diff --git a/docs/tutorials/01_chemistry_hamiltonian.ipynb b/docs/tutorials/01_chemistry_hamiltonian.ipynb index 16d11a8..de3af43 100644 --- a/docs/tutorials/01_chemistry_hamiltonian.ipynb +++ b/docs/tutorials/01_chemistry_hamiltonian.ipynb @@ -19,7 +19,7 @@ " - Draw samples from the ansatz using the ``Sampler`` primitive\n", "4. **Step 4: Post-process results**\n", " - Self-consistent configuration recovery loop\n", - " - Post-process the full set of bitstring samples, using prior knowledge of particle number and the most updated orbital occupancy information obtained from the ground state approximations at each iteration.\n", + " - Post-process the full set of bitstring samples, using prior knowledge of particle number and the average orbital occupancy calculated on the most recent iteration.\n", " - Probabilistically create batches of subsamples from recovered bitstrings.\n", " - Project and diagonalize the molecular Hamiltonian over each sampled subspace.\n", " - Save the minimum ground state energy found across all batches and update the avg orbital occupancy.\n", @@ -123,7 +123,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Overwritten attributes get_ovlp get_hcore of \n" + "Overwritten attributes get_hcore get_ovlp of \n" ] } ], @@ -236,8 +236,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "Gate counts (w/o pre-init passes): OrderedDict({'rz': 7405, 'sx': 6014, 'ecr': 2232, 'x': 315, 'measure': 32, 'barrier': 1})\n", - "Gate counts (w/ pre-init passes): OrderedDict({'rz': 4163, 'sx': 3189, 'ecr': 1262, 'x': 208, 'measure': 32, 'barrier': 1})\n" + "Gate counts (w/o pre-init passes): OrderedDict({'rz': 7403, 'sx': 6014, 'ecr': 2232, 'x': 315, 'measure': 32, 'barrier': 1})\n", + "Gate counts (w/ pre-init passes): OrderedDict({'rz': 4163, 'sx': 3189, 'ecr': 1262, 'x': 209, 'measure': 32, 'barrier': 1})\n" ] } ], @@ -468,7 +468,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -500,8 +500,8 @@ "axs[0].set_yticklabels(yt1)\n", "axs[0].axhline(y=n2_exact, color=\"red\", linestyle=\"--\", label=\"Exact\")\n", "axs[0].set_title(\"Approximated Ground State Energy vs SQD Iterations\")\n", - "axs[0].set_xlabel(\"Iteration Index\")\n", - "axs[0].set_ylabel(\"Energy (Ha)\")\n", + "axs[0].set_xlabel(\"Iteration Index\", fontdict={'fontsize': 12})\n", + "axs[0].set_ylabel(\"Energy (Ha)\", fontdict={'fontsize': 12})\n", "axs[0].legend()\n", "\n", "# Plot orbital occupancy\n", @@ -509,8 +509,8 @@ "axs[1].set_xticks(x2)\n", "axs[1].set_xticklabels(x2)\n", "axs[1].set_title(\"Avg Occupancy per Spatial Orbital\")\n", - "axs[1].set_xlabel(\"Orbital Index\")\n", - "axs[1].set_ylabel(\"Avg Occupancy\")\n", + "axs[1].set_xlabel(\"Orbital Index\", fontdict={'fontsize': 12})\n", + "axs[1].set_ylabel(\"Avg Occupancy\", fontdict={'fontsize': 12})\n", "\n", "plt.tight_layout()\n", "plt.show()" diff --git a/docs/tutorials/02_qubit_hamiltonian.ipynb b/docs/tutorials/02_qubit_hamiltonian.ipynb index abb24de..200a854 100644 --- a/docs/tutorials/02_qubit_hamiltonian.ipynb +++ b/docs/tutorials/02_qubit_hamiltonian.ipynb @@ -8,7 +8,7 @@ "\n", "In this tutorial we implement a [Qiskit pattern](https://docs.quantum.ibm.com/guides/intro-to-patterns) showing how to post-process quantum samples to compute an approximation to the ground state of a XX-Z spin-1/2 chain and two-point correlators. We will use the sample-based quantum diagonalization (SQD) technique introduced by [Robledo-Moreno et al., 2024](https://arxiv.org/abs/2405.05068).\n", "\n", - "While a Qiskit Pattern typically involves 4 steps, the aim of this tutorial is to focus on the post-processing of the samples obtained from a quantum circuit whose support coincides with that of the ground state. Consequently, we generate a synthetic set of bitstrings to define the subspace and do not design an ansatz nor sample from a quantum circuit in this tutorial.\n", + "While a Qiskit pattern typically involves 4 steps, the aim of this tutorial is to focus on the post-processing of the samples obtained from a quantum circuit whose support coincides with that of the ground state. Consequently, we generate a synthetic set of bitstrings to define the subspace and do not design an ansatz nor sample from a quantum circuit in this tutorial.\n", "\n", "The pattern we will implement is as follows:\n", "\n", @@ -17,7 +17,7 @@ "2. **Step 2: Optimize the problem**\n", " - N/A\n", "3. **Step 3: Execute experiments**\n", - " - N/A: Will generate synthetic QPU samples\n", + " - N/A: Will generate synthetic quantum samples\n", "4. **Step 4: Post-process results**\n", " - Project the Hamiltonian onto the subspace spanned by the samples\n", " - Diagonalize the Hamiltonian in the subspace to approximate the ground state" @@ -36,7 +36,7 @@ "$$\n", "\n", "with $\\alpha_i$ being real coefficients and $P_i$ Pauli strings. A wide class\n", - "of many-body Hamiltonians can be written as the linear combination of poly-many \n", + "of many-body Hamiltonians can be written as the linear combination of polynomially-many \n", "Pauli strings, including interacting-electron Hamiltonians, spin Hamiltonians, etc.\n", "\n", "In particular, we consider the ground state properties of the antiferromagnetic XX-Z spin-1/2 chain\n", @@ -145,7 +145,7 @@ "source": [ "### Step 4: Post-process the results\n", "\n", - "Using the [scipy.sparse.linalg.eigsh](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html#eigsh) arguments, we request the ``k=4`` to specify we want ``4`` eigenstates, and we set ``which=\"SA\"`` to specify we want the smallest algebraic eigenstates." + "Using the [scipy.sparse.linalg.eigsh](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html#eigsh) arguments, we request ``\"k\": 4`` to specify we want ``4`` eigenstates, and we set ``\"which\": \"SA\"`` to specify we want the smallest algebraic eigenstates." ] }, { @@ -315,19 +315,9 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 7, "metadata": {}, "outputs": [ - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'single-site magnetization')" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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", @@ -350,7 +340,8 @@ " [r\"$\\langle\\sigma^x_i\\rangle$\", r\"$\\langle\\sigma^y_i\\rangle$\", r\"$\\langle\\sigma^z_i\\rangle$\"]\n", ")\n", "plt.xlabel(\"site, $i$\")\n", - "plt.ylabel(\"single-site magnetization\")" + "plt.ylabel(\"single-site magnetization\")\n", + "plt.show()" ] }, { @@ -358,7 +349,7 @@ "metadata": {}, "source": [ "Once we have computed the average magnetization on each site, we can compute the \n", - "connected correlator as well." + "connected correlators as well." ] }, { @@ -417,19 +408,9 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 9, "metadata": {}, "outputs": [ - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'spin-spin correlators')" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - }, { "data": { "image/png": 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", @@ -455,7 +436,8 @@ "\n", "plt.legend([r\"$C^x(\\ell)$\", r\"$C^y(\\ell)$\", r\"$C^z(\\ell)$\"])\n", "plt.xlabel(r\"site, $\\ell$\")\n", - "plt.ylabel(\"spin-spin correlators\")" + "plt.ylabel(\"spin-spin correlators\")\n", + "plt.show()" ] } ],