{ "cells": [ { "cell_type": "markdown", "id": "55a74081-f24f-4dbb-84d5-bc9ca35c38bb", "metadata": {}, "source": [ "# QAOA Tutorial" ] }, { "cell_type": "code", "execution_count": 1, "id": "235b617e-835f-4cd8-b0eb-31e6ff126661", "metadata": {}, "outputs": [], "source": [ "# This example is from:\n", "# https://quantum.cloud.ibm.com/docs/en/tutorials/quantum-approximate-optimization-algorithm\n", "\n", "# Modified for Quantum Rings SDK" ] }, { "cell_type": "code", "execution_count": 2, "id": "47423a29-cbef-4a54-b521-66bc9cbf953c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Find this qiskit code at: https://learning.quantum.ibm.com/tutorial/quantum-approximate-optimization-algorithm\n", "import os\n", "import rustworkx as rx\n", "from rustworkx.visualization import mpl_draw as draw_graph\n", "import numpy as np\n", "\n", "n = 5\n", "\n", "graph = rx.PyGraph()\n", "graph.add_nodes_from(np.arange(0, n, 1))\n", "edge_list = [(0, 1, 1.0), (0, 2, 1.0), (0, 4, 1.0), (1, 2, 1.0), (2, 3, 1.0), (3, 4, 1.0)]\n", "graph.add_edges_from(edge_list)\n", "draw_graph(graph, node_size=600, with_labels=True)" ] }, { "cell_type": "code", "execution_count": 3, "id": "550c4e9b-4a25-4dd1-82a1-c57d7dba8634", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cost Function Hamiltonian: SparsePauliOp(['IIIZZ', 'IIZIZ', 'ZIIIZ', 'IIZZI', 'IZZII', 'ZZIII'],\n", " coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])\n" ] } ], "source": [ "from qiskit.quantum_info import SparsePauliOp\n", "def build_max_cut_paulis(graph: rx.PyGraph) -> list[tuple[str, float]]:\n", " \"\"\"Convert the graph to Pauli list.\n", "\n", " This function does the inverse of `build_max_cut_graph`\n", " \"\"\"\n", " pauli_list = []\n", " for edge in list(graph.edge_list()):\n", " paulis = [\"I\"] * len(graph)\n", " paulis[edge[0]], paulis[edge[1]] = \"Z\", \"Z\"\n", "\n", " weight = graph.get_edge_data(edge[0], edge[1])\n", "\n", " pauli_list.append((\"\".join(paulis)[::-1], weight))\n", "\n", " return pauli_list\n", "\n", "\n", "max_cut_paulis = build_max_cut_paulis(graph)\n", "\n", "cost_hamiltonian = SparsePauliOp.from_list(max_cut_paulis)\n", "print(\"Cost Function Hamiltonian:\", cost_hamiltonian)" ] }, { "cell_type": "code", "execution_count": 4, "id": "1fd3ace7-d0c9-43ac-8036-64bf5e6f7e0e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit.circuit.library import QAOAAnsatz\n", "\n", "circuit = QAOAAnsatz(cost_operator=cost_hamiltonian, reps=2)\n", "circuit.measure_all()\n", "\n", "circuit.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 5, "id": "e38bdaa0-da5a-49cf-8b79-497b48831bec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "ParameterView([ParameterVectorElement(β[0]), ParameterVectorElement(β[1]), ParameterVectorElement(γ[0]), ParameterVectorElement(γ[1])])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit.parameters" ] }, { "cell_type": "code", "execution_count": 6, "id": "464d4d8c-e656-4f19-aee1-83c35f1ad36c", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#from qiskit_ibm_runtime import QiskitRuntimeService\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "\n", "\n", "# QiskitRuntimeService.save_account(channel=\"ibm_quantum\", token=\"\", overwrite=True, set_as_default=True)\n", "#service = QiskitRuntimeService(channel='ibm_quantum')\n", "#backend = service.least_busy(min_num_qubits=127)\n", "#print(backend)\n", "\n", "from quantumrings.toolkit.qiskit import QrRuntimeService\n", "from quantumrings.toolkit.qiskit import QrBackendV2\n", "\n", "my_token = os.environ[\"QR_TOKEN\"]\n", "my_account = os.environ[\"QR_ACCOUNT\"]\n", "my_backend = \"scarlet_quantum_rings\"\n", "\n", "qr_services = QrRuntimeService(name = my_account, token = my_token)\n", "qr_backend = qr_services.backend(name = my_backend)\n", "\n", "# Create pass manager for transpilation\n", "pm = generate_preset_pass_manager(optimization_level=3,\n", " backend=qr_backend)\n", "\n", "candidate_circuit = pm.run(circuit)\n", "candidate_circuit.draw('mpl', fold=False, idle_wires=False)" ] }, { "cell_type": "code", "execution_count": 7, "id": "efa0e407-b25c-433a-8d61-844a70e1c5b6", "metadata": {}, "outputs": [], "source": [ "initial_gamma = np.pi\n", "initial_beta = np.pi/2\n", "init_params = [initial_gamma, initial_beta, initial_gamma, initial_beta]" ] }, { "cell_type": "code", "execution_count": 8, "id": "d7e2a02f-e9a7-46dc-b940-942ed78a4f00", "metadata": {}, "outputs": [], "source": [ "def cost_func_estimator(params, ansatz, hamiltonian, estimator):\n", "\n", " # transform the observable defined on virtual qubits to\n", " # an observable defined on all physical qubits\n", " isa_hamiltonian = hamiltonian.apply_layout(ansatz.layout)\n", "\n", " pub = (ansatz, isa_hamiltonian, params)\n", " job = estimator.run([pub])\n", "\n", " results = job.result()[0]\n", " cost = results.data.evs\n", "\n", " objective_func_vals.append(cost)\n", "\n", "\n", " return cost" ] }, { "cell_type": "code", "execution_count": 9, "id": "358285f8-8283-40e7-8683-7c7f7da80a7f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " message: Optimization terminated successfully.\n", " success: True\n", " status: 1\n", " fun: -2.3269959688186646\n", " x: [ 4.582e+00 1.231e+00 1.992e+00 1.489e+00]\n", " nfev: 38\n", " maxcv: 0.0\n" ] } ], "source": [ "#from qiskit_ibm_runtime import Session, EstimatorV2 as Estimator\n", "from qiskit_ibm_runtime import Session\n", "from scipy.optimize import minimize\n", "\n", "from quantumrings.toolkit.qiskit import QrEstimatorV2 as Estimator\n", "\n", "objective_func_vals = [] # Global variable\n", "with Session(backend=qr_backend) as session:\n", " # If using qiskit-ibm-runtime<0.24.0, change `mode=` to `session=`\n", " #estimator = Estimator(mode=session)\n", "\n", " estimator = Estimator(backend=qr_backend)\n", " estimator.options.default_shots = 1000\n", "\n", " # Set simple error suppression/mitigation options\n", " estimator.options.dynamical_decoupling.enable = True\n", " estimator.options.dynamical_decoupling.sequence_type = \"XY4\"\n", " estimator.options.twirling.enable_gates = True\n", " estimator.options.twirling.num_randomizations = \"auto\"\n", "\n", " result = minimize(\n", " cost_func_estimator,\n", " init_params,\n", " args=(candidate_circuit, cost_hamiltonian, estimator),\n", " method=\"COBYLA\",\n", " tol=1e-2,\n", " )\n", " print(result)" ] }, { "cell_type": "code", "execution_count": 10, "id": "c1f00782-7cc8-4863-b0c1-ceb828a15beb", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.figure(figsize=(12, 6))\n", "plt.plot(objective_func_vals)\n", "plt.xlabel(\"Iteration\")\n", "plt.ylabel(\"Cost\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "0f8b60df-3df9-40d2-958a-389e816c82d2", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimized_circuit = candidate_circuit.assign_parameters(result.x)\n", "optimized_circuit.draw('mpl', fold=False, idle_wires=False)" ] }, { "cell_type": "code", "execution_count": 12, "id": "b8917ad7-fe1e-4baf-a28d-ce77fff18b2e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{18: 0.0434, 20: 0.107, 10: 0.043, 11: 0.1044, 22: 0.1058, 9: 0.107, 5: 0.0889, 25: 0.0111, 28: 0.0108, 13: 0.0416, 14: 0.0303, 7: 0.0027, 3: 0.0112, 30: 0.0099, 12: 0.0351, 26: 0.0844, 21: 0.043, 1: 0.0106, 4: 0.011, 29: 0.0034, 17: 0.0325, 19: 0.0311, 6: 0.0095, 8: 0.0004, 24: 0.0044, 2: 0.0036, 27: 0.011, 16: 0.0004, 31: 0.001, 0: 0.001, 23: 0.0002, 15: 0.0003}\n" ] } ], "source": [ "#from qiskit_ibm_runtime import SamplerV2 as Sampler\n", "from quantumrings.toolkit.qiskit import QrSamplerV2 as Sampler\n", "\n", "# If using qiskit-ibm-runtime<0.24.0, change `mode=` to `backend=`\n", "sampler = Sampler(backend=qr_backend)\n", "\n", "sampler.options.default_shots = 10000\n", "\n", "# Set simple error suppression/mitigation options\n", "sampler.options.dynamical_decoupling.enable = True\n", "sampler.options.dynamical_decoupling.sequence_type = \"XY4\"\n", "sampler.options.twirling.enable_gates = True\n", "sampler.options.twirling.num_randomizations = \"auto\"\n", "\n", "pub= (optimized_circuit, )\n", "job = sampler.run([pub], shots=int(1e4))\n", "counts_int = job.result()[0].data.meas.get_int_counts()\n", "counts_bin = job.result()[0].data.meas.get_counts()\n", "shots = sum(counts_int.values())\n", "final_distribution_int = {key: val/shots for key, val in counts_int.items()}\n", "final_distribution_bin = {key: val/shots for key, val in counts_bin.items()}\n", "print(final_distribution_int)" ] }, { "cell_type": "code", "execution_count": 13, "id": "d3a8835b-32a9-4fbb-9759-ee25b4970327", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Result bitstring: [0, 0, 1, 0, 1]\n" ] } ], "source": [ "# auxiliary functions to sample most likely bitstring\n", "def to_bitstring(integer, num_bits):\n", " result = np.binary_repr(integer, width=num_bits)\n", " return [int(digit) for digit in result]\n", "\n", "keys = list(final_distribution_int.keys())\n", "values = list(final_distribution_int.values())\n", "most_likely = keys[np.argmax(np.abs(values))]\n", "most_likely_bitstring = to_bitstring(most_likely, len(graph))\n", "most_likely_bitstring.reverse()\n", "\n", "print(\"Result bitstring:\", most_likely_bitstring)" ] }, { "cell_type": "code", "execution_count": 14, "id": "257eab92-f1d9-4eed-8373-a00d47b56148", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib\n", "\n", "matplotlib.rcParams.update({\"font.size\": 10})\n", "final_bits = final_distribution_bin\n", "values = np.abs(list(final_bits.values()))\n", "top_4_values = sorted(values, reverse=True)[:4]\n", "positions = []\n", "for value in top_4_values:\n", " positions.append(np.where(values == value)[0])\n", "fig = plt.figure(figsize=(11, 6))\n", "ax = fig.add_subplot(1, 1, 1)\n", "plt.xticks(rotation=45)\n", "plt.title(\"Result Distribution\")\n", "plt.xlabel(\"Bitstrings (reversed)\")\n", "plt.ylabel(\"Probability\")\n", "ax.bar(list(final_bits.keys()), list(final_bits.values()), color=\"tab:grey\")\n", "for p in positions:\n", " ax.get_children()[int(p[0])].set_color(\"tab:purple\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "id": "d0296ac6-5e61-494d-9308-fa05513cd40f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# auxiliary function to plot graphs\n", "def plot_result(G, x):\n", " colors = [\"tab:grey\" if i == 0 else \"tab:purple\" for i in x]\n", " pos, default_axes = rx.spring_layout(G), plt.axes(frameon=True)\n", " rx.visualization.mpl_draw(G, node_color=colors, node_size=100, alpha=0.8, pos=pos)\n", "\n", "\n", "plot_result(graph, most_likely_bitstring)" ] }, { "cell_type": "code", "execution_count": 16, "id": "a3c277a0-61cb-4169-a4e5-fa1e431b01a4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The value of the cut is: 5\n" ] } ], "source": [ "from typing import Sequence\n", "def evaluate_sample(x: Sequence[int], graph: rx.PyGraph) -> float:\n", " assert len(x) == len(list(graph.nodes())), \"The length of x must coincide with the number of nodes in the graph.\"\n", " return sum(x[u] * (1 - x[v]) + x[v] * (1 - x[u]) for u, v in list(graph.edge_list()))\n", "\n", "\n", "cut_value= evaluate_sample(most_likely_bitstring, graph)\n", "print('The value of the cut is:', cut_value)" ] }, { "cell_type": "code", "execution_count": null, "id": "13a52dad-c1dc-4515-8118-d07eaeb3c918", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ee098c17-9561-4033-a103-95e0625c0e82", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "8df50820-beea-4fe6-9255-1384d83bc952", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }