{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QAOA Problems" ] }, { "attachments": { "image.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "The shallowest depth version of the QAOA consists of the application of two unitary operators: the problem unitary and the driver unitary. The first of these depends on the parameter $\\gamma$ and applies a phase to pairs of bits according to the problem-specific cost operator $C$:\n", "\n", "$$\n", " U_C \\! \\left(\\gamma \\right) = e^{-i \\gamma C } = \\prod_{j < k} e^{-i \\gamma w_{jk} Z_j Z_k}\n", "$$\n", "\n", "whereas the driver unitary depends on the parameter $\\beta$, is problem-independent, and serves to drive transitions between bitstrings within the superposition state:\n", "\n", "$$\n", " \\newcommand{\\gammavector}{\\boldsymbol{\\gamma}}\n", " \\newcommand{\\betavector}{\\boldsymbol{\\beta}}\n", " U_B \\! \\left(\\beta \\right) = e^{-i \\beta B} = \\prod_j e^{- i \\beta X_j},\n", " \\quad \\qquad\n", " B = \\sum_j X_j\n", "$$\n", "\n", "where $X_j$ is the Pauli $X$ operator on qubit $j$. These operators can be implemented by sequentially evolving under each term of the product; specifically the problem unitary is applied with a sequence of two-body interactions while the driver unitary is a single qubit rotation on each qubit. For higher-depth versions of the algorithm the two unitaries are sequentially re-applied each with their own $\\beta$ or $\\gamma$. The number of applications of the pair of unitaries is represented by the hyperparameter $p$ with parameters $\\gammavector = (\\gamma_1, \\dots, \\gamma_p)$ and $\\betavector = (\\beta_1, \\dots, \\beta_p)$. For $n$ qubits, we prepare the parameterized state\n", "\n", "$$\n", " \\newcommand{\\bra}[1]{\\langle #1|}\n", " \\newcommand{\\ket}[1]{|#1\\rangle}\n", " | \\gammavector , \\betavector \\rangle = U_B(\\beta_p) U_C(\\gamma_p ) \\cdots U_B(\\beta_1) U_C(\\gamma_1 ) \\ket{+}^{\\otimes n},\n", "$$\t\t\n", "where $\\ket{+}^{\\otimes n}$ is the symmetric superposition of computational basis states. \n", "\n", "![image.png](attachment:image.png)\n", "\n", "The optimization problems we study in this work are defined through a cost function with a corresponding quantum operator C given by\n", "\n", "$$\n", " C = \\sum_{j < k} w_{jk} Z_j Z_k\n", "$$\n", "\n", "where $Z_j$ dnotes the Pauli $Z$ operator on qubit $j$, and the $w_{jk}$ correspond to scalar weights with values $\\{0, \\pm1\\}$. Because these clauses act on at most two qubits, we are able to associate a graph with a given problem instance with weighted edges given by the $w_{jk}$ adjacency matrix." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import networkx as nx\n", "import numpy as np\n", "import scipy.optimize\n", "import cirq\n", "import recirq\n", "\n", "%matplotlib inline\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# theme colors\n", "QBLUE = '#1967d2'\n", "QRED = '#ea4335ff'\n", "QGOLD = '#fbbc05ff'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hardware Grid\n", "\n", "First, we study problem graphs which match the connectivity of our hardware, which we term \"Hardware Grid problems\". Despite results showing that problems on such graphs are efficient to solve on average, we study these problems as they do not require routing. This family of problems is composed of random instances generated by sampling $w_{ij}$ to be $\\pm 1$ for edges in the device topology or a subgraph thereof." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from recirq.qaoa.problems import get_all_hardware_grid_problems\n", "import cirq.contrib.routing as ccr\n", "\n", "hg_problems = get_all_hardware_grid_problems(\n", " device_graph=ccr.gridqubits_to_graph_device(recirq.get_device_obj_by_name('Sycamore23').qubits),\n", " central_qubit=cirq.GridQubit(6,3),\n", " n_instances=10,\n", " rs=np.random.RandomState(5)\n", ") \n", "\n", "instance_i = 0\n", "n_qubits = 23\n", "problem = hg_problems[n_qubits, instance_i]\n", "\n", "fig, ax = plt.subplots(figsize=(6,5))\n", "pos = {i: coord for i, coord in enumerate(problem.coordinates)}\n", "nx.draw_networkx(problem.graph, pos=pos, with_labels=False, node_color=QBLUE)\n", "if True: # toggle edge labels\n", " edge_labels = {(i1, i2): f\"{weight:+d}\"\n", " for i1, i2, weight in problem.graph.edges.data('weight')}\n", " nx.draw_networkx_edge_labels(problem.graph, pos=pos, edge_labels=edge_labels)\n", "ax.axis('off')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sherrington-Kirkpatrick model\n", "\n", "Next, we study instances of the Sherrington-Kirkpatrick (SK) model, defined on the complete graph with $w_{ij}$ randomly chosen to be $\\pm 1$. This is a canonical example of a frustrated spin glass and is most penalized by routing, which can be performed optimally using the linear swap networks at the cost of a linear increase in circuit depth. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from recirq.qaoa.problems import get_all_sk_problems\n", "\n", "n_qubits = 17\n", "all_sk_problems = get_all_sk_problems(max_n_qubits=17, n_instances=10, rs=np.random.RandomState(5))\n", "sk_problem = all_sk_problems[n_qubits, instance_i]\n", "\n", "fig, ax = plt.subplots(figsize=(6,5))\n", "pos = nx.circular_layout(sk_problem.graph)\n", "nx.draw_networkx(sk_problem.graph, pos=pos, with_labels=False, node_color=QRED)\n", "if False: # toggle edge labels\n", " edge_labels = {(i1, i2): f\"{weight:+d}\"\n", " for i1, i2, weight in sk_problem.graph.edges.data('weight')}\n", " nx.draw_networkx_edge_labels(sk_problem.graph, pos=pos, edge_labels=edge_labels)\n", "ax.axis('off')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3-regular MaxCut\n", "\n", "Finally, we study instances of the MaxCut problem on 3-regular graphs. This is a prototypical discrete optimization problem with a low, fixed node degree but a high dimension which cannot be trivially mapped to a planar architecture. It more closely matches problems of industrial interest. For these problems, we use an automated routing algorithm to heuristically insert SWAP operations." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from recirq.qaoa.problems import get_all_3_regular_problems\n", "\n", "n_qubits = 22\n", "instance_i = 0\n", "threereg_problems = get_all_3_regular_problems(max_n_qubits=22, n_instances=10, rs=np.random.RandomState(5))\n", "threereg_problem = threereg_problems[n_qubits, instance_i]\n", "\n", "fig, ax = plt.subplots(figsize=(6,5))\n", "pos = nx.spring_layout(threereg_problem.graph, seed=11)\n", "nx.draw_networkx(threereg_problem.graph, pos=pos, with_labels=False, node_color=QGOLD)\n", "if False: # toggle edge labels\n", " edge_labels = {(i1, i2): f\"{weight:+d}\"\n", " for i1, i2, weight in threereg_problem.graph.edges.data('weight')}\n", " nx.draw_networkx_edge_labels(threereg_problem.graph, pos=pos, edge_labels=edge_labels)\n", "ax.axis('off')\n", "fig.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }