{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Leakage characterization using GST\n", "This tutorial demonstrates how to perform GST on a \"leaky-qubit\" described by a 3-level (instead of the desired 2-level) system. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pygsti\n", "import pygsti.modelpacks.legacy.std1Q_XYI as std1Q\n", "import numpy as np\n", "import scipy.linalg as sla\n", "#import pickle" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def to_3level_unitary(U_2level):\n", " U_3level = np.zeros((3,3),complex)\n", " U_3level[0:2,0:2] = U_2level\n", " U_3level[2,2] = 1.0\n", " return U_3level\n", "\n", "def unitary_to_gmgate(U):\n", " return pygsti.tools.change_basis( \n", " pygsti.tools.unitary_to_std_process_mx(U), 'std','gm')\n", "\n", "def state_to_gmvec(state):\n", " pygsti.tools.stdmx_to_gmvec\n", "\n", "Us = pygsti.tools.internalgates.standard_gatename_unitaries()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mdl_2level_ideal = std1Q.target_model()\n", "mdl_2level_ideal.sim = \"matrix\" # so we can create reports later on" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "rho0 = np.array( [[1,0,0],\n", " [0,0,0],\n", " [0,0,0]], complex)\n", "E0 = rho0\n", "E1 = np.array( [[0,0,0],\n", " [0,1,0],\n", " [0,0,1]], complex)\n", "\n", "sslbls = pygsti.baseobjs.ExplicitStateSpace(['Qubit+Leakage'],[3])\n", "mdl_3level_ideal = pygsti.models.ExplicitOpModel(sslbls, 'gm')\n", "mdl_3level_ideal['rho0'] = pygsti.tools.stdmx_to_gmvec(rho0)\n", "mdl_3level_ideal['Mdefault'] = pygsti.modelmembers.povms.TPPOVM([('0',pygsti.tools.stdmx_to_gmvec(E0)),\n", " ('1',pygsti.tools.stdmx_to_gmvec(E1))],\n", " evotype='default')\n", "\n", "mdl_3level_ideal['Gi'] = unitary_to_gmgate( to_3level_unitary(Us['Gi']))\n", "mdl_3level_ideal['Gx'] = unitary_to_gmgate( to_3level_unitary(Us['Gxpi2']))\n", "mdl_3level_ideal['Gy'] = unitary_to_gmgate( to_3level_unitary(Us['Gypi2']))\n", "mdl_3level_ideal.sim = \"matrix\" # so we can create reports later on" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sigmaX = np.array([[0,1],[1,0]],complex)\n", "rot = sla.expm(1j * 0.1 * sigmaX)\n", "Uleakage = np.identity(3,complex)\n", "Uleakage[1:3,1:3] = rot\n", "leakageOp = unitary_to_gmgate(Uleakage)\n", "#print(Uleakage)\n", "\n", "#Guess of a model w/just unitary leakage\n", "mdl_3level_guess = mdl_3level_ideal.copy()\n", "mdl_3level_guess['Gi'] = np.dot(leakageOp, mdl_3level_guess['Gi'])\n", "#mdl_3level_guess['Gx'] = np.dot(leakageOp, mdl_3level_guess['Gx'])\n", "#mdl_3level_guess['Gy'] = np.dot(leakageOp, mdl_3level_guess['Gy'])\n", "\n", "#Actual model used for data generation (some depolarization too)\n", "mdl_3level_noisy = mdl_3level_ideal.depolarize(op_noise=0.005, spam_noise=0.01)\n", "mdl_3level_noisy['Gi'] = np.dot(leakageOp, mdl_3level_noisy['Gi'])\n", "#mdl_3level_noisy['Gx'] = np.dot(leakageOp, mdl_3level_noisy['Gx'])\n", "#mdl_3level_noisy['Gy'] = np.dot(leakageOp, mdl_3level_noisy['Gy'])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#print(mdl_3level_guess)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# get sequences using expected model\n", "find_fiducials = False\n", "\n", "if find_fiducials:\n", " prepfids, measfids = pygsti.algorithms.find_fiducials(\n", " mdl_3level_guess, omit_identity=False, max_fid_length=4, verbosity=4)\n", " pygsti.io.write_circuit_list(\"example_files/leakage_prepfids.txt\", prepfids)\n", " pygsti.io.write_circuit_list(\"example_files/leakage_measfids.txt\", measfids)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# If files missing, run previous cell at least once with find_fiducials = True\n", "prepfids = pygsti.io.read_circuit_list(\"example_files/leakage_prepfids.txt\")\n", "measfids = pygsti.io.read_circuit_list(\"example_files/leakage_measfids.txt\")\n", "germs = std1Q.germs\n", "maxLengths = [1,]\n", "expList = pygsti.circuits.create_lsgst_circuits(mdl_3level_noisy, prepfids, measfids, germs, maxLengths)\n", "ds = pygsti.data.simulate_data(mdl_3level_noisy, expList, 1000, 'binomial', seed=1234)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "results_2level = pygsti.run_stdpractice_gst(ds, mdl_2level_ideal, prepfids, measfids,\n", " germs, maxLengths, modes=\"CPTP\", verbosity=3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "results_3level = pygsti.run_stdpractice_gst(ds, mdl_3level_ideal, prepfids, measfids,\n", " germs, maxLengths, modes=\"CPTP,True\",\n", " models_to_test={'True': mdl_3level_noisy}, \n", " verbosity=4, advanced_options={'all': {'tolerance': 1e-2}})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pygsti.report.construct_standard_report(\n", " {'two-level': results_2level, 'three-level': results_3level},\n", " \"Leakage Example Report\"\n", ").write_html('example_files/leakage_report')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#try a different basis:\n", "gm_basis = pygsti.baseobjs.Basis.cast('gm',9)\n", " \n", "leakage_basis_mxs = [ np.sqrt(2)/3*(np.sqrt(3)*gm_basis[0] + 0.5*np.sqrt(6)*gm_basis[8]),\n", " gm_basis[1], gm_basis[4], gm_basis[7],\n", " gm_basis[2], gm_basis[3], gm_basis[5], gm_basis[6],\n", " 1/3*(np.sqrt(3)*gm_basis[0] - np.sqrt(6)*gm_basis[8]) ]\n", "#for mx in leakage_basis_mxs:\n", "# pygsti.tools.print_mx(mx)\n", "\n", "check = np.zeros( (9,9), complex)\n", "for i,m1 in enumerate(leakage_basis_mxs):\n", " for j,m2 in enumerate(leakage_basis_mxs):\n", " check[i,j] = np.trace(np.dot(m1,m2))\n", "assert(np.allclose(check, np.identity(9,complex)))\n", "\n", "leakage_basis = pygsti.baseobjs.ExplicitBasis(leakage_basis_mxs, name=\"LeakageBasis\", \n", " longname=\"2+1 level leakage basis\", real=True,\n", " labels=['I','X','Y','Z','LX0','LX1','LY0','LY1','L'])\n", "\n", "def changebasis_3level_model(mdl):\n", " new_mdl = mdl.copy()\n", " new_mdl.preps['rho0'] = pygsti.modelmembers.states.FullState(\n", " pygsti.tools.change_basis(mdl.preps['rho0'].to_dense(), gm_basis, leakage_basis))\n", " new_mdl.povms['Mdefault'] = pygsti.modelmembers.povms.UnconstrainedPOVM(\n", " [('0', pygsti.tools.change_basis(mdl.povms['Mdefault']['0'].to_dense(), gm_basis, leakage_basis)),\n", " ('1', pygsti.tools.change_basis(mdl.povms['Mdefault']['1'].to_dense(), gm_basis, leakage_basis))],\n", " evotype='default')\n", " \n", " for lbl,op in mdl.operations.items():\n", " new_mdl.operations[lbl] = pygsti.modelmembers.operations.FullArbitraryOp(\n", " pygsti.tools.change_basis(op.to_dense(), gm_basis, leakage_basis))\n", " new_mdl.basis = leakage_basis\n", " return new_mdl\n", "\n", "def changebasis_3level_results(results):\n", " new_results = results.copy()\n", " for estlbl,est in results.estimates.items():\n", " for mlbl,mdl in est.models.items():\n", " if isinstance(mdl,(list,tuple)): #assume a list/tuple of models\n", " new_results.estimates[estlbl].models[mlbl] = \\\n", " [ changebasis_3level_model(m) for m in mdl ]\n", " else:\n", " new_results.estimates[estlbl].models[mlbl] = changebasis_3level_model(mdl)\n", " return new_results\n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "results_3level_leakage_basis = changebasis_3level_results( results_3level ) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pygsti.report.construct_standard_report(\n", " {'two-level': results_2level, 'three-level': results_3level_leakage_basis},\n", " \"Leakage Example Report\"\n", ").write_html('example_files/leakage_report')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Open the report [here](example_files/leakage_report/main.html)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# use \"kite\" density-matrix structure\n", "def to_2plus1_superop(superop_2level):\n", " ret = np.zeros((5,5),'d')\n", " ret[0:4,0:4] = superop_2level.to_dense()\n", " ret[4,4] = 1.0 #leave leakage population where it is\n", " return ret\n", "\n", "#Tack on a single extra \"0\" for the 5-th dimension corresponding\n", "# to the classical leakage level population.\n", "eps = 0.01 # ideally zero, a smallish number to seed the GST optimiation away from 0-leakage so it doesn't get stuck there.\n", "rho0 = np.concatenate( (mdl_2level_ideal.preps['rho0'].to_dense(),[eps]), axis=0)\n", "E0 = np.concatenate( (mdl_2level_ideal.povms['Mdefault']['0'].to_dense(),[eps]), axis=0)\n", "E1 = np.concatenate( (mdl_2level_ideal.povms['Mdefault']['1'].to_dense(),[eps]), axis=0)\n", "\n", "\n", "statespace = pygsti.baseobjs.ExplicitStateSpace([('Qubit',),('Leakage',)],[(2,),(1,)])\n", "mdl_2plus1_ideal = pygsti.models.ExplicitOpModel(statespace, 'gm')\n", "mdl_2plus1_ideal['rho0'] = rho0\n", "mdl_2plus1_ideal['Mdefault'] = pygsti.modelmembers.povms.UnconstrainedPOVM([('0',E0),('1',E1)],\n", " evotype='default', state_space=statespace)\n", "\n", "mdl_2plus1_ideal['Gi'] = to_2plus1_superop(mdl_2level_ideal['Gi'])\n", "mdl_2plus1_ideal['Gx'] = to_2plus1_superop(mdl_2level_ideal['Gx'])\n", "mdl_2plus1_ideal['Gy'] = to_2plus1_superop(mdl_2level_ideal['Gy'])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mdl_2plus1_ideal.sim = \"matrix\" # so we can construct report below\n", "results_2plus1 = pygsti.run_long_sequence_gst(ds, mdl_2plus1_ideal, prepfids, measfids,\n", " germs, maxLengths, verbosity=2,\n", " advanced_options={\"starting_point\": \"target\",\n", " \"tolerance\": 1e-8, # (lowering tolerance from 1e-6 gave a better fit)\n", " \"estimate_label\": \"kite\"})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pygsti.report.construct_standard_report(\n", " {'two-level': results_2level, 'three-level': results_3level_leakage_basis,\n", " 'two+one level': results_2plus1},\n", " \"Leakage Example Report\"\n", ").write_html('example_files/leakage_report', autosize='none')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Open the report [here](example_files/leakage_report/main.html)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.12" } }, "nbformat": 4, "nbformat_minor": 2 }