From 9d6592f0cae9590af9a31d49d66ec227421dd641 Mon Sep 17 00:00:00 2001 From: Owen Lockwood <42878312+lockwo@users.noreply.github.com> Date: Tue, 9 Apr 2024 14:19:44 +0100 Subject: [PATCH] Add variational-quantum-eigensolver.ipynb Originally created in Qiskit/qiskit-ibm-runtime#235 Co-authored-by: ElePT Co-authored-by: Frank Harkins Co-authored-by: Ikko Hamamura Co-authored-by: Jessie Yu Co-authored-by: Jim Garrison Co-authored-by: Junye Huang Co-authored-by: Kevin Tian Co-authored-by: Paul Nation Co-authored-by: Rathish Cholarajan Co-authored-by: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Co-authored-by: Sanket Panda Co-authored-by: jspark971 Co-authored-by: kevin-tian Co-authored-by: lerongil --- .../variational-quantum-eigensolver.ipynb | 693 ++++++++++++++++++ 1 file changed, 693 insertions(+) create mode 100644 tutorials/runtime/variational-quantum-eigensolver/variational-quantum-eigensolver.ipynb diff --git a/tutorials/runtime/variational-quantum-eigensolver/variational-quantum-eigensolver.ipynb b/tutorials/runtime/variational-quantum-eigensolver/variational-quantum-eigensolver.ipynb new file mode 100644 index 00000000000..f1bf4ca96fd --- /dev/null +++ b/tutorials/runtime/variational-quantum-eigensolver/variational-quantum-eigensolver.ipynb @@ -0,0 +1,693 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "a6f69b77", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "[Variational quantum algorithms](https://arxiv.org/abs/2012.09265) are promising candidate hybrid-algorithms for observing the utility of quantum computation on noisy near-term devices. Variational algorithms are characterized by the use of a classical optimization algorithm to iteratively update a parameterized trial solution, or \"ansatz\". Chief among these methods is the Variational Quantum Eigensolver (VQE) that aims to solve for the ground state of a given Hamiltonian represented as a linear combination of Pauli terms, with an ansatz circuit where the number of parameters to optimize over is polynomial in the number of qubits. Given that size of the full solution vector is exponential in the number of qubits, successful minimization using VQE requires, in general, additional problem specific information to define the structure of the ansatz circuit.\n", + "\n", + "\n", + "Executing a VQE algorithm requires the following 3 components:\n", + "\n", + " 1. Hamiltonian and ansatz (problem specification)\n", + " 2. Qiskit Runtime estimator\n", + " 3. Classical optimizer\n", + " \n", + "Although the Hamiltonian and ansatz require domain specific knowledge to construct, these details are immaterial to the Runtime, and we can execute a wide class of VQE problems in the same manner. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "7db2e559", + "metadata": {}, + "source": [ + "## Setup\n", + "\n", + "Here we import the tools needed for a VQE experiment." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a0a48442", + "metadata": {}, + "outputs": [], + "source": [ + "# General imports\n", + "import numpy as np\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Pre-defined ansatz circuit and operator class for Hamiltonian\n", + "from qiskit.circuit.library import EfficientSU2\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "\n", + "# SciPy minimizer routine\n", + "from scipy.optimize import minimize\n", + "\n", + "# Plotting functions\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bc380c46", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibmq_mumbai'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# runtime imports\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, Session\n", + "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", + "\n", + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "988ee237", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n", + "\n", + "Here we define the problem instance for our VQE algorithm. Although the problem in question can come from a variety of domains, the form for execution through Qiskit Runtime is the same. Qiskit provides a convenience class for expressing Hamiltonians in Pauli form, and a collection of widely used ansatz circuits in the [`qiskit.circuit.library`](https://docs.quantum-computing.ibm.com/api/qiskit/circuit_library).\n", + "\n", + "Here, our example Hamiltonian is derived from a quantum chemistry problem" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "0ad66539", + "metadata": {}, + "outputs": [], + "source": [ + "hamiltonian = SparsePauliOp.from_list(\n", + " [(\"YZ\", 0.3980), (\"ZI\", -0.3980), (\"ZZ\", -0.0113), (\"XX\", 0.1810)]\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "acb83d48", + "metadata": {}, + "source": [ + "Our choice of ansatz is the `EfficientSU2` that, by default, linearly entangles qubits, making it ideal for quantum hardware with limited connectivity." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "59bffe5e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": { + "image/png": { + "height": 174, + "width": 820 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz = EfficientSU2(hamiltonian.num_qubits)\n", + "ansatz.decompose().draw(\"mpl\", style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "5bd1f7da", + "metadata": {}, + "source": [ + "From the previous figure we see that our ansatz circuit is defined by a vector of parameters, $\\theta_{i}$, with the total number given by:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "aa325696", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "num_params = ansatz.num_parameters\n", + "num_params" + ] + }, + { + "cell_type": "markdown", + "id": "ac6f36e3", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution." + ] + }, + { + "cell_type": "markdown", + "id": "ed01c675-6506-4779-bf71-74f0de9212fb", + "metadata": {}, + "source": [ + "To reduce the total job execution time, Qiskit Runtime V2 primitives only accept circuits (ansatz) and observables (Hamiltonian) that conforms to the instructions and connectivity supported by the target system (referred to as instruction set architecture (ISA) circuits and observables, respectively)." + ] + }, + { + "cell_type": "markdown", + "id": "3390069d-572c-472c-abb5-9cde12fd82a2", + "metadata": {}, + "source": [ + "### ISA Circuit" + ] + }, + { + "cell_type": "markdown", + "id": "ad6ddd99-b680-4ac4-b2d8-c0ac6266e6e8", + "metadata": {}, + "source": [ + "We can schedule a series of [`qiskit.transpiler`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler) passes to optimize our circuit for a selected backend and make it compatible with the instruction set architecture (ISA) of the backend. This can be easily done using a preset pass manager from `qiskit.transpiler` and its `optimization_level` parameter.\n", + "\n", + "- [`optimization_level`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler_preset#preset-pass-manager-generation): The lowest optimization level just does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits and adds swap gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates and qubits decohere over time, the shorter circuits should give better results." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "1834cb22", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "target = backend.target\n", + "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", + "\n", + "ansatz_isa = pm.run(ansatz)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "20d9923c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 7, + "metadata": { + "image/png": { + "height": 174, + "width": 1647 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz_isa.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "id": "aab9e309-d643-496f-ad4b-c90173102ad6", + "metadata": {}, + "source": [ + "### ISA Observable" + ] + }, + { + "cell_type": "markdown", + "id": "6c9e5dcd", + "metadata": {}, + "source": [ + "Similarly, we need to transform the Hamiltonian to make it backend compatible before running jobs with [`Runtime Estimator V2`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2#run). We can perform the transformation using the `apply_layout` the method of `SparsePauliOp` object." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "3451901c", + "metadata": {}, + "outputs": [], + "source": [ + "hamiltonian_isa = hamiltonian.apply_layout(layout=ansatz_isa.layout)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b4d480b3", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives.\n", + "\n", + "Like many classical optimization problems, the solution to a VQE problem can be formulated as minimization of a scalar cost function. By definition, VQE looks to find the ground state solution to a Hamiltonian by optimizing the ansatz circuit parameters to minimize the expectation value (energy) of the Hamiltonian. With the Qiskit Runtime [`Estimator`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2) directly taking a Hamiltonian and parameterized ansatz, and returning the necessary energy, the cost function for a VQE instance is quite simple.\n", + "\n", + "Note that the `run()` method of [Qiskit Runtime `EstimatorV2`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2) takes an iterable of `primitive unified blocs (PUBs)`. Each PUB is an iterable in the format `(circuit, observables, parameter_values: Optional, precision: Optional)`." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "b22a1b00", + "metadata": {}, + "outputs": [], + "source": [ + "def cost_func(params, ansatz, hamiltonian, estimator):\n", + " \"\"\"Return estimate of energy from estimator\n", + "\n", + " Parameters:\n", + " params (ndarray): Array of ansatz parameters\n", + " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", + " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", + " estimator (EstimatorV2): Estimator primitive instance\n", + "\n", + " Returns:\n", + " float: Energy estimate\n", + " \"\"\"\n", + " pub = (ansatz, [hamiltonian], [params])\n", + " result = estimator.run(pubs=[pub]).result()\n", + " energy = result[0].data.evs[0]\n", + "\n", + " return energy" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "179ba2c4", + "metadata": {}, + "source": [ + "Note that, in addition to the array of optimization parameters that must be the first argument, we use additional arguments to pass the terms needed in the cost function." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "91afc41c", + "metadata": {}, + "source": [ + "### Creating a callback function\n", + "\n", + "Callback functions are a standard way for users to obtain additional information about the status of an iterative algorithm. The standard SciPy callback routine allows for returning only the interim vector at each iteration. However, it is possible to do much more than this. Here, we show how to use a mutable object, such as a dictionary, to store the current vector at each iteration, for example in case we need to restart the routine due to failure, and also return the current iteration number and average time per iteration. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3b2f5808", + "metadata": {}, + "outputs": [], + "source": [ + "def build_callback(ansatz, hamiltonian, estimator, callback_dict):\n", + " \"\"\"Return callback function that uses Estimator instance,\n", + " and stores intermediate values into a dictionary.\n", + "\n", + " Parameters:\n", + " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", + " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", + " estimator (EstimatorV2): Estimator primitive instance\n", + " callback_dict (dict): Mutable dict for storing values\n", + "\n", + " Returns:\n", + " Callable: Callback function object\n", + " \"\"\"\n", + "\n", + " def callback(current_vector):\n", + " \"\"\"Callback function storing previous solution vector,\n", + " computing the intermediate cost value, and displaying number\n", + " of completed iterations and average time per iteration.\n", + "\n", + " Values are stored in pre-defined 'callback_dict' dictionary.\n", + "\n", + " Parameters:\n", + " current_vector (ndarray): Current vector of parameters\n", + " returned by optimizer\n", + " \"\"\"\n", + " # Keep track of the number of iterations\n", + " callback_dict[\"iters\"] += 1\n", + " # Set the prev_vector to the latest one\n", + " callback_dict[\"prev_vector\"] = current_vector\n", + " # Compute the value of the cost function at the current vector\n", + " # This adds an additional function evaluation\n", + " pub = (ansatz, [hamiltonian], [current_vector])\n", + " result = estimator.run(pubs=[pub]).result()\n", + " current_cost = result[0].data.evs[0]\n", + " callback_dict[\"cost_history\"].append(current_cost)\n", + " # Print to screen on single line\n", + " print(\n", + " \"Iters. done: {} [Current cost: {}]\".format(callback_dict[\"iters\"], current_cost),\n", + " end=\"\\r\",\n", + " flush=True,\n", + " )\n", + "\n", + " return callback" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "9f705072", + "metadata": {}, + "outputs": [], + "source": [ + "callback_dict = {\n", + " \"prev_vector\": None,\n", + " \"iters\": 0,\n", + " \"cost_history\": [],\n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "e80ff7d9", + "metadata": {}, + "source": [ + "We can now use a classical optimizer of our choice to minimize the cost function. Here, we use the [COBYLA routine from SciPy through the `minimize` function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html). Note that when running on real quantum hardware, the choice of optimizer is important, as not all optimizers handle noisy cost function landscapes equally well.\n", + "\n", + "To begin the routine, we specify a random initial set of parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d6b90cca", + "metadata": {}, + "outputs": [], + "source": [ + "x0 = 2 * np.pi * np.random.random(num_params)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d4587c1d-5d59-47aa-b36c-b6d07b5f84e4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5.07056716, 1.86434912, 1.27835939, 3.41939336, 5.05479277,\n", + " 1.863352 , 2.71667884, 5.03560174, 1.95941096, 3.16362623,\n", + " 5.92007134, 5.27294266, 1.72488001, 1.66385271, 4.23805393,\n", + " 5.34258604])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x0" + ] + }, + { + "cell_type": "markdown", + "id": "67d09ca9", + "metadata": {}, + "source": [ + "\n", + "Because we are sending a large number of jobs that we would like to execute together, we use a [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session) to execute all the generated circuits in one block. Here `args` is the standard SciPy way to supply the additional parameters needed by the cost function." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "61a802d2-5c58-4495-a617-f15fabef367e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iters. done: 169 [Current cost: -0.6057352426069124]\r" + ] + } + ], + "source": [ + "# To run on local simulator:\n", + "# 1. Use the Estimator from qiskit.primitives instead.\n", + "# 2. Remove the Session context manager below.\n", + "with Session(backend=backend) as session:\n", + " estimator = Estimator(session=session)\n", + " estimator.options.default_shots = 10_000\n", + "\n", + " callback = build_callback(ansatz_isa, hamiltonian_isa, estimator, callback_dict)\n", + "\n", + " res = minimize(\n", + " cost_func,\n", + " x0,\n", + " args=(ansatz_isa, hamiltonian_isa, estimator),\n", + " method=\"cobyla\",\n", + " callback=callback,\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "937f5a6e", + "metadata": {}, + "source": [ + "At the terminus of this routine we have a result in the standard SciPy `OptimizeResult` format. From this we see that it took `nfev` number of cost function evaluations to obtain the solution vector of parameter angles (`x`) that, when plugged into the ansatz circuit, yield the approximate ground state solution we were looking for." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "4e76845a-3fa0-4d12-86b5-de5b2bdee86c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " message: Optimization terminated successfully.\n", + " success: True\n", + " status: 1\n", + " fun: -0.6111644347854737\n", + " x: [ 6.916e+00 1.971e+00 ... 4.950e+00 5.211e+00]\n", + " nfev: 169\n", + " maxcv: 0.0" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res" + ] + }, + { + "cell_type": "markdown", + "id": "50b94af2", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "733431ad", + "metadata": {}, + "source": [ + "If the procedure terminates correctly, then the `prev_vector` and `iters` values in our `callback_dict` dictionary should be equal to the solution vector and total number of function evaluations, respectively. This is easy to verify:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "31dc35ea-6554-4ca7-9c3b-0b5394c46e4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all(callback_dict[\"prev_vector\"] == res.x)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "a90d1664-1728-4a8a-bb11-03f15e3f5639", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "callback_dict[\"iters\"] == res.nfev" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "19459b48", + "metadata": {}, + "source": [ + "We can also now view the progress towards convergence as monitored by the cost history at each iteration:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "8501d609", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 436, + "width": 588 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(range(callback_dict[\"iters\"]), callback_dict[\"cost_history\"])\n", + "ax.set_xlabel(\"Iterations\")\n", + "ax.set_ylabel(\"Cost\")\n", + "plt.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "ee3ac2fa", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.21.1'" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "11c9e788", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.1'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "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": "3.11.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}