{ "cells": [ { "cell_type": "markdown", "id": "66419b7d", "metadata": {}, "source": [ "We are looking at the problem Max $k$XOR, where each variable is involved in $D+1$ clauses and has no overlapping constraints.\n", "\n", "This is code comparing one-local algorithms: Hirvonen's threshold algorithm and Farhi's QAOA at depth 1." ] }, { "cell_type": "code", "execution_count": 1, "id": "538e24e5", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_78203/3810261615.py:3: MatplotlibDeprecationWarning: \n", "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist, which provide the same functionality instead.\n", " from mpl_toolkits.axes_grid.inset_locator import (inset_axes, InsetPosition, mark_inset)\n" ] } ], "source": [ "from functools import lru_cache\n", "from matplotlib.ticker import StrMethodFormatter\n", "from mpl_toolkits.axes_grid.inset_locator import (inset_axes, InsetPosition, mark_inset)\n", "from numpy import cos, sin, tan, arctan as atan\n", "from scipy.optimize import minimize\n", "from scipy.special import binom, erf\n", "from sympy import exp, simplify, expand, expand_trig, trigsimp\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sympy\n", "import time\n", "plt.rc('axes', axisbelow=True)" ] }, { "cell_type": "code", "execution_count": 2, "id": "478adeea", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting time: Sat Sep 11 18:13:44 2021\n" ] } ], "source": [ "print(\"Starting time:\", time.ctime())" ] }, { "cell_type": "markdown", "id": "57557cb9", "metadata": {}, "source": [ "# QAOA for Max 3XOR" ] }, { "cell_type": "code", "execution_count": 3, "id": "a16babfd", "metadata": {}, "outputs": [], "source": [ "def qaoa_perf_3xor(s, D):\n", " return s/ ( 1 + 3/(1 - s*s)**D)**0.5" ] }, { "cell_type": "code", "execution_count": 4, "id": "b2d3a947", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sin{\\left(\\gamma \\right)}}{\\left(1 + 3 \\left(1 - \\sin^{2}{\\left(\\gamma \\right)}\\right)^{- D}\\right)^{0.5}}$" ], "text/plain": [ "(1 + 3*(1 - sin(gamma)**2)**(-D))**(-0.5)*sin(gamma)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gamma = sympy.Symbol('gamma')\n", "D_symbol = sympy.Symbol('D')\n", "qaoa_perf_3xor(sympy.sin(gamma), D_symbol)" ] }, { "cell_type": "code", "execution_count": 5, "id": "6c1f7305", "metadata": {}, "outputs": [], "source": [ "Ds = [5, 10, 20, 50, 100, 500, 1000, 5000, 10000, 50000, 500000]\n", "inps = np.linspace(0, 3, 100000)" ] }, { "cell_type": "code", "execution_count": 6, "id": "d8aeff7f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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