{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Parameters & Optimisation\n", "In this tutorial, parameters are introduced within a circuit and used to quickly adjust values within it as part of an optimisation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.optimize import minimize\n", "\n", "import lightworks as lw" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, the parameterized circuit is created. This is a Reck interferometer, which has a triangular shape, and should be capable of implementing any unitary matrix across its modes. \n", "\n", "Each unit cell of the interferometer contains an external phase shift and a Mach-Zehnder interferometer, comprised of two 50:50 beam splitters with a phase shift between them. For each of the unit cells, a theta and phi parameter are created and added to the dictionary, these are then assigned to the corresponding phase shift elements. All parameters are configured with bounds of $0-2\\pi$ and labels are assigned which are utilized when displaying the circuit." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "0\n", "1\n", "2\n", "3\n", "4\n", "\n", "\n", "PS\n", "φ = phi_0_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_0_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_0_1\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_0_1\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_0_2\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_0_2\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_0_3\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_0_3\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_1_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_1_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_1_1\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_1_1\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_1_2\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_1_2\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_2_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_2_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_2_1\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_2_1\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = phi_3_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = theta_3_0\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create new circuit\n", "n_modes = 5\n", "reck = lw.PhotonicCircuit(n_modes)\n", "\n", "# For storing parameters\n", "pdict = lw.ParameterDict()\n", "\n", "for i in range(n_modes - 1):\n", " for j in range(0, n_modes - 1 - i, 1):\n", " reck.barrier([j, j + 1]) # Use barrier to separate unit cells\n", "\n", " # Create new parameters for theta and phi\n", " theta, phi = f\"theta_{i}_{j}\", f\"phi_{i}_{j}\"\n", " pdict[theta] = lw.Parameter(0, bounds=[0, 2 * np.pi], label=theta)\n", " pdict[phi] = lw.Parameter(0, bounds=[0, 2 * np.pi], label=phi)\n", " # Then add parameterized components to circuit\n", " reck.ps(j, pdict[phi])\n", " reck.bs(j)\n", " reck.ps(j + 1, pdict[theta])\n", " reck.bs(j)\n", "\n", "reck.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimisation\n", "\n", "To demonstrate circuit parameterization, we will configure an optimisation in which a random unitary matrix is generated and the parameters of the circuit then modified to implement this unitary as closely as possible. This would traditionally be achieved by a unitary decomposition procedure, but there may be some cases in which this is not possible and a process as below would be more suitable, such as in high error rate circuit.\n", "\n", "For the optimisation, we define a fom function, which updates the circuit parameters with the determined values and then finds the fidelity of the implemented unitary with the target unitary matrix. In this case we choose the fidelity to be defined as\n", "\n", "$$\\text{F} = \\frac{1}{N}\\text{Tr}(|U_t|\\cdot|U|),$$\n", "\n", "where N is the number of modes, $U_t$ is the target unitary and $U$ is the implemented unitary.\n", "\n", "A callback function is also defined for the purpose of tracking the evolution of the figure of merit." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def get_fidelity(unitary, target_u):\n", " \"\"\"Finds fidelity between implemented and target unitary.\"\"\"\n", " n = unitary.shape[0]\n", " return 1 / n * np.trace(abs(np.conj(target_u.T)) @ abs(unitary))\n", "\n", "\n", "def fom(params, circuit, pdict, target_u):\n", " \"\"\"Updates parameters and returns figure of merit for the optimisation.\"\"\"\n", " # Update parameter dictionary with the optimisation values\n", " for i, param in enumerate(pdict):\n", " pdict[param] = params[i]\n", " unitary = circuit.U # Get unitary matrix implemented by the circuit\n", " return -get_fidelity(unitary, target_u) # Negative as minimising\n", "\n", "\n", "def callback(params):\n", " \"\"\"\n", " Define callback function to be able to track the progress of the fom after\n", " each iteration. This can only accept the params argument, meaning all other\n", " components required to save the fom need to be included through using the\n", " global operator.\n", " \"\"\"\n", " global opt_progress, reck, pdict, target_u # noqa: PLW0602\n", " opt_progress.append(-fom(params, reck, pdict, target_u))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimisation can then be configured, in this case the SciPy minimize function is chosen. The initial values are set to all be $\\pi/2$, and for the bounds, we use the get_bounds method of the parameter dictionary to recover the bounds set on creation of each parameter.\n", "\n", "The optimisation is then run, using the provided callback function to store progress data." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Generate random unitary to implement\n", "target_u = lw.random_unitary(n_modes, seed=99)\n", "\n", "# Set initial values as pi/2\n", "init_values = [np.pi / 2] * len(pdict)\n", "# Retrieve bounds from the parameter dictionary\n", "bounds = list(pdict.get_bounds().values())\n", "\n", "opt_progress = [] # Store fom values\n", "res = minimize(\n", " fom,\n", " init_values,\n", " args=(reck, pdict, target_u),\n", " bounds=bounds,\n", " callback=callback,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Results\n", "Once the optimization is complete we can view the value of the figure of merit after each iteration. As can be seen, using the fidelity measurement defined above we are able to near perfectly implement the transformation on chip." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(opt_progress)\n", "plt.xlabel(\"Iteration\")\n", "plt.ylabel(\"Unitary Fidelity\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final configuration of the circuit can also be displayed, using the show_parameter_values option to see the actual phase settings." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "0\n", "1\n", "2\n", "3\n", "4\n", "\n", "\n", "PS\n", "φ = 1.5708\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.7014\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.6479\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 1.4376\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.8898\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 1.9792\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.0002\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.7982\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 3.5345\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 1.6787\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.4563\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 1.1834\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 5.7853\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.5329\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 3.3738\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 2.0115\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 2.6717\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 1.4493\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 1.64\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "PS\n", "φ = 0.9763\n", "\n", "\n", "\n", "\n", "\n", "BS\n", "r = 0.5\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Configure circuit to optimal configuration\n", "for i, param in enumerate(pdict):\n", " pdict[param] = res.x[i]\n", "\n", "reck.display(show_parameter_values=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And finally, we can plot the target and implemented unitary side by side to check they are visually equivalent." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(13, 6))\n", "\n", "ax[0].imshow(abs(target_u))\n", "ax[0].set_title(\"Target Unitary\")\n", "\n", "ax[1].imshow(abs(reck.U))\n", "ax[1].set_title(\"Circuit Unitary\")\n", "\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "venv", "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": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 2 }