{ "cells": [ { "cell_type": "markdown", "id": "c04e3ac9", "metadata": {}, "source": [ "# Differential equation resolution\n", "\n", "## Introduction\n", "\n", "We present here a Perceval implementation of a Quantum Machine Learning algorithm for solving differential equations. Its aims is to approximate the solution to the differential equation considered in \\[1\\]:\n", "\n", "$$\n", "\\frac{d f}{d x}+\\lambda f(x)(\\kappa+\\tan (\\lambda x))=0\n", "$$\n", "\n", "with boundary condition $f(0)=f_{0}$. The analytical solution is $f(x)=f_0\\exp (-\\kappa \\lambda x) \\cos (\\lambda x)$.\n", "\n", "### QML Loss Function Definition\n", "\n", "In order to use QML to solve this differential equation, we first need to derive from it a loss function whose minimum is associated to its analytical solution.\n", "\n", "Let $F\\left[\\left\\{d^{m} f / d x^{m}\\right\\}_{m},f, x\\right]=0$ be a general differential equation verified by $f(x)$, where $F[.]$ is an operator acting on $f(x)$, its derivatives and $x$. For the solving of a differential equation, the loss function described in \\[1\\] consists of two terms\n", "\n", "$$\n", " \\mathcal{L}_{\\boldsymbol{\\theta}}\\left[\\left\\{d^{m} g / d x^{m}\\right\\}_{m},g, x\\right]:=\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\mathrm{diff})}\\left[\\left\\{d^{m} g / d x^{m}\\right\\}_{m},g, x\\right]+\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\text {boundary})}[g, x].\n", "$$\n", "\n", "The first term $\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\mathrm{diff})}$ corresponds to the differential equation which has been discretised over a fixed regular grid of $M$ points noted $x_i$:\n", "\n", "$$\n", " \\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\mathrm{diff})}\\left[\\left\\{d^{m} g / d x^{m}\\right\\}_{m},g, x\\right]:=\\frac{1}{M} \\sum_{i=1}^{M} L\\left(F\\left[d_{x}^m g\\left(x_{i}\\right), g\\left(x_{i}\\right), x_{i}\\right], 0\\right),\n", "$$\n", "\n", "where $L(a,b) := (a - b)^2$ is the squared distance between two arguments. The second term $\\mathcal{L}_{\\boldsymbol{\\theta}}^{(\\text {boundary })}$ is associated to the initial conditions of our desired solution. It is defined as: \n", "\n", "$$\n", " \\mathcal{L}_{\\boldsymbol{\\theta}}^{\\text {(boundary) }}[g, x]:=\\eta L\\left(g(x_0), f_{0}\\right),\n", "$$\n", " \n", "where $\\eta$ is the weight granted to the boundary condition and $f_{0}$ is given by $f(x_0) = f_0$. \n", "\n", "Given a function approximator $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$, the loss function above will be minimised using a classical algorithm, updating the parameters $\\boldsymbol{\\theta}$ based on samples obtained using a quantum device.\n", "\n", "### Quantum circuit architecture\n", "\n", "The feature map used is presented in \\[2,3,4\\]. The quantum circuit architecture from \\[4\\] is expressed as $\\mathcal{U}(x, \\boldsymbol{\\theta}):=\\mathcal{W}^{(2)}\\left(\\boldsymbol{\\theta}_{2}\\right) \\mathcal{S}(x) \\mathcal{W}^{(1)}\\left(\\boldsymbol{\\theta}_{1}\\right).$ The phase-shift operator $\\mathcal{S}(x)$ incorporates the $x$ dependency of the function we wish to approximate. It is sandwiched between two universal interferometers $\\mathcal{W}^{(1)}(\\boldsymbol{\\theta_1})$ and $\\mathcal{W}^{(2)}(\\boldsymbol{\\theta_2})$, where the beam-splitter parameters $\\boldsymbol{\\theta_1}$ and $\\boldsymbol{\\theta_2}$ of this mesh architecture are tunable to enable training of the circuit.\n", "The output measurement operator, noted $\\mathcal{M}(\\boldsymbol{\\lambda})$, is the projection on the Fock states obtained using photon-number resolving detectors, multiplied by some coefficients $\\boldsymbol{\\lambda}$ which can also be tunable. Formally, we have:\n", "\n", "$$ \\mathcal{M}(\\boldsymbol{\\lambda}) = \\sum_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\lambda_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\mathbf{\\left | n^{(f)}\\right \\rangle}\\mathbf{\\left \\langle n^{(f)}\\right |},\n", "$$\n", "\n", "where the sum is taken over all $\\binom{n+m-1}{n}$ possible Fock states considering $n$ photons in $m$ modes. Let $\\mathbf{\\left | n^{(i)}\\right \\rangle} = \\left |n^{(i)}_1,n^{(i)}_2,\\dots,n^{(i)}_m\\right \\rangle$ be the input state consisting of $n$ photons where $n^{(i)}_j$ is the number of photons in input mode $j$. Given these elements, the circuit's output $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ is given by the following expectation value:\n", "\n", "$$\n", "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\left\\langle\\mathbf{n}^{(i)}\\left|\\mathcal{U}^{\\dagger}(x, \\boldsymbol{\\theta}) \\mathcal{M}(\\boldsymbol{\\lambda}) \\mathcal{U}(x, \\boldsymbol{\\theta})\\right| \\mathbf{n}^{(i)}\\right\\rangle.\n", "$$\n", "\n", "This expression can be rewritten as the following Fourier series \\[4\\]\n", "\n", "$$\n", "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\sum_{\\omega \\in \\Omega_{n}} c_{\\omega}(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda}) e^{i \\omega x},\n", "$$\n", "\n", "where $\\Omega_n = \\{-n, -n+1, \\dots, n-1, n \\}$ is the frequency spectrum one can reach with $n$ incoming photons and $\\{c_\\omega(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda})\\}$ are the Fourier coefficients. The $\\boldsymbol{\\lambda}$ parameters are sampled randomly in the interval $[-a;a]$, with $a$ a randomly chosen integer. $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ will serve as a function approximator for this chosen differential equation. Differentiation in the loss function is discretised as $\\frac{df}{dx} \\simeq \\frac{f(x+\\Delta x) - f(x-\\Delta x)}{2\\Delta x}$.\n", "\n", "$n, m,$ and $\\boldsymbol{\\lambda}$ are variable parameters defined below. $\\Delta x$ is the mesh size." ] }, { "cell_type": "markdown", "id": "e9df16c8", "metadata": {}, "source": [ "## Perceval Simulation\n", "\n", "### Initialisation" ] }, { "cell_type": "code", "execution_count": 1, "id": "7918962c", "metadata": {}, "outputs": [], "source": [ "import perceval as pcvl\n", "import numpy as np\n", "from math import comb, pi\n", "from scipy.optimize import minimize\n", "import time\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "import tqdm as tqdm" ] }, { "cell_type": "markdown", "id": "04323b71", "metadata": {}, "source": [ "We will run this notebook with 4 photons. We could use more photons, but the result with 4 photons is already satisfying." ] }, { "cell_type": "code", "execution_count": 2, "id": "f59b62f8", "metadata": {}, "outputs": [], "source": [ "nphotons = 4" ] }, { "cell_type": "markdown", "id": "bd3c3eaf", "metadata": {}, "source": [ "### Differential equation parameters\n", "\n", "We define here the value of the differential equation parameters and boundary condition $\\lambda, \\kappa, f_0$." ] }, { "cell_type": "code", "execution_count": 3, "id": "debd15cc", "metadata": {}, "outputs": [], "source": [ "# Differential equation parameters\n", "lambd = 8\n", "kappa = 0.1\n", "\n", "def F(u_prime, u, x): # DE, works with numpy arrays\n", " return u_prime + lambd * u * (kappa + np.tan(lambd * x))" ] }, { "cell_type": "code", "execution_count": 4, "id": "4c18efbf", "metadata": {}, "outputs": [], "source": [ "# Boundary condition (f(x_0)=f_0)\n", "x_0 = 0\n", "f_0 = 1" ] }, { "cell_type": "code", "execution_count": 5, "id": "ac67fd52", "metadata": {}, "outputs": [], "source": [ "# Modeling parameters\n", "n_grid = 50 # number of grid points of the discretized differential equation\n", "range_min = 0 # minimum of the interval on which we wish to approximate our function\n", "range_max = 1 # maximum of the interval on which we wish to approximate our function\n", "X = np.linspace(range_min, range_max-range_min, n_grid) # Optimisation grid" ] }, { "cell_type": "code", "execution_count": 6, "id": "45a02405", "metadata": {}, "outputs": [], "source": [ "# Differential equation's exact solution - for comparison\n", "def u(x):\n", " return np.exp(- kappa*lambd*x)*np.cos(lambd*x)" ] }, { "cell_type": "code", "execution_count": 7, "id": "9c8830ee", "metadata": {}, "outputs": [], "source": [ "# Parameters of the quantum machine learning procedure\n", "N = nphotons # Number of photons\n", "m = nphotons # Number of modes\n", "eta = 5 # weight granted to the initial condition\n", "a = 200 # Approximate boundaries of the interval that the image of the trial function can cover\n", "fock_dim = comb(N + m - 1, N)\n", "# lambda coefficients for all the possible outputs\n", "lambda_random = 2 * a * np.random.rand(fock_dim) - a\n", "# dx serves for the numerical differentiation of f\n", "dx = (range_max-range_min) / (n_grid - 1)" ] }, { "cell_type": "code", "execution_count": 8, "id": "355b87c8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "|1,1,1,1>\n" ] } ], "source": [ "# Input state with N photons and m modes\n", "input_state = pcvl.BasicState([1]*N+[0]*(m-N))\n", "print(input_state)" ] }, { "cell_type": "markdown", "id": "58385605", "metadata": {}, "source": [ "## Definition of the circuit\n", "\n", "We will generate a Haar-random initial unitary using QR decomposition built in Perceval `Matrix.random_unitary`, the circuit is defined by the combination of 3 sub-circuits - the intermediate phase is a parameter." ] }, { "cell_type": "code", "execution_count": 9, "id": "5dd4d6c3", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "W1\n", "\n", "\n", "Φ=px\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "W2\n", "\n", "\n", "\n", "\n", "0\n", "1\n", "2\n", "3\n", "0\n", "1\n", "2\n", "3\n", "" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"Haar unitary parameters\"\n", "# number of parameters used for the two universal interferometers (2*m**2 per interferometer)\n", "parameters = np.random.normal(size=4*m**2)\n", "\n", "px = pcvl.P(\"px\")\n", "c = pcvl.Unitary(pcvl.Matrix.random_unitary(m, parameters[:2 * m ** 2]), name=\"W1\")\\\n", " // (0, pcvl.PS(px))\\\n", " // pcvl.Unitary(pcvl.Matrix.random_unitary(m, parameters[2 * m ** 2:]), name=\"W2\")\n", "\n", "backend = pcvl.BackendFactory().get_backend(\"SLOS\")\n", "backend.set_circuit(pcvl.Unitary(pcvl.Matrix.random_unitary(m)))\n", "backend.preprocess([input_state])\n", "\n", "pcvl.pdisplay(c)" ] }, { "cell_type": "markdown", "id": "5d9333b0", "metadata": {}, "source": [ "### Expectation value and loss function computation\n", "\n", "The expectation value of the measurement operator $\\mathcal{M}(\\boldsymbol{\\lambda})$ is obtained directly from Fock state probabilities computed by Perceval. Given this expectation value, the code snippet below computes the loss function defined in the Introduction.\n", "\n", "Note the use of the `all_prob` simulator method giving directly access to the probabilities of all possible output states, including null probabilities. This calculation is optimized in SLOS backend." ] }, { "cell_type": "code", "execution_count": 10, "id": "597cce98", "metadata": {}, "outputs": [], "source": [ "def computation(params):\n", " global current_loss\n", " global computation_count\n", " \"compute the loss function of a given differential equation in order for it to be optimized\"\n", " computation_count += 1\n", " f_theta_0 = 0 # boundary condition\n", " coefs = lambda_random # coefficients of the M observable\n", " # initial condition with the two universal interferometers and the phase shift in the middle\n", " U_1 = pcvl.Matrix.random_unitary(m, params[:2 * m ** 2])\n", " U_2 = pcvl.Matrix.random_unitary(m, params[2 * m ** 2:])\n", "\n", " px = pcvl.P(\"x\")\n", " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n", "\n", " px.set_value(pi * x_0)\n", " backend.set_circuit(c)\n", " f_theta_0 = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", " # boundary condition given a weight eta\n", " loss = eta * (f_theta_0 - f_0) ** 2 * len(X)\n", "\n", " # Y[0] is before the domain we are interested in (used for differentiation), x_0 is at Y[1]\n", " Y = np.zeros(n_grid + 2)\n", "\n", " # x_0 is at the beginning of the domain, already calculated\n", " Y[1] = f_theta_0\n", "\n", " px.set_value(pi * (range_min - dx))\n", " backend.set_circuit(c)\n", " Y[0] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", "\n", " for i in range(1, n_grid):\n", " x = X[i]\n", " px.set_value(pi * x)\n", " backend.set_circuit(c)\n", " Y[i + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", " px.set_value(pi * (range_max + dx))\n", " backend.set_circuit(c)\n", " Y[n_grid + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n", "\n", " # Differentiation\n", " Y_prime = (Y[2:] - Y[:-2])/(2*dx)\n", "\n", " loss += np.sum((F(Y_prime, Y[1:-1], X))**2)\n", "\n", " current_loss = loss / len(X)\n", " return current_loss" ] }, { "cell_type": "markdown", "id": "8acf5506", "metadata": {}, "source": [ "### Classical optimisation\n", "\n", "Finally the code below performs the optimisation procedure using the loss function defined in the previous section. To this end, we use a Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimiser \\[5\\] from the SciPy library." ] }, { "cell_type": "code", "execution_count": 11, "id": "281dbb29", "metadata": {}, "outputs": [], "source": [ "def callbackF(parameters):\n", " \"\"\"callback function called by scipy.optimize.minimize allowing to monitor progress\"\"\"\n", " global current_loss\n", " global computation_count\n", " global loss_evolution\n", " global start_time\n", " now = time.time()\n", " pbar.set_description(\"M= %d Loss: %0.5f #computations: %d elapsed: %0.5f\" % \n", " (m, current_loss, computation_count, now-start_time))\n", " pbar.update(1)\n", " loss_evolution.append((current_loss, now-start_time))\n", " computation_count = 0\n", " start_time = now" ] }, { "cell_type": "code", "execution_count": 12, "id": "465db5d2", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "M= 4 Loss: 0.72454 #computations: 130 elapsed: 0.28313: : 73it [00:18, 4.04it/s]" ] } ], "source": [ "computation_count = 0\n", "current_loss = 0\n", "start_time = time.time()\n", "loss_evolution = []\n", "\n", "pbar = tqdm.tqdm()\n", "res = minimize(computation, parameters, callback=callbackF, method='BFGS', options={'gtol': 1E-2})" ] }, { "cell_type": "markdown", "id": "1be681a8", "metadata": {}, "source": [ "After the optimisation procedure has been completed, the optimal unitary parameters (in `res.x`) can be used to determine the quantum circuit beam-splitter and phase-shifter angles for an experimental realisation." ] }, { "cell_type": "code", "execution_count": 13, "id": "21726b0c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Unitary parameters [-0.06975017 -0.2137749 0.29586715 0.11662899 1.78980495 -2.54981998\n", " -1.21246855 -0.46867516 -0.39196635 0.36029635 0.65176279 0.05994574\n", " 1.03156629 2.36041462 -0.42133297 0.67378479 -0.35411464 0.48441608\n", " -0.16111306 0.47896372 -1.22189285 -2.52519371 1.5340219 -1.83381874\n", " 1.33130887 1.13673999 0.00560069 0.05349467 0.71196851 -0.90530917\n", " -1.49103508 0.74363026 -0.32739784 2.06170087 0.48562344 2.34570651\n", " 0.14646483 1.68797966 0.50301463 1.61160724 -0.67540257 0.80145772\n", " 1.3156154 1.04994756 -0.65910936 0.27274244 1.74786101 1.38742211\n", " -0.1995193 -0.19458001 0.79737876 3.44089144 -0.18072235 0.18529995\n", " 1.22062705 -0.55575132 0.34037724 -0.73251121 1.9526591 -0.86919895\n", " 0.72383362 0.21801201 0.7345075 1.57703996]\n" ] } ], "source": [ "print(\"Unitary parameters\", res.x)" ] }, { "cell_type": "markdown", "id": "3b6c5da8", "metadata": {}, "source": [ "### Plotting the approximation\n", "\n", "We now plot the result of our optimisation in order to compare the QML algorithm's output and the analytical solution." ] }, { "cell_type": "code", "execution_count": 14, "id": "6bede765", "metadata": {}, "outputs": [], "source": [ "def plot_solution(m, N, X, optim_params, lambda_random):\n", " Y = []\n", " U_1 = pcvl.Matrix.random_unitary(m, optim_params[:2 * m ** 2])\n", " U_2 = pcvl.Matrix.random_unitary(m, optim_params[2 * m ** 2:])\n", " px = pcvl.P(\"x\")\n", " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n", "\n", " for x in X:\n", " px.set_value(pi * x)\n", " backend.set_circuit(c)\n", " f_theta = np.sum(np.multiply(backend.all_prob(input_state), lambda_random))\n", " Y.append(f_theta)\n", " exact = u(X)\n", " plt.plot(X, Y, label=\"Approximation with {} photons\".format(N))" ] }, { "cell_type": "code", "execution_count": 15, "id": "b997c635", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.linspace(range_min, range_max, 200)\n", "\n", "# Change the plot size\n", "default_figsize = mpl.rcParamsDefault['figure.figsize']\n", "mpl.rcParams['figure.figsize'] = [2 * value for value in default_figsize]\n", "\n", "plot_solution(m, N, X, res.x, lambda_random)\n", "\n", "plt.plot(X, u(X), 'r', label='Analytical solution')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "id": "f819bb4b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Loss function value')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot([v[0] for v in loss_evolution])\n", "plt.yscale(\"log\")\n", "plt.xlabel(\"Number of epochs\")\n", "plt.ylabel(\"Loss function value\")" ] }, { "cell_type": "markdown", "id": "e53fa645", "metadata": {}, "source": [ "## References\n", "\n", "> [1] O. Kyriienko, A. E. Paine, and V. E. Elfving, “Solving nonlinear differential equations with differentiable quantum circuits”, [Physical Review A](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.052416) **103**, 052416 (2021).\n", "\n", "> [2] A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, “Data re-uploading for a universal quantum classifier”, [Quantum](https://quantum-journal.org/papers/q-2020-02-06-226/) **4**, 226 (2020).\n", "\n", "> [3] M. Schuld, R. Sweke, and J. J. Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models”, [Physical Review A]( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.032430) **103**, 032430 (2021).\n", "\n", "> [4] B. Y. Gan, D. Leykam, D. G. Angelakis, and D. G. Angelakis, “Fock State-enhanced Expressivity of Quantum Machine Learning Models”, in [Conference on Lasers andElectro-Optics](https://opg.optica.org/abstract.cfm?uri=CLEO_AT-2021-JW1A.73) (2021), paper JW1A.73. Optica Publishing Group, (2021).\n", "\n", "> [5] R. Fletcher, Practical methods of optimization. [John Wiley & Sons](https://onlinelibrary.wiley.com/doi/book/10.1002/9781118723203). (2013)." ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 5 }