diff --git a/.github/ACKNOWLEDGMENTS.md b/.github/ACKNOWLEDGMENTS.md index 4b280f8e1..d00f565d4 100644 --- a/.github/ACKNOWLEDGMENTS.md +++ b/.github/ACKNOWLEDGMENTS.md @@ -29,3 +29,7 @@ * [Guillaume Thekkadath](https://www2.physics.ox.ac.uk/contacts/people/thekkadath) (University of Oxford) - :smiley_cat: Master cat herder * [Trevor Vincent](https://github.com/trevor-vincent) (Xanadu) - :apple: master of gravitation + +* [Ilan Tzitrin](https://github.com/ilan-tz) (Xanadu, University of Toronto) 🚞 local optimist + +* [J. Eli Bourassa](https://github.com/elib20) (Xanadu, University of Toronto) 🏄 GKP surfer diff --git a/docs/gallery/cubic_circuit.svg b/docs/gallery/cubic_circuit.svg index 186f90057..ab5db2665 100644 --- a/docs/gallery/cubic_circuit.svg +++ b/docs/gallery/cubic_circuit.svg @@ -1,5 +1,5 @@ - + @@ -9,9 +9,6 @@ - - - @@ -26,92 +23,69 @@ - - - - - - - - - - - + - - - - - - - - - - + + + + + + + - + - - - - - - - - + - - - - - + + + + + + - + - - - - - - - + + + + + + - + - + - - - - - - - - - + + + + + + + - + - - - - - + + + + + + + - + - - - - - - - - - + + + + + + diff --git a/docs/gallery/gallery.rst b/docs/gallery/gallery.rst index 741cd8eb7..fdff71212 100644 --- a/docs/gallery/gallery.rst +++ b/docs/gallery/gallery.rst @@ -94,6 +94,11 @@ If you develop a new circuit and measurement scheme to prepare a non-Gaussian st :description: :doc:`Four-headed cat states ` :figure: gallery/four_cat.png +.. customgalleryitem:: + :tooltip: GKP states + :description: :doc:`GKP states ` + :figure: gallery/gkp.png + .. raw:: html
diff --git a/docs/gallery/gkp.ipynb b/docs/gallery/gkp.ipynb new file mode 100644 index 000000000..afecc3c16 --- /dev/null +++ b/docs/gallery/gkp.ipynb @@ -0,0 +1,411 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# GKP states" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T19:40:13.314552Z", + "start_time": "2020-01-20T19:40:13.305550Z" + } + }, + "source": [ + "Authors: Ilan Tzitrin and J. Eli Bourassa\n", + "\n", + "In this tutorial, we numerically simulate the preparation of an approximate Gottesman-Kitaev-Preskill (GKP) state using an optical circuit. The state we target is\n", + "\n", + "$\\left|0_\\Delta\\right> \\approx S(0.196)[0.661\\left|0\\right> - 0.343\\left|2\\right> + 0.253\\left|4\\right> - 0.368\\left|6\\right> + 0.377\\left|8\\right> + 0.323\\left|10\\right> + 0.365\\left|12\\right>]$,\n", + "\n", + "which has 96.9% fidelity to the normalizable GKP state $\\left|0_\\Delta\\right>$ for $\\Delta = 10 \\text{ dB}$. \n", + "\n", + "For more on GKP states, including the notation and terminology, see \"Towards practical qubit computation using approximate error-correcting grid states\" [arXiv:1910.03673](https://arxiv.org/abs/1910.03673) by I. Tzitrin, J. E. Bourassa, N. C. Menicucci, and K. K Sabapathy and the blog post [Riding bosonic qubits towards fault-tolerant quantum computation](https://medium.com/xanaduai/riding-bosonic-qubits-towards-fault-tolerant-quantum-computation-95b92c78cb43).\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T19:49:01.369843Z", + "start_time": "2020-01-20T19:49:01.353114Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "from qutip import wigner, Qobj, wigner_cmap\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "from matplotlib import cm\n", + "\n", + "import strawberryfields as sf\n", + "from strawberryfields.ops import *\n", + "from thewalrus.quantum import state_vector, density_matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ideal Preparation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we setup some basic parameters, like the value of the photon-number-resolving detectors we will use to herald and the amount of squeezing and displacement to use. The origin of these parameters is discussed in the reference above." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:11:02.845377Z", + "start_time": "2020-01-20T20:11:02.838377Z" + } + }, + "outputs": [], + "source": [ + "m1, m2 = 5, 7\n", + "params = np.array([-1.38155106, -1.21699567, 0.7798817, 1.04182349, \n", + " 0.87702211, 0.90243916, 1.48353639, 1.6962906 , \n", + " -0.24251599, 0.1958])\n", + "sq_r = params[:3]\n", + "bs_theta1, bs_theta2, bs_theta3 = params[3:6]\n", + "bs_phi1, bs_phi2, bs_phi3 = params[6:9]\n", + "sq_virt = params[9]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we setup a 3-mode quantum circuit in Strawberry Fields and obtain the covariance matrix and vector of means of the Gaussian state." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:45:42.013639Z", + "start_time": "2020-01-20T20:45:42.001652Z" + } + }, + "outputs": [], + "source": [ + "nmodes = 3\n", + "prog = sf.Program(nmodes)\n", + "eng = sf.Engine(\"gaussian\")\n", + "\n", + "with prog.context as q:\n", + " for k in range(3):\n", + " Sgate(sq_r[k]) | q[k]\n", + "\n", + " BSgate(bs_theta1, bs_phi1) | (q[0], q[1])\n", + " BSgate(bs_theta2, bs_phi2) | (q[1], q[2])\n", + " BSgate(bs_theta3, bs_phi3) | (q[0], q[1])\n", + " \n", + " Sgate(sq_virt) | q[2]\n", + "\n", + "state = eng.run(prog).state\n", + "mu, cov = state.means(), state.cov()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:08:40.384809Z", + "start_time": "2020-01-20T20:08:40.378807Z" + } + }, + "outputs": [], + "source": [ + "# Here we use the sf circuit drawer and standard linux utilities\n", + "# to generate an svg representing the circuit\n", + "file, _ = prog.draw_circuit()\n", + "filepdf = file[0:-3]+\"pdf\"\n", + "filepdf = filepdf.replace(\"circuit_tex/\",\"\")\n", + "filecrop = filepdf.replace(\".pdf\",\"-crop.pdf\")\n", + "name = \"gkp_circuit.svg\"\n", + "!pdflatex $file > /dev/null 2>&1\n", + "!pdfcrop $filepdf > /dev/null 2>&1\n", + "!pdf2svg $filecrop $name" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a graphical representation of the circuit. It is always assumed that the input is vacuum in all the modes.
\n", + "![img](./gkp_circuit.svg)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now inspect the covariance matrix and vector of means. Note that the vector of means is zero since we did not use displacement gates in the circuit above. This is due to the symmetry of the GKP wavefunction about the origin in phase space." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:45:44.912712Z", + "start_time": "2020-01-20T20:45:44.906722Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0. 0. 0. 0. 0.]\n", + "[[ 5.00170445 0.15101176 -3.12729025 -3.93663741 -0.57864296 0.45079939]\n", + " [ 0.15101176 4.88633214 -3.69458049 -1.32442707 3.78723601 -0.30858687]\n", + " [-3.12729025 -3.69458049 4.798272 3.42705308 -2.38393578 0.05410287]\n", + " [-3.93663741 -1.32442707 3.42705308 5.56202806 1.90025335 2.97323959]\n", + " [-0.57864296 3.78723601 -2.38393578 1.90025335 6.15012337 3.65219485]\n", + " [ 0.45079939 -0.30858687 0.05410287 2.97323959 3.65219485 5.4342486 ]]\n" + ] + } + ], + "source": [ + "print(np.round(mu, 10))\n", + "print(np.round(cov, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now use The Walrus to obtain the Fock representation of the Gaussian state emerging in the 3rd mode when modes 1 and 2 are heralded in the values $n_1=5$ and $n_2=7$. We also calculate the probability of success in heralding the state." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:45:46.916980Z", + "start_time": "2020-01-20T20:45:46.891976Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The probability of successful heralding is 0.00106.\n" + ] + } + ], + "source": [ + "cutoff = 25\n", + "psi = state_vector(mu, cov, post_select={0: m1, 1: m2}, normalize=False, cutoff=cutoff)\n", + "p_psi = np.linalg.norm(psi)\n", + "psi = psi / p_psi\n", + "print('The probability of successful heralding is {:.5f}.'.format(p_psi ** 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now plot the photon-number distribution of the heralded state. Note that the state has zero support on the odd Fock states due to its symmetry, and the support tapers off after $n=8$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:45:49.472496Z", + "start_time": "2020-01-20T20:45:49.292043Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.bar(np.arange(cutoff), np.abs(psi) ** 2)\n", + "plt.xlim(-1, 22)\n", + "plt.xticks(np.arange(0, 22, 2))\n", + "plt.xlabel('$i$')\n", + "plt.ylabel(r'$p_i$')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now plot the Wigner function of the heralded state:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:45:53.872155Z", + "start_time": "2020-01-20T20:45:52.219528Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "grid = 300\n", + "xvec = np.linspace(-5,5, grid)\n", + "Wp = wigner(Qobj(psi), xvec, xvec)\n", + "wmap = wigner_cmap(Wp)\n", + "sc1 = np.max(Wp)\n", + "nrm = mpl.colors.Normalize(-sc1, sc1)\n", + "fig, axes = plt.subplots(1, 1, figsize=(5, 4))\n", + "plt1 = axes.contourf(xvec, xvec, Wp, 60, cmap=cm.RdBu, norm=nrm)\n", + "axes.contour(xvec, xvec, Wp, 60, cmap=cm.RdBu, norm=nrm)\n", + "axes.set_title(\"Wigner function of the heralded state\");\n", + "cb1 = fig.colorbar(plt1, ax=axes)\n", + "fig.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and a cut of the Wigner function along $p=0$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-01-20T20:45:56.313743Z", + "start_time": "2020-01-20T20:45:55.791153Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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