSA and gradient descent comparison # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ # -# At this point, nothing else remains but to check which of these approaches did -# better! +# At this point, nothing else remains but to check which of these approaches did better! import matplotlib.pyplot as plt plt.figure(figsize=(10, 6)) @@ -302,7 +293,7 @@ def run_optimizer(optimizer, cost_function, init_param, num_steps, interval): plt.plot(exec_history_grad, cost_history_grad, label="Gradient descent") plt.plot(exec_history_spsa, cost_history_spsa, label="SPSA") -plt.xlabel("Device executions", fontsize=14) +plt.xlabel("Circuit executions", fontsize=14) plt.ylabel("Cost function value", fontsize=14) plt.grid() @@ -316,15 +307,15 @@ def run_optimizer(optimizer, cost_function, init_param, num_steps, interval): # compared to gradient descent! # # Let's take a deeper dive to see how much better it actually is by computing -# the ratio of required device executions to reach an absolute accuracy of 0.01. +# the ratio of required circuit executions to reach an absolute accuracy of 0.01. # grad_execs_to_prec = exec_history_grad[np.where(np.array(cost_history_grad) < -0.99)[0][0]] spsa_execs_to_prec = exec_history_spsa[np.where(np.array(cost_history_spsa) < -0.99)[0][0]] -print(f"Device execution ratio: {np.round(grad_execs_to_prec/spsa_execs_to_prec, 3)}.") +print(f"Circuit execution ratio: {np.round(grad_execs_to_prec/spsa_execs_to_prec, 3)}.") ############################################################################## # This means that SPSA found the minimum up to an absolute accuracy of 0.01 while -# using ten times fewer device executions than gradient descent! That's a huge +# using multiple times fewer circuit executions than gradient descent! That's an important # saving, especially when running the algorithm on actual quantum hardware. # # SPSA and the variational quantum eigensolver @@ -398,14 +389,18 @@ def circuit(param): # This random seed was used in the original VQE demo and is known to allow the # gradient descent algorithm to converge to the global minimum. np.random.seed(0) -init_param = np.random.normal(0, np.pi, (2, num_qubits, 3), requires_grad=True) +param_shape = (2, num_qubits, 3) +init_param = np.random.normal(0, np.pi, param_shape, requires_grad=True) # Initialize the optimizer - optimal step size was found through a grid search opt = qml.GradientDescentOptimizer(stepsize=2.2) +# We spend 2 * 15 circuit evaluations per parameter per step, as there are +# 15 Hamiltonian terms +execs_per_step = 2 * 15 * np.prod(param_shape) # Run the optimization cost_history_grad, exec_history_grad = run_optimizer( - opt, cost_function, init_param, num_steps_grad, 3 + opt, cost_function, init_param, num_steps_grad, 3, execs_per_step ) final_energy = cost_history_grad[-1] @@ -426,11 +421,11 @@ def circuit(param): plt.xticks(fontsize=13) plt.yticks(fontsize=13) -plt.xlabel("Device executions", fontsize=14) +plt.xlabel("Circuit executions", fontsize=14) plt.ylabel("Energy (Ha)", fontsize=14) plt.grid() -plt.axhline(y=true_energy, color="black", linestyle="dashed", label="True energy") +plt.axhline(y=true_energy, color="black", linestyle="--", label="True energy") plt.legend(fontsize=14) @@ -448,23 +443,19 @@ def circuit(param): # ^^^^^^^^^^^^^ # # Now let's perform the same experiment using SPSA for the VQE optimization. -# SPSA should use only 2 device executions per term in the expectation value. +# SPSA should use only 2 circuit executions per term in the expectation value. # Since there are 15 terms and we choose 160 iterations with two evaluations for # each gradient estimate, we expect 4800 total device -# executions. Again we create a new device and cost function in order to reset -# the number of executions. - -noisy_device = qml.device( - "qiskit.aer", wires=num_qubits, shots=1000, noise_model=noise_model -) -cost_function = qml.QNode(circuit, noisy_device) +# executions. num_steps_spsa = 160 opt = qml.SPSAOptimizer(maxiter=num_steps_spsa, c=0.3, a=1.5) -# Run the SPSA algorithm +# We spend 2 * 15 circuit evaluations per step, as there are 15 Hamiltonian terms +execs_per_step = 2 * 15 +# Run the optimization cost_history_spsa, exec_history_spsa = run_optimizer( - opt, cost_function, init_param, num_steps_spsa, 20 + opt, cost_function, init_param, num_steps_spsa, 20, execs_per_step ) final_energy = cost_history_spsa[-1] @@ -476,15 +467,16 @@ def circuit(param): ############################################################################## # The SPSA optimization seems to have found a similar energy value. # We again take a look at how the optimization curves compare, in particular -# with respect to the device executions spent on the task. +# with respect to the circuit executions spent on the task. plt.figure(figsize=(10, 6)) plt.plot(exec_history_grad, cost_history_grad, label="Gradient descent") plt.plot(exec_history_spsa, cost_history_spsa, label="SPSA") +plt.axhline(y=true_energy, color="black", linestyle="--", label="True energy") plt.title("$H_2$ energy from VQE using gradient descent vs. SPSA", fontsize=16) -plt.xlabel("Device executions", fontsize=14) +plt.xlabel("Circuit executions", fontsize=14) plt.ylabel("Energy (Ha)", fontsize=14) plt.grid() @@ -504,7 +496,7 @@ def circuit(param): # ---------- # # SPSA is a useful optimization technique that may be particularly beneficial on -# near-term quantum hardware. It uses significantly fewer device executions to achieve +# near-term quantum hardware. It uses significantly fewer circuit executions to achieve # comparable results as gradient-based methods, giving it the potential # to save time and resources. It can be a good alternative to # gradient-based methods when the optimization problem involves executing From 6d02ffc1feae30291a04c7c91f53fdaa71a29e39 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 15:16:30 +0100 Subject: [PATCH 16/52] large update, include gradient evaluation discussion --- demonstrations/tutorial_here_comes_the_sun.py | 246 ++++++++++++++---- .../tutorial_stochastic_parameter_shift.py | 4 +- 2 files changed, 203 insertions(+), 47 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index eef90518db..b2a1ed31dd 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -18,7 +18,7 @@ *Author: David Wierichs — Posted: xx March 2023.* Variational quantum algorithms have been promoted to be useful for many applications. -When designing such an algorithm, a central task is to choose the quantum circuit ansatz, +When designing these algorithms, a central task is to choose the quantum circuit ansatz, which provides a parametrization of quantum states. In the course of the variational algorithm, the circuit parameters are then optimized in order to minimize some cost function. The choice of the ansatz can have a big impact on the quantum states that can be found @@ -26,7 +26,7 @@ It also typically affects the cost of executing the algorithm on quantum hardware, and the strength of the noise that enters the computation. Finally, the application itself often influences, or -even fixes, the choice of ansatz, leading to constraints in the ansatz design. +even fixes, the choice of ansatz, which can lead to constraints in the ansatz design. .. figure:: ../demonstrations/here_comes_the_sun/pennylane_guy_scratching_head_in_front_of_circuits.png :align: center @@ -40,20 +40,22 @@ category of circuits. It is therefore interesting to construct circuit ansätze that are rather generic and -avoid arbitrary choices in the design that bias the optimization landscape. -On such approach is to perform the most general operations *locally* on a few qubits -and to reduce the design question to choosing the sets of qubits these operations are -applied to (as well as their order). In particular, we consider a general local operation +avoid arbitrary choices in the design that might bias the optimization landscape. +One such approach is to perform the most general operations *locally* on a few qubits +and to reduce the design question to choosing the subsets of qubits these operations are +applied to (as well as their order). In particular, we will consider a general local operation that comes without any preferred optimization direction. .. figure:: ../demonstrations/here_comes_the_sun/sun_fabric.png :align: center :width: 50% -In this tutorial, you will learn about a particular quantum gate which can act like -*any* gate on the corresponding qubits by chosing the parameters accordingly. -We will then look at a custom differentiation rule for this gate, construct -a simple ansatz, and use it in a toy minimization problem. +In this tutorial, you will learn about ``qml.SpecialUnitary``, a particular quantum gate which +can act like *any* gate on the corresponding qubits by chosing the parameters accordingly. +Then we will look at a custom derivative rule for this gate and compare it to two +alternative differentiation strategies. Finally, we will compare the performance of +``qml.SpecialUnitary`` for a toy minimization problem to the one of two alternative general +local gates. Let's start with a brief math intro (no really, just a little bit). @@ -107,22 +109,27 @@ cost function :math:`C` that should be minimized. If we want to use gradient-based optimization for this task, we need a method to compute the gradient :math:`\nabla C` in addition to the cost function itself. As derived in the publication [#wiersema]_, this is possible on quantum hardware -as long as the :math:`\mathrm{SU}(N)` gate itself can be implemented. +for :math:`\mathrm{SU}(N)` gates as long as the gates themselves can be implemented. +The implementation in PennyLane follows the decomposition idea described in App. F3, the +main text of [#wiersema]_ additionally proposes a method that scales better in some scenarios +but requires additional gates to be available on the quantum hardware. Here we will focus on the +former method. + We will not go through the entire derivation, but note the following key points: #. The gradient with respect to all :math:`d` parameters of an :math:`\mathrm{SU}(N)` gate can be computed using :math:`2d` auxiliary circuits. Each of the circuits contains one additional operation compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation - angles :math:`\pm\frac{\pi}{2}. Not that these Pauli rotations act on up to :math:`n` + angles :math:`\pm\frac{\pi}{2}. Note that these Pauli rotations act on up to :math:`n` qubits. - #. This differentiation uses automatic differentiation during compilation and postprocessing, - which becomes expensive for large :math:`n`, but the differentiation is quantum - hardware-compatible. + #. This differentiation method uses automatic differentiation during compilation and + classical coprocessing steps, but is compatible with quantum hardware. For large :math:`n`, + the classical processing steps quickly may become prohibitively expensive. #. The computed gradient is not an approximative technique but allows for an exact computation of the gradient on simulators. On quantum hardware, this leads to unbiased gradient estimators. #. With ``qml.SpecialUnitary`` and its gradient we effectively implement a so-called - Riemannian gradient flow on the qubits the gate acts on. + Riemannian gradient flow *locally*, i.e. on the qubits the gate acts on. The implementation in PennyLane takes care of creating the additional circuits and evaluating them, together with adequate post-processing into the gradient :math:`\nabla C`. @@ -131,34 +138,181 @@ :align: center :width: 50% -Comparing ansatz structures ---------------------------- +Comparing gradient methods +-------------------------- -We discussed above that there are many circuit architectures available and that choosing -a suitable ansatz is important but can be difficult. Here we will compare a simple ansatz -based on the ``qml.SpecialUnitary`` gate discussed above to other approaches that fully -parametrize the special unitary group for the respective number of qubits. -In particular, we will compare ``qml.SpecialUnitary`` to standard decompositions from the -literature that parametrize :math:`\mathrm{SU}(N)` with elementary gates, as well as to a sequence -of Pauli rotation gates that also allows to create any special unitary. -Let us start by defining the decomposition of a two-qubit unitary. -We choose the decomposition, which is optimal but not unique, from [#vatan]_. -The Pauli rotation sequence is available in PennyLane -via ``qml.ArbitraryUnitary`` and we will not need to implement it ourselves. +Before we dive into using ``qml.SpecialUnitary`` in an optimization task, let's compare +a few methods to compute the gradient with respect to the parameters of such a gate. +In particular, we will look at a finite difference approach, the stochastic parameter-shift +rule, and the custom gradient method we described above. +We will use the standard central difference recipe given by -- introduce one or two other ansätze with actually fewer parameters. +.. math:: + \partial_{\text{FD},\theta_j}C(\bm{\theta}) + =\left[C\left(\bm{\theta}+\frac{\delta}{2}\bm{e}_j\right) + -C\left(\bm{\theta}-\frac{\delta}{2}\bm{e}_j\right)\right] / \delta. + +Here, :math:`\delta` is a shift parameter we need to choose and :math:`\bm{e}_j` is the +:math:`j`-th canonical basis vector, i.e. the all-zeros vector with a one in the +:math:`j`-th entry. +The stochastic parameter-shift rule is a differentiation recipe developed for multi-parameter +gates like the :math:`\mathrm{SU}(N)` gates [#banchi]_. It involves the approximate +evaluation of an integration by sampling *splitting times* :math:`\tau` and evaluating an +expression close to the non-stochastic parameter-shift rule for each sample. For more details, +also consider the +:doc:`demo on the stochastic parameter-shift rule `. + +So let's dive into a toy example and explore the three gradient methods! +We start by defining a simple one-qubit circuit that contains a single :math:`\mathrm{SU}(2)` +gate and measures the expectation value of :math:`H=\frac{3}{5} Z - \frac{4}{5} Y`. +As ``qml.SpecialUnitary`` requires automatic differentiation subroutines even for the +hardware-ready derivative recipe, we will make use of PyTorch. """ import pennylane as qml import numpy as np +import torch + +dev = qml.device("default.qubit", wires=1) +H = 0.6 * qml.PauliZ(0) - 0.8 * qml.PauliY(0) + +@qml.qnode(dev, interface="torch") +def circuit(theta): + qml.SpecialUnitary(theta, wires=0) + return qml.expval(H) + +theta = torch.tensor([0.4, 0.2, -0.5], requires_grad=True) +energy = circuit(theta) + +print(energy) + +############################################################################## +# Now we need to set up the differentiation methods. For this demonstration, we will +# keep the first and last entry of ``theta`` fixed and only compute the gradient for the +# second parameter. +# +# We start with the central difference +# recipe, using a shift parameter of :math:`\delta=10^{-5}`. This choice of :math:`\delta` +# will be useful for the exactly simulated gradient but as we will see further below, +# it is much too small for realistic shot budgets on quantum hardware. + +# We compute the derivative with respect to the second entry of theta, so we need e_2: +unit_vector = torch.tensor([0., 1., 0.]) + +def central_diff_grad(theta, delta): + plus_eval = circuit(theta + delta / 2 * unit_vector) + minus_eval = circuit(theta - delta / 2 * unit_vector) + return (plus_eval - minus_eval) / delta -# TODO: remove import and timing -import time -start = time.process_time() -qml.enable_return() +delta = 1e-5 +print(central_diff_grad(theta, delta)) +############################################################################## +# Next up, we implement the stochastic parameter-shift rule. Of course we do not do +# so in full generality but for the particular circuit in this example. We will +# sample ten splitting times to obtain the gradient entry. For each splitting time, +# we need to insert a Pauli-:math:`Y` rotation (because :math:`\theta_2` belongs to +# the Pauli-:math:`Y` component of :math:`A(\bm{\theta})`). For this we define +# an auxiliary circuit. + +@qml.qnode(dev, interface="torch") +def aux_circuit(theta, tau, sign): + qml.SpecialUnitary(tau * theta, wires=0) + # This corresponds to the parameter-shift evaluations of RY at 0 + qml.RY(-sign * np.pi/2, wires=0) + qml.SpecialUnitary((1 - tau) * theta, wires=0) + return qml.expval(H) + + +def stochastic_parshift_grad(theta, num_samples): + grad = 0 + splitting_times = np.random.random(size=num_samples) + for tau in splitting_times: + # Evaluate the two-term parameter-shift rule of the auxiliar circuit + grad += (aux_circuit(theta, tau, 1.) - aux_circuit(theta, tau, -1.)) + return (grad / num_samples).detach() + +num_samples = 10 +print(stochastic_parshift_grad(theta, num_samples)) + +############################################################################## +# Finally, we can make use of the custom parameter-shift rule introduced in +# [#wiersema]_, which is readily available in PennyLane. Due to the implementation +# chosen internally, the full gradient is returned, so that we need to pick the +# gradient entry for the second entry manually. For this small toy problem, this is +# not an issue. + +sun_grad = lambda theta: qml.gradients.param_shift(circuit)(theta)[0][1] +print(sun_grad(theta)) + +############################################################################## +# We obtained three values for the gradient of interest, and they do not agree. +# So what is going on here? First, let's use automatic differentiation to compute +# the exact value and see which method agrees with it. + +energy.backward() +exact_grad = theta.grad[1] +print(exact_grad) + +############################################################################## +# As we can see, the custom differentiation method gave us the correct result, +# confirmed by automatic differentiation. Why do the other methods disagree? +# This is because the central difference recipe is an *approximate* gradient +# method. This means it has an error even if all circuit evaluations are +# made exact (up to numerical precision) like in the example above. +# As for the stochastic parameter-shift rule, you may already guess why there is +# a deviation: indeed, the *stochastic* nature of this method leads to derivative +# values that are scattered around the true value. It is an unbiased estimator, +# so that the average will approach the exact value with increasinlgy many evaluations. +# To demonstrate this, let's compute the same derivative many times and plot +# a histogram of what we get. We'll do so for ``num_samples=10`` and ``num_samples=100``. + +import matplotlib.pyplot as plt +from tqdm import tqdm + +fig, ax = plt.subplots(1, 1, figsize=(5, 4)) +for num_samples in [10, 100]: + grads = [stochastic_parshift_grad(theta, num_samples) for _ in tqdm(range(10))] + ax.hist(grads, label=f"{num_samples} samples") +ylim = ax.get_ylim() +ax.plot([exact_grad] * 2, ylim, ls="--", c="k", label="Exact") +ax.set(xlabel=r"$\partial_{SPS,\theta_2}C(\theta)$", ylim=ylim) +ax.legend() +plt.show() + +############################################################################## +# As we can see, the stochastic parameter-shift rule comes with a variance +# that can be reduced at the additional cost of evaluating the auxiliary circuit +# for more splitting times. +# +# On quantum hardware, all measurement results are statistical by nature anyways. +# So how does this stochasticity combine with the exact and stochastic nature +# of the three differentiation methods? We will not go into detail here but refer +# to [#wiersema]_ which shows that the custom differentiation rule proposed in the +# main text leads to the lowest mean squared error. For a single-qubit circuit +# similar to the one above, the derivative and expected variance are shown in the +# following plot from the manuscript: +# +# .. figure:: ../demonstrations/here_comes_the_sun/sampled_grad.pdf +# :align: center +# :width: 80% +# +# Comparing ansatz structures +# --------------------------- +# +# We discussed above that there are many circuit architectures available and that choosing +# a suitable ansatz is important but can be difficult. Here we will compare a simple ansatz +# based on the ``qml.SpecialUnitary`` gate discussed above to other approaches that fully +# parametrize the special unitary group for the respective number of qubits. +# In particular, we will compare ``qml.SpecialUnitary`` to standard decompositions from the +# literature that parametrize :math:`\mathrm{SU}(N)` with elementary gates, as well as to a sequence +# of Pauli rotation gates that also allows to create any special unitary. +# Let us start by defining the decomposition of a two-qubit unitary. +# We choose the decomposition, which is optimal but not unique, from [#vatan]_. +# The Pauli rotation sequence is available in PennyLane +# via ``qml.ArbitraryUnitary`` and we will not need to implement it ourselves. def two_qubit_decomp(params, wires): """Implement an arbitrary SU(4) gate on two qubits @@ -183,7 +337,7 @@ def two_qubit_decomp(params, wires): operations = { "Decomposition": two_qubit_decomp, "PauliRot sequence": qml.ArbitraryUnitary, - "\mathrm{SU}(N) gate": qml.SpecialUnitary, + "$\mathrm{SU}(N)$ gate": qml.SpecialUnitary, } ############################################################################## @@ -209,7 +363,7 @@ def two_qubit_decomp(params, wires): H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) # Compute the ground state energy E_min = np.linalg.eigvalsh(H).min() -print(E_min) +print(f"Ground state energy: {E_min:.5f}") H = qml.Hermitian(H, wires=wires) ############################################################################## @@ -218,13 +372,9 @@ def two_qubit_decomp(params, wires): # architecture with two blocks and each operation acting on ``num_wires_op=2`` qubits. # For this we define a ``QNode``: -# TODO: Remove -num_blocks = 2 num_wires_op = 2 d = num_wires_op**4 - 1 # d = 15 for two-qubit operations dev = qml.device("default.qubit", wires=num_wires) -# TODO: Remove the following line -param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) # two blocks with two layers each. Each layer contains three operations with d parameters each param_shape = (2, 2, 3, d) init_params = np.zeros(param_shape) @@ -268,12 +418,11 @@ def circuit(params, operation=None): ############################################################################## # With this configuration, let's run the optimization! -""" energies = {} for name, operation in operations.items(): params = init_params.copy() energy = [] - for step in range(num_steps): + for step in tqdm(range(num_steps)): cost = qnode(params, operation) params = params - learning_rate * grad_fn(params, operation) energy.append(cost) # Store energy value @@ -288,8 +437,6 @@ def circuit(params, operation=None): # outcomes differ notably. But let's take a look at the relative error in energy across the # optimization process. -import matplotlib.pyplot as plt - fig, ax = plt.subplots(1, 1) for name, energy in energies.items(): error = (energy - E_min) / abs(E_min) @@ -298,8 +445,8 @@ def circuit(params, operation=None): ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() -""" +exit() ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` # than for the other two general unitaries, while using the same number of parameters. This @@ -311,6 +458,9 @@ def circuit(params, operation=None): # by applying the parameter-shift rule, enabling training on quantum hardware # and shot-based simulators. # + + +""" # TODO: REVERT num_wires reduction once we can JIT the decomposition of SpecialUnitary? or: # As this simulation is more costly, we reduce the number of qubits to four. Therefore, we # require a new toy Hamiltonian and initial parameters, which we initialize together with @@ -374,6 +524,7 @@ def qnode_shots(params, operation, key): ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() +""" # # References @@ -389,6 +540,11 @@ def qnode_shots(params, operation, key): # R. Wiersema, D. Lewis, D. Wierichs, J. F. Carrasquilla, and N. Killoran, # in preparation, arXiv:23xx.xxxxx, (2023) # +# .. [#banchi] +# +# Leonardo Banchi and Gavin E. Crooks. "Measuring Analytic Gradients of +# General Quantum Evolution with the Stochastic Parameter Shift Rule." +# `Quantum **5** 386 `__ (2021). # # About the author # ---------------- diff --git a/demonstrations/tutorial_stochastic_parameter_shift.py b/demonstrations/tutorial_stochastic_parameter_shift.py index 441cfab79a..2bd88900e0 100644 --- a/demonstrations/tutorial_stochastic_parameter_shift.py +++ b/demonstrations/tutorial_stochastic_parameter_shift.py @@ -393,7 +393,7 @@ def spsr_circuit(gate_pars, s=None, sign=+1): # # Leonardo Banchi and Gavin E. Crooks. "Measuring Analytic Gradients of # General Quantum Evolution with the Stochastic Parameter Shift Rule." -# `arXiv:2005.10299 `__ (2020). +# `Quantum **5** 386 `__ (2021). # # .. [#li2016] # @@ -416,4 +416,4 @@ def spsr_circuit(gate_pars, s=None, sign=+1): # # About the author # ---------------- -# .. include:: ../_static/authors/nathan_killoran.txt \ No newline at end of file +# .. include:: ../_static/authors/nathan_killoran.txt From 75038804bc25d65e2e2b106b26df843a83c04343 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 15:32:11 +0100 Subject: [PATCH 17/52] some jax --- demonstrations/tutorial_here_comes_the_sun.py | 117 ++++-------------- 1 file changed, 27 insertions(+), 90 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index b2a1ed31dd..b6c1e66340 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -173,6 +173,10 @@ import pennylane as qml import numpy as np import torch +import jax +jax.config.update("jax_enable_x64", True) +jax.config.update("jax_platform_name", "cpu") +jnp = jax.numpy dev = qml.device("default.qubit", wires=1) H = 0.6 * qml.PauliZ(0) - 0.8 * qml.PauliY(0) @@ -182,6 +186,7 @@ def circuit(theta): qml.SpecialUnitary(theta, wires=0) return qml.expval(H) +_theta = jnp.array([0.4, 0.2, -0.5]) theta = torch.tensor([0.4, 0.2, -0.5], requires_grad=True) energy = circuit(theta) @@ -217,7 +222,8 @@ def central_diff_grad(theta, delta): # the Pauli-:math:`Y` component of :math:`A(\bm{\theta})`). For this we define # an auxiliary circuit. -@qml.qnode(dev, interface="torch") +@jax.jit +@qml.qnode(dev, interface="jax") def aux_circuit(theta, tau, sign): qml.SpecialUnitary(tau * theta, wires=0) # This corresponds to the parameter-shift evaluations of RY at 0 @@ -232,10 +238,10 @@ def stochastic_parshift_grad(theta, num_samples): for tau in splitting_times: # Evaluate the two-term parameter-shift rule of the auxiliar circuit grad += (aux_circuit(theta, tau, 1.) - aux_circuit(theta, tau, -1.)) - return (grad / num_samples).detach() + return (grad / num_samples) num_samples = 10 -print(stochastic_parshift_grad(theta, num_samples)) +print(stochastic_parshift_grad(_theta, num_samples)) ############################################################################## # Finally, we can make use of the custom parameter-shift rule introduced in @@ -267,19 +273,23 @@ def stochastic_parshift_grad(theta, num_samples): # values that are scattered around the true value. It is an unbiased estimator, # so that the average will approach the exact value with increasinlgy many evaluations. # To demonstrate this, let's compute the same derivative many times and plot -# a histogram of what we get. We'll do so for ``num_samples=10`` and ``num_samples=100``. +# a histogram of what we get. We'll do so for ``num_samples=2``, ``10`` and ``100``. import matplotlib.pyplot as plt from tqdm import tqdm -fig, ax = plt.subplots(1, 1, figsize=(5, 4)) -for num_samples in [10, 100]: - grads = [stochastic_parshift_grad(theta, num_samples) for _ in tqdm(range(10))] - ax.hist(grads, label=f"{num_samples} samples") +plt.rcParams.update({"font.size": 12}) + +fig, ax = plt.subplots(1, 1, figsize=(6, 4)) +colors = ["xkcd:peach", "xkcd:seafoam green", "xkcd:light purple"] +for num_samples, color in zip([2, 10, 100], colors): + grads = [stochastic_parshift_grad(_theta, num_samples) for _ in tqdm(range(1000))] + ax.hist(grads, label=f"{num_samples} samples", alpha=0.8, color=color) ylim = ax.get_ylim() ax.plot([exact_grad] * 2, ylim, ls="--", c="k", label="Exact") -ax.set(xlabel=r"$\partial_{SPS,\theta_2}C(\theta)$", ylim=ylim) +ax.set(xlabel=r"$\partial_{SPS,\theta_2}C(\theta)$", ylabel="Frequency", ylim=ylim) ax.legend() +plt.tight_layout() plt.show() ############################################################################## @@ -402,12 +412,13 @@ def circuit(params, operation=None): ############################################################################## # We can now proceed to preparing the optimization task using this circuit # and an optimization routine of our choice. For simplicity, we run a vanilla gradient -# descent optimization with fixed learning rate for 200 steps. For auto-differentiation -# we make use of JAX. +# descent optimization with fixed learning rate for 200 steps. This time, we use JAX +# for auto-differentiation. import jax jax.config.update("jax_enable_x64", True) +jax.config.update("jax_platform_name", "cpu") learning_rate = 5e-4 num_steps = 500 @@ -422,7 +433,7 @@ def circuit(params, operation=None): for name, operation in operations.items(): params = init_params.copy() energy = [] - for step in tqdm(range(num_steps)): + for step in range(num_steps): cost = qnode(params, operation) params = params - learning_rate * grad_fn(params, operation) energy.append(cost) # Store energy value @@ -438,94 +449,20 @@ def circuit(params, operation=None): # optimization process. fig, ax = plt.subplots(1, 1) -for name, energy in energies.items(): +for (name, energy), c in zip(energies.items(), colors): error = (energy - E_min) / abs(E_min) - ax.plot(list(range(len(error))), error, label=name) + ax.plot(list(range(len(error))), error, label=name, c=c) ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() -exit() ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` # than for the other two general unitaries, while using the same number of parameters. This # means that we found a particularly well-trainable parametrization of the local unitaries which -# allows to reduce the energy of the prepared quantum state more easily. -# -# Finally, let's look at the optimization behaviour with a shot-based device. After all, -# PennyLane supports the differentiation of all three two-qubit operations we are using -# by applying the parameter-shift rule, enabling training on quantum hardware -# and shot-based simulators. -# - - -""" -# TODO: REVERT num_wires reduction once we can JIT the decomposition of SpecialUnitary? or: -# As this simulation is more costly, we reduce the number of qubits to four. Therefore, we -# require a new toy Hamiltonian and initial parameters, which we initialize together with -# the shot-based device. - -num_wires = 4 -wires = list(range(num_wires)) -np.random.seed(62213) - -coefficients = np.random.randn(4**num_wires - 1) -basis = qml.ops.qubit.special_unitary.pauli_basis_matrices(num_wires) # Create the Pauli basis -H = qml.math.tensordot(coefficients, basis, axes=[[0], [0]]) -E_min = np.linalg.eigvalsh(H).min() -H = qml.Hermitian(H, wires=wires) -# TODO: Decide between the following lines -# param_shape = (num_blocks, num_wires_op, num_wires // num_wires_op, d) -param_shape = (2, 2, num_wires // 2, d) -init_params = jax.numpy.zeros(param_shape) - -dev_shots = qml.device("lightning.qubit", wires=num_wires, shots=100) - -def qnode_shots(params, operation, key): - dev = qml.device("default.qubit.jax", wires=4, shots=100, prng_key=key) - _qnode = qml.QNode(circuit, dev, interface="jax", diff_method="parameter-shift") - return _qnode(params, operation) - -#grad_fn = jax.jit(jax.grad(qnode_shots), static_argnums=1) -#qnode_shots = jax.jit(qnode_shots, static_argnums=1) -grad_fn = jax.grad(qnode_shots) - -num_steps = 200 - -# TODO: remove -from tqdm import tqdm - -energies_shots = {} -for name, operation in operations.items(): - key = jax.random.PRNGKey(821321) - params = init_params.copy() - energy = [] - for step in tqdm(range(num_steps)): - key, use_key = jax.random.split(key) - cost = qnode_shots(params, operation, use_key) - key, use_key = jax.random.split(key) - params = params - learning_rate * grad_fn(params, operation, use_key) - energy.append(cost) # Store energy value - if step % 10 == 0: # Report current energy - print(cost) - - key, use_key = jax.random.split(key) - energy.append(qnode_shots(params, operation, key)) # Final energy value - energies_shots[name] = energy - -end = time.process_time() -print(end - start) -fig, ax = plt.subplots(1, 1) -for name in operations.keys(): - error = (energies_shots[name] - E_min) / abs(E_min) - ax.plot(list(range(len(error))), error, label=name) - -ax.set(xlabel="Iteration", ylabel="Relative error") -ax.legend() -plt.show() -""" - +# allows to reduce the energy of the prepared quantum state more easily, while using the same +# number of parameters. # # References # ---------- From a03ad6ac0f88f6aefba1e66b6eae06589fa86492 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 15:32:25 +0100 Subject: [PATCH 18/52] add paper plot --- .../here_comes_the_sun/sampled_grad.pdf | Bin 0 -> 148082 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 demonstrations/here_comes_the_sun/sampled_grad.pdf diff --git a/demonstrations/here_comes_the_sun/sampled_grad.pdf b/demonstrations/here_comes_the_sun/sampled_grad.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4f66f9884828debe90d40360319407953381189d GIT binary patch literal 148082 zcmagG1yoeu_XkQ#BaCzn(j_s>&?QL2P$DJWU6O)yhcrVBNFyQLN_TgPv>@Fj@P_X% 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z0Wm_H?{&-Ys|;~bk_Zu+!}}Kq4lo?3!2tLy Date: Tue, 28 Feb 2023 16:52:05 +0100 Subject: [PATCH 20/52] black --- demonstrations/tutorial_here_comes_the_sun.py | 29 ++++++++++++------- 1 file changed, 18 insertions(+), 11 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index 0642cb64c0..532e575848 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -65,11 +65,11 @@ The gate we will look at is given by a specific parametrization of the special unitary group :math:`\mathrm{SU}(N)`, where :math:`N=2^n` is the Hilbert space dimension of the gate for :math:`n` qubits. Mathematically, the group can be defined as the set of operators -(or matrices) that can be inverted by taking their adjoint and that have +(or matrices) that can be inverted by taking their adjoint and that have determinant :math:`1`. All gates acting on :math:`n` qubits are elements of :math:`\mathrm{SU}(N)` up to a global phase. -The group :math:`\mathrm{SU}(N)` is a Lie group, and its associated Lie algebra +The group :math:`\mathrm{SU}(N)` is a Lie group, and its associated Lie algebra is :math:`\mathfrak{su}(N)`. For our purposes it will be sufficient to look at a matrix representation of the algebra and we may define it as @@ -79,7 +79,7 @@ We will use so-called canonical coordinates for the algebra which are simply the coefficients of an algebra element :math:`\Omega` in the Pauli basis: - + .. math:: \Omega &= \sum_{m=1}^d \theta_m G_m\\ @@ -97,7 +97,7 @@ The number of coordinates and of Pauli words in :math:`\mathcal{P}^{(n)}` is :math:`d=4^n-1`. Therefore, this will be the number of parameters a single ``qml.SpecialUnitary`` gate acting on -:math:`n` qubits will take. For example, it takes just three parameters for a single qubit and +:math:`n` qubits will take. For example, it takes just three parameters for a single qubit and a moderate number of 15 parameters for two qubits, but already requires 63 parameters for three qubits. @@ -120,12 +120,12 @@ #. The gradient with respect to all :math:`d` parameters of an :math:`\mathrm{SU}(N)` gate can be computed using :math:`2d` auxiliary circuits. Each of the circuits contains one additional operation compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation - angles :math:`\pm\frac{\pi}{2}. Note that these Pauli rotations act on up to :math:`n` + angles :math:`\pm\frac{\pi}{2}. Note that these Pauli rotations act on up to :math:`n` qubits. #. This differentiation method uses automatic differentiation during compilation and classical coprocessing steps, but is compatible with quantum hardware. For large :math:`n`, the classical processing steps quickly may become prohibitively expensive. - #. The computed gradient is not an approximative technique but allows for an exact computation + #. The computed gradient is not an approximative technique but allows for an exact computation of the gradient on simulators. On quantum hardware, this leads to unbiased gradient estimators. #. With ``qml.SpecialUnitary`` and its gradient we effectively implement a so-called @@ -156,7 +156,7 @@ gates like the :math:`\mathrm{SU}(N)` gates [#banchi]_. It involves the approximate evaluation of an integration by sampling *splitting times* :math:`\tau` and evaluating an expression close to the non-stochastic parameter-shift rule for each sample. For more details, -also consider the +also consider the :doc:`demo on the stochastic parameter-shift rule `. So let's dive into a toy example and explore the three gradient methods! @@ -169,6 +169,7 @@ import pennylane as qml import numpy as np import jax + jax.config.update("jax_enable_x64", True) jax.config.update("jax_platform_name", "cpu") jnp = jax.numpy @@ -176,10 +177,12 @@ dev = qml.device("default.qubit", wires=1) H = 0.6 * qml.PauliZ(0) - 0.8 * qml.PauliY(0) + def qfunc(theta): qml.SpecialUnitary(theta, wires=0) return qml.expval(H) + circuit = qml.QNode(qfunc, dev, interface="jax", diff_method="parameter-shift") theta = jnp.array([0.4, 0.2, -0.5]) @@ -195,7 +198,8 @@ def qfunc(theta): # it is much too small for realistic shot budgets on quantum hardware. # We compute the derivative with respect to the second entry of theta, so we need e_2: -unit_vector = np.array([0., 1., 0.]) +unit_vector = np.array([0.0, 1.0, 0.0]) + def central_diff_grad(theta, delta): plus_eval = circuit(theta + delta / 2 * unit_vector) @@ -214,12 +218,13 @@ def central_diff_grad(theta, delta): # the Pauli-:math:`Y` component of :math:`A(\bm{\theta})`). For this we define # an auxiliary circuit. + @jax.jit @qml.qnode(dev, interface="jax") def aux_circuit(theta, tau, sign): qml.SpecialUnitary(tau * theta, wires=0) # This corresponds to the parameter-shift evaluations of RY at 0 - qml.RY(-sign * np.pi/2, wires=0) + qml.RY(-sign * np.pi / 2, wires=0) qml.SpecialUnitary((1 - tau) * theta, wires=0) return qml.expval(H) @@ -229,8 +234,9 @@ def stochastic_parshift_grad(theta, num_samples): splitting_times = np.random.random(size=num_samples) for tau in splitting_times: # Evaluate the two-term parameter-shift rule of the auxiliar circuit - grad += (aux_circuit(theta, tau, 1.) - aux_circuit(theta, tau, -1.)) - return (grad / num_samples) + grad += aux_circuit(theta, tau, 1.0) - aux_circuit(theta, tau, -1.0) + return grad / num_samples + num_samples = 10 print(f"Stochastic parameter-shift: {stochastic_parshift_grad(theta, num_samples):.5f}") @@ -316,6 +322,7 @@ def stochastic_parshift_grad(theta, num_samples): # The Pauli rotation sequence is available in PennyLane # via ``qml.ArbitraryUnitary`` and we will not need to implement it ourselves. + def two_qubit_decomp(params, wires): """Implement an arbitrary SU(4) gate on two qubits using the decomposition from Theorem 5 in From 52b3c2c309cc705dc54c484b08089fcacb465736 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 17:01:10 +0100 Subject: [PATCH 21/52] tmp --- demonstrations/tutorial_here_comes_the_sun.py | 4 ++++ demos_optimization.rst | 4 ++-- 2 files changed, 6 insertions(+), 2 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index 532e575848..63d416d9d8 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -423,6 +423,7 @@ def circuit(params, operation=None): ############################################################################## # With this configuration, let's run the optimization! +""" energies = {} for name, operation in operations.items(): params = init_params.copy() @@ -436,12 +437,14 @@ def circuit(params, operation=None): energy.append(qnode(params, operation)) # Final energy value energies[name] = energy +""" ############################################################################## # So, did it work? Judging from the intermediate energy values it seems that the optimization # outcomes differ notably. But let's take a look at the relative error in energy across the # optimization process. +""" fig, ax = plt.subplots(1, 1) for (name, energy), c in zip(energies.items(), colors): error = (energy - E_min) / abs(E_min) @@ -450,6 +453,7 @@ def circuit(params, operation=None): ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() +""" ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` diff --git a/demos_optimization.rst b/demos_optimization.rst index 6ed8c6e0e8..16208fd21e 100644 --- a/demos_optimization.rst +++ b/demos_optimization.rst @@ -164,8 +164,8 @@ in quantum neural networks. :tags: optimization barren plateaus .. gallery-item:: - :tooltip: Construct and optimize circuits with generic quantum gates - :figure: demonstrations/here_comes_the_sun/thumbnail_tutorial_here_comes_the_sun.jpg + :tooltip: Construct and optimize circuits with SU(N) 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The gradient with respect to all :math:`d` parameters of an :math:`\mathrm{SU}(N)` gate can be computed using :math:`2d` auxiliary circuits. Each of the circuits contains one additional operation compared to the original circuit, namely a ``qml.PauliRot`` gate with rotation - angles :math:`\pm\frac{\pi}{2}. Note that these Pauli rotations act on up to :math:`n` + angles :math:`\pm\frac{\pi}{2}`. Note that these Pauli rotations act on up to :math:`n` qubits. #. This differentiation method uses automatic differentiation during compilation and classical coprocessing steps, but is compatible with quantum hardware. For large :math:`n`, @@ -193,9 +193,9 @@ def qfunc(theta): # second parameter. # # We start with the central difference -# recipe, using a shift parameter of :math:`\delta=10^{-4}`. This choice of :math:`\delta` -# will be useful for the exactly simulated gradient but as we will see further below, -# it is much too small for realistic shot budgets on quantum hardware. +# recipe, using a shift scale of :math:`\delta=0.75`. This choice of :math:`\delta`, +# which is much larger than usual for numerical differentiation on classical computers, +# is adapted to the scenario of shot-based gradients, as demonstrated further below. # We compute the derivative with respect to the second entry of theta, so we need e_2: unit_vector = np.array([0.0, 1.0, 0.0]) @@ -207,7 +207,7 @@ def central_diff_grad(theta, delta): return (plus_eval - minus_eval) / delta -delta = 1e-4 +delta = 0.75 print(f"Central difference: {central_diff_grad(theta, delta):.5f}") ############################################################################## @@ -303,9 +303,17 @@ def stochastic_parshift_grad(theta, num_samples): # similar to the one above, the derivative and expected variance are shown in the # following plot from the manuscript: # -# .. figure:: ../demonstrations/here_comes_the_sun/sampled_grad.pdf +# .. figure:: ../demonstrations/here_comes_the_sun/sampled_grad.png # :align: center # :width: 80% +# +# As we can see, the custom :math:`\mathrm{SU}(N)` parameter-shift rule produces the +# gradient estimates with the smallest variance. +# The central difference gradient shown here was obtained using the shift +# scale :math:`\delta=0.75` as well. As we can see, this suppresses the variance down to +# a level comparable to the one for the shift rule derivatives. As shown in App. F3 of +# [#wiersema]_, this scale indeed is close to the optimal choice if we were to compute +# the gradient with 100 shots per circuit. # # Comparing ansatz structures # --------------------------- From 0343d5cbeaf06ba79b0ee826bb7051f4162f1af9 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 21:11:07 +0100 Subject: [PATCH 24/52] black --- demonstrations/tutorial_here_comes_the_sun.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index c4e4789670..886779be55 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -306,7 +306,7 @@ def stochastic_parshift_grad(theta, num_samples): # .. figure:: ../demonstrations/here_comes_the_sun/sampled_grad.png # :align: center # :width: 80% -# +# # As we can see, the custom :math:`\mathrm{SU}(N)` parameter-shift rule produces the # gradient estimates with the smallest variance. # The central difference gradient shown here was obtained using the shift From f2162732347e6ec370934824f27180749a8c5e04 Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 21:13:58 +0100 Subject: [PATCH 25/52] uncomment. improve line breaks/naming --- demonstrations/tutorial_here_comes_the_sun.py | 14 +++++--------- 1 file changed, 5 insertions(+), 9 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index 886779be55..f2cfe402e5 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -386,13 +386,13 @@ def two_qubit_decomp(params, wires): ############################################################################## # Using the toy problem Hamiltonian and the three ansätze for :math:`\mathrm{SU}(N)` operations # from above, we create a circuit template that applies these operations in a brick-layer -# architecture with two blocks and each operation acting on ``num_wires_op=2`` qubits. +# architecture with two blocks and each operation acting on ``locality=2`` qubits. # For this we define a ``QNode``: -num_wires_op = 2 -d = num_wires_op**4 - 1 # d = 15 for two-qubit operations +locality = 2 +d = locality**4 - 1 # d = 15 for two-qubit operations dev = qml.device("default.qubit", wires=num_wires) -# two blocks with two layers each. Each layer contains three operations with d parameters each +# two blocks with two layers. Each layer contains three operations with d parameters param_shape = (2, 2, 3, d) init_params = np.zeros(param_shape) @@ -407,7 +407,7 @@ def circuit(params, operation=None): for i, params_layer in enumerate(params_block): for j, params_op in enumerate(params_layer): wires_op = [ - w % num_wires for w in range(num_wires_op * j + i, num_wires_op * (j + 1) + i) + w % num_wires for w in range(locality * j + i, locality * (j + 1) + i) ] operation(params_op, wires_op) return qml.expval(H) @@ -431,7 +431,6 @@ def circuit(params, operation=None): ############################################################################## # With this configuration, let's run the optimization! -""" energies = {} for name, operation in operations.items(): params = init_params.copy() @@ -445,14 +444,12 @@ def circuit(params, operation=None): energy.append(qnode(params, operation)) # Final energy value energies[name] = energy -""" ############################################################################## # So, did it work? Judging from the intermediate energy values it seems that the optimization # outcomes differ notably. But let's take a look at the relative error in energy across the # optimization process. -""" fig, ax = plt.subplots(1, 1) for (name, energy), c in zip(energies.items(), colors): error = (energy - E_min) / abs(E_min) @@ -461,7 +458,6 @@ def circuit(params, operation=None): ax.set(xlabel="Iteration", ylabel="Relative error") ax.legend() plt.show() -""" ############################################################################## # We find that the optimization indeed performs significantly better for ``qml.SpecialUnitary`` From 05f6b344e52755c5b7aa08994c89ed34509f8fac Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 21:19:48 +0100 Subject: [PATCH 26/52] hist colors --- demonstrations/tutorial_here_comes_the_sun.py | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/demonstrations/tutorial_here_comes_the_sun.py b/demonstrations/tutorial_here_comes_the_sun.py index f2cfe402e5..ecbfdb73fb 100644 --- a/demonstrations/tutorial_here_comes_the_sun.py +++ b/demonstrations/tutorial_here_comes_the_sun.py @@ -75,7 +75,8 @@ .. math:: - \mathfrak{su}(N) = \{\Omega \in \mathbb{C}^{N\times N}| \Omega^\dagger=-\Omega, \Tr{\Omega}=0\}. + \mathfrak{su}(N) = + \{\Omega \in \mathbb{C}^{N\times N}| \Omega^\dagger=-\Omega, \operatorname{Tr}[\Omega]=0\}. We will use so-called canonical coordinates for the algebra which are simply the coefficients of an algebra element :math:`\Omega` in the Pauli basis: @@ -279,14 +280,14 @@ def stochastic_parshift_grad(theta, num_samples): plt.rcParams.update({"font.size": 12}) fig, ax = plt.subplots(1, 1, figsize=(6, 4)) -colors = ["xkcd:peach", "xkcd:seafoam green", "xkcd:light purple"] +colors = ["#90CCFF", "#DF74AF", "#EED0B0"] for num_samples, color in zip([2, 10, 100], colors): grads = [stochastic_parshift_grad(theta, num_samples) for _ in range(1000)] ax.hist(grads, label=f"{num_samples} samples", alpha=0.8, color=color) ylim = ax.get_ylim() ax.plot([exact_grad] * 2, ylim, ls="--", c="k", label="Exact") ax.set(xlabel=r"$\partial_{SPS,\theta_2}C(\theta)$", ylabel="Frequency", ylim=ylim) -ax.legend() +ax.legend(loc="upper left") plt.tight_layout() plt.show() From 28f148517aac8bba3440388c6a5ebda121e7d43a Mon Sep 17 00:00:00 2001 From: dwierichs Date: Tue, 28 Feb 2023 22:24:01 +0100 Subject: [PATCH 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