{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#
Variational Quantum Eigensolver for an Interacting Scalar Field
\n", "\n", "Ryan LaRose
\n", "PHY 855/955 Final Project
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abstract
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we compute the ground state energy for a real scalar field with $\\lambda \\phi^4$ interaction. We use the Variational Quantum Eigensolver (VQE) with a product state ansatz consisting of three parameters. The notebook is designed to run on the \"Aspen-4-3Q-A\" lattice on [Rigetti Quantum Cloud Services](https://www.rigetti.com/qcs) which consists of three superconducting qubits, or on a quantum computer simulator designed to mimic this chip.\n", "\n", "Note that the code must be in a script to run on the actual quantum chip. This notebook is primarily for instructive purposes to explain what is happening in the script, the code of which is identical to this notebook." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Installing Software
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you don't have the necessary software installed (or are running on Binder), run the cells below. This will automatically install all the other requirements for the notebook." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\"\"\"Install software, if necessary. (Uncomment these lines if needed, then run the cell.)\"\"\"\n", "#!pip install pyquil==2.4.0\n", "#!pip install matplotlib\n", "#!pip install scipy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Imports
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first import the necessary packages. The software pyQuil is developed by Rigetti, a start-up quantum computing company founded by Chad Rigetti in California. Other companies have quantum computers (e.g. IBM and Google) as well as their own software to use them [1]. IBM's computers are based on a queue system, which makes is difficult to run variational quantum algorithms. Google's quantum computers are not currently open to the public. For these reasons, we use Rigetti." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "\"\"\"Imports.\"\"\"\n", "from math import pi\n", "import time\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.optimize import minimize\n", "\n", "from pyquil import Program, get_qc\n", "from pyquil.gates import H, S, RX, MEASURE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Constants and Parameters
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code cell below defines two important quantities for this notebook. First, the parameter `omega` dictates the interaction strength of the field (see Hamiltonian below). Second, the `computer` is which computer we will use to execute the algorithm. Quantum computer simulators are classical programs designed to mimic the (noiseless) evolution of a quantum computer. It is possible to artificially inject a noise model into a quantum computer simulator, which can be useful in a variety of situations." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "\"\"\"Parmeters/constants.\"\"\"\n", "# Value of \\omega_\\phi [1] which determines the interaction strength\n", "# omega = 1 <==> no interaction, omega --> 0 <==> large interaction\n", "omega = 0.5\n", "\n", "# Computer to run on\n", "simulator = \"3q-qvm\"\n", "qcomputer = \"Aspen-4-3Q-A\"\n", "computer = get_qc(qcomputer, as_qvm=True) # Change to as_qvm=False to run on QC. Must have reservation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Scalar Quantum Field theory
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider the scalar quantum field with $\\lambda \\phi^4$ interaction term, the Lagrangian of which can be written\n", "\n", "\\begin{equation}\n", " \\mathcal{L} = \\frac{1}{2} \\partial_\\mu \\phi \\partial^\\mu \\phi - \\frac{1}{2} m_0^2 \\phi^2 - \\frac{\\lambda_0^2}{4!} \\phi^4 .\n", "\\end{equation}\n", "\n", "Here, $m_0$ is the bare mass of the field. The physical mass gets affected by the interaction term $\\lambda_0 \\phi^4$. It is possible to renormalize the theory by computing the physical mass via $m = E_1 - E_0$ [2]. In this code, we only consider computing the ground state energy $E_0$. The first excited state energy could be computed by similar methods, for example those of [3].\n", "\n", "The steps to obtaining a qubit Hamiltonian from such a Lagrangian are described in detail in my write-up and slides. Below, we will use the form of the Hamiltonian derived in [4] for three qubits. \n", "\n", "\n", "We do mention one effect due to discretization. Namely, our lattice simulation is valid only at low energies (momenta), as can be seen by the following plot. This plot shows the continuous dispersion related and the discrete dispresion relation. The region where they overlap (at low momenta) is the valid region for our simulation. Note that coefficients in this plot were chosen arbitrarily for visual appearance. The effective shape of both curve and physics is contained in this plot, however." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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