{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "cellView": "form", "execution": { "iopub.execute_input": "2025-05-30T10:30:56.437709Z", "iopub.status.busy": "2025-05-30T10:30:56.437481Z", "iopub.status.idle": "2025-05-30T10:30:56.441448Z", "shell.execute_reply": "2025-05-30T10:30:56.440916Z" }, "id": "4yPUsdJxSXFq" }, "outputs": [], "source": [ "# @title Copyright 2021 The Cirq Developers\n", "# Licensed under the Apache License, Version 2.0 (the \"License\");\n", "# you may not use this file except in compliance with the License.\n", "# You may obtain a copy of the License at\n", "#\n", "# https://www.apache.org/licenses/LICENSE-2.0\n", "#\n", "# Unless required by applicable law or agreed to in writing, software\n", "# distributed under the License is distributed on an \"AS IS\" BASIS,\n", "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", "# See the License for the specific language governing permissions and\n", "# limitations under the License." ] }, { "cell_type": "markdown", "metadata": { "id": "zC1qlUJoSXhm" }, "source": [ "\n", " \n", " \n", " \n", " \n", "
\n", " View on QuantumAI\n", " \n", " Run in Google Colab\n", " \n", " View source on GitHub\n", " \n", " Download notebook\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:30:56.444144Z", "iopub.status.busy": "2025-05-30T10:30:56.443936Z", "iopub.status.idle": "2025-05-30T10:31:11.109955Z", "shell.execute_reply": "2025-05-30T10:31:11.108913Z" }, "id": "bd9529db1c0b" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "installing cirq...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\r\n", "tensorflow-metadata 1.17.1 requires protobuf<4.22,>=4.21.6; python_version < \"3.11\", but you have protobuf 5.29.5 which is incompatible.\u001b[0m\u001b[31m\r\n", "\u001b[0m" ] }, { "name": "stdout", "output_type": "stream", "text": [ "installed cirq.\n" ] } ], "source": [ "try:\n", " import cirq\n", "except ImportError:\n", " print(\"installing cirq...\")\n", " !pip install --quiet cirq\n", " import cirq\n", "\n", " print(\"installed cirq.\")" ] }, { "cell_type": "markdown", "metadata": { "id": "07034e5e3982" }, "source": [ "# Cross-Entropy Benchmarking Theory\n", "\n", "Cross-Entropy Benchmarking (XEB) uses the properties of random quantum programs to determine the fidelity of a wide variety of circuits. When applied to circuits with many qubits, XEB can characterize the performance of a large device. When applied to deep, two-qubit circuits it can be used to accurately characterize a two-qubit interaction potentially leading to better calibration." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:11.113117Z", "iopub.status.busy": "2025-05-30T10:31:11.112696Z", "iopub.status.idle": "2025-05-30T10:31:11.117755Z", "shell.execute_reply": "2025-05-30T10:31:11.116907Z" }, "id": "1348715511ca" }, "outputs": [], "source": [ "# Standard imports\n", "import numpy as np\n", "\n", "from cirq.contrib.svg import SVGCircuit" ] }, { "cell_type": "markdown", "metadata": { "id": "26129d0ff1c0" }, "source": [ "## The action of random circuits with noise\n", "An XEB experiment collects data from the execution of random circuits\n", "subject to noise. The effect of applying a random circuit with unitary $U$ is\n", "modeled as $U$ followed by a depolarizing channel. The result is that the\n", "initial state $|šœ“āŸ©$ is mapped to a density matrix $Ļ_U$ as follows:\n", "\n", "$$\n", " |šœ“āŸ© ā†’ Ļ_U = f |šœ“_UāŸ©āŸØšœ“_U| + (1 - f) I / D\n", "$$\n", "\n", "where $|šœ“_UāŸ© = U|šœ“āŸ©$, $D$ is the dimension of the Hilbert space, $I / D$ is the\n", "maximally mixed state, and $f$ is the fidelity with which the circuit is\n", "applied.\n", "\n", "For this model to be accurate, we require $U$ to be a random circuit that scrambles errors. In practice, we use a particular circuit ansatz consisting of random single-qubit rotations interleaved with entangling gates." ] }, { "cell_type": "markdown", "metadata": { "id": "d940bfde9209" }, "source": [ "### Possible single-qubit rotations\n", "Geometrically, we choose 8 axes in the XY plane to perform a quarter-turn (pi/2 rotation) around. This is followed by a rotation around the Z axis of 8 different magnitudes.\n", "\n", "These 8*8 possible rotations are chosen randomly when constructing the circuit." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:11.121047Z", "iopub.status.busy": "2025-05-30T10:31:11.120339Z", "iopub.status.idle": "2025-05-30T10:31:11.128432Z", "shell.execute_reply": "2025-05-30T10:31:11.127581Z" }, "id": "bb896019c42a" }, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exponents = np.linspace(0, 7 / 4, 8)\n", "exponents" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:11.130792Z", "iopub.status.busy": "2025-05-30T10:31:11.130509Z", "iopub.status.idle": "2025-05-30T10:31:11.136554Z", "shell.execute_reply": "2025-05-30T10:31:11.135781Z" }, "id": "81e2ce9562a5" }, "outputs": [ { "data": { "text/plain": [ "([cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=0.0),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=0.25),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=0.5),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=0.75),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=1.0),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=1.25),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=1.5),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.0, x_exponent=0.5, z_exponent=1.75),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.25, x_exponent=0.5, z_exponent=0.0),\n", " cirq.PhasedXZGate(axis_phase_exponent=0.25, x_exponent=0.5, z_exponent=0.25)],\n", " '...')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import itertools\n", "\n", "SINGLE_QUBIT_GATES = [\n", " cirq.PhasedXZGate(x_exponent=0.5, z_exponent=z, axis_phase_exponent=a)\n", " for a, z in itertools.product(exponents, repeat=2)\n", "]\n", "SINGLE_QUBIT_GATES[:10], '...'" ] }, { "cell_type": "markdown", "metadata": { "id": "72ff411420ef" }, "source": [ "### Random circuit\n", "\n", "We use `cirq.experiments.random_quantum_circuit_generation.random_rotations_between_two_qubit_circuit` to generate a random two-qubit circuit. Note that we provide the possible single-qubit rotations from above and declare that our two-qubit operation is the $\\sqrt{i\\mathrm{SWAP}}$ gate." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:11.139215Z", "iopub.status.busy": "2025-05-30T10:31:11.138775Z", "iopub.status.idle": "2025-05-30T10:31:12.167339Z", "shell.execute_reply": "2025-05-30T10:31:12.166415Z" }, "id": "50f3e9622ff8" }, "outputs": [ { "data": { "image/svg+xml": [ "0: 1: PhXZ(a=0,x=0.5,z=0.75)PhXZ(a=1.5,x=0.5,z=1.5)iSwapiSwap^0.5PhXZ(a=1.5,x=0.5,z=0)PhXZ(a=0,x=0.5,z=1)iSwapiSwap^0.5PhXZ(a=0.5,x=0.5,z=1.5)PhXZ(a=1,x=0.5,z=1.25)iSwapiSwap^0.5PhXZ(a=0.5,x=0.5,z=0.75)PhXZ(a=0.5,x=0.5,z=0)iSwapiSwap^0.5PhXZ(a=1.25,x=0.5,z=0.5)PhXZ(a=1.5,x=0.5,z=0)" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import cirq_google as cg\n", "from cirq.experiments import random_quantum_circuit_generation as rqcg\n", "\n", "q0, q1 = cirq.LineQubit.range(2)\n", "circuit = rqcg.random_rotations_between_two_qubit_circuit(\n", " q0,\n", " q1,\n", " depth=4,\n", " two_qubit_op_factory=lambda a, b, _: cirq.SQRT_ISWAP(a, b),\n", " single_qubit_gates=SINGLE_QUBIT_GATES,\n", ")\n", "SVGCircuit(circuit)" ] }, { "cell_type": "markdown", "metadata": { "id": "b422486e30c9" }, "source": [ "## Estimating fidelity\n", "\n", "Let $O_U$ be an observable that is diagonal in the computational\n", "basis. Then the expectation value of $O_U$ on $Ļ_U$ is given by\n", "\n", "$$\n", " Tr(Ļ_U O_U) = f āŸØšœ“_U|O_U|šœ“_UāŸ© + (1 - f) Tr(O_U / D).\n", "$$\n", "\n", "This equation shows how $f$ can be estimated, since $Tr(Ļ_U O_U)$ can be\n", "estimated from experimental data, and $āŸØšœ“_U|O_U|šœ“_UāŸ©$ and $Tr(O_U / D)$ can be\n", "computed.\n", "\n", "Let $e_U = āŸØšœ“_U|O_U|šœ“_UāŸ©$, $u_U = Tr(O_U / D)$, and $m_U$ denote the experimental\n", "estimate of $Tr(Ļ_U O_U)$. We can write the following linear equation (equivalent to the\n", "expression above):\n", "\n", "$$\n", " m_U = f e_U + (1-f) u_U \\\\\n", " m_U - u_U = f (e_U - u_U)\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:12.170910Z", "iopub.status.busy": "2025-05-30T10:31:12.169926Z", "iopub.status.idle": "2025-05-30T10:31:12.244915Z", "shell.execute_reply": "2025-05-30T10:31:12.243987Z" }, "id": "1cef06bfac12" }, "outputs": [], "source": [ "# Make long circuits (which we will truncate)\n", "MAX_DEPTH = 100\n", "N_CIRCUITS = 10\n", "circuits = [\n", " rqcg.random_rotations_between_two_qubit_circuit(\n", " q0,\n", " q1,\n", " depth=MAX_DEPTH,\n", " two_qubit_op_factory=lambda a, b, _: cirq.SQRT_ISWAP(a, b),\n", " single_qubit_gates=SINGLE_QUBIT_GATES,\n", " )\n", " for _ in range(N_CIRCUITS)\n", "]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:12.247855Z", "iopub.status.busy": "2025-05-30T10:31:12.247163Z", "iopub.status.idle": "2025-05-30T10:31:12.253076Z", "shell.execute_reply": "2025-05-30T10:31:12.252155Z" }, "id": "9bd38c9d20c8" }, "outputs": [ { "data": { "text/plain": [ "array([ 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We will truncate to these lengths\n", "cycle_depths = np.arange(1, MAX_DEPTH + 1, 9)\n", "cycle_depths" ] }, { "cell_type": "markdown", "metadata": { "id": "b573f20ea0d2" }, "source": [ "### Execute circuits\n", "Cross-Entropy Benchmarking (XEB) requires sampled bitstrings from the device being benchmarked *as well as* the true probabilities from a noiseless simulation. We find these quantities for all `(cycle_depth, circuit)` permutations." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:12.256136Z", "iopub.status.busy": "2025-05-30T10:31:12.255507Z", "iopub.status.idle": "2025-05-30T10:31:40.756024Z", "shell.execute_reply": "2025-05-30T10:31:40.755280Z" }, "id": "de9e2414d46f" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] }, { "name": "stdout", 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"stream", "text": [ "." ] }, { "name": "stdout", "output_type": "stream", "text": [ "." ] } ], "source": [ "pure_sim = cirq.Simulator()\n", "\n", "# Pauli Error. If there is an error, it is either X, Y, or Z\n", "# with probability E_PAULI / 3\n", "E_PAULI = 5e-3\n", "noisy_sim = cirq.DensityMatrixSimulator(noise=cirq.depolarize(E_PAULI))\n", "\n", "# These two qubit circuits have 2^2 = 4 probabilities\n", "DIM = 4\n", "\n", "records = []\n", "for cycle_depth in cycle_depths:\n", " for circuit_i, circuit in enumerate(circuits):\n", "\n", " # Truncate the long circuit to the requested cycle_depth\n", " circuit_depth = cycle_depth * 2 + 1\n", " assert circuit_depth <= len(circuit)\n", " trunc_circuit = circuit[:circuit_depth]\n", "\n", " # Pure-state simulation\n", " psi = pure_sim.simulate(trunc_circuit).final_state_vector\n", " pure_probs = np.abs(psi) ** 2\n", "\n", " # Noisy execution\n", " meas_circuit = trunc_circuit + cirq.measure(q0, q1)\n", " sampled_inds = noisy_sim.sample(meas_circuit, repetitions=10_000).values[:, 0]\n", " sampled_probs = np.bincount(sampled_inds, minlength=DIM) / len(sampled_inds)\n", "\n", " # Save the results\n", " records += [\n", " {\n", " 'circuit_i': circuit_i,\n", " 'cycle_depth': cycle_depth,\n", " 'circuit_depth': circuit_depth,\n", " 'pure_probs': pure_probs,\n", " 'sampled_probs': sampled_probs,\n", " }\n", " ]\n", " print('.', end='', flush=True)" ] }, { "cell_type": "markdown", "metadata": { "id": "9902c82e0ff3" }, "source": [ "## What's the observable\n", "\n", "What is $O_U$? Let's define it to be the observable that gives the sum of all probabilities, i.e.\n", "\n", "$$\n", " O_U |x \\rangle = p(x) |x \\rangle\n", "$$\n", "\n", "for any bitstring $x$. We can use this to derive expressions for our quantities of interest.\n", "\n", "$$\n", "e_U = \\langle \\psi_U | O_U | \\psi_U \\rangle \\\\\n", " = \\sum_x a_x^* \\langle x | O_U | x \\rangle a_x \\\\\n", " = \\sum_x p(x) \\langle x | O_U | x \\rangle \\\\\n", " = \\sum_x p(x) p(x)\n", "$$\n", "\n", "$e_U$ is simply the sum of squared ideal probabilities. $u_U$ is a normalizing factor that only depends on the operator. Since this operator has the true probabilities in the definition, they show up here anyways.\n", "\n", "$$\n", "u_U = \\mathrm{Tr}[O_U / D] \\\\\n", " = 1/D \\sum_x \\langle x | O_U | x \\rangle \\\\\n", " = 1/D \\sum_x p(x)\n", "$$\n", "\n", "For the measured values, we use the definition of an expectation value\n", "$$\n", "\\langle f(x) \\rangle_\\rho = \\sum_x p(x) f(x)\n", "$$\n", "It becomes notationally confusing because remember: our operator on basis states returns the ideal probability of that basis state $p(x)$. The probability of observing a measured basis state is estimated from samples and denoted $p_\\mathrm{est}(x)$ here.\n", "\n", "$$\n", "m_U = \\mathrm{Tr}[\\rho_U O_U] \\\\\n", " = \\langle O_U \\rangle_{\\rho_U} = \\sum_{x} p_\\mathrm{est}(x) p(x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:40.759087Z", "iopub.status.busy": "2025-05-30T10:31:40.758829Z", "iopub.status.idle": "2025-05-30T10:31:40.764481Z", "shell.execute_reply": "2025-05-30T10:31:40.763888Z" }, "id": "9770fc8cf5ba" }, "outputs": [], "source": [ "for record in records:\n", " e_u = np.sum(record['pure_probs'] ** 2)\n", " u_u = np.sum(record['pure_probs']) / DIM\n", " m_u = np.sum(record['pure_probs'] * record['sampled_probs'])\n", " record.update(e_u=e_u, u_u=u_u, m_u=m_u)" ] }, { "cell_type": "markdown", "metadata": { "id": "e139a1abca2b" }, "source": [ "Remember:\n", "\n", "$$\n", " m_U - u_U = f (e_U - u_U)\n", "$$\n", "\n", "We estimate f by performing least squares\n", "minimization of the sum of squared residuals\n", "\n", "$$\n", " \\sum_U \\left(f (e_U - u_U) - (m_U - u_U)\\right)^2\n", "$$\n", "\n", "over different random circuits. The solution to the\n", "least squares problem is given by\n", "\n", "$$\n", " f = (āˆ‘_U (m_U - u_U) * (e_U - u_U)) / (āˆ‘_U (e_U - u_U)^2)\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:40.767336Z", "iopub.status.busy": "2025-05-30T10:31:40.766799Z", "iopub.status.idle": "2025-05-30T10:31:40.785416Z", "shell.execute_reply": "2025-05-30T10:31:40.784864Z" }, "id": "2698b1ce5218" }, "outputs": [ { "data": { "text/html": [ "
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circuit_icycle_depthcircuit_depthpure_probssampled_probse_uu_um_uyxnumeratordenominator
0013[0.12499999, 0.12499999, 0.12499999, 0.625][0.1238, 0.126, 0.1265, 0.6237]0.437500.250.4368500.1868500.187500.0350340.035156
1113[0.12499998, 0.12499998, 0.02144662, 0.72855335][0.1222, 0.1303, 0.0318, 0.7157]0.562500.250.5536700.3036700.312500.0948970.097656
2213[0.21338837, 0.64016503, 0.03661165, 0.10983497][0.215, 0.6296, 0.0407, 0.1147]0.468750.250.4630150.2130150.218750.0465970.047852
3313[2.2204466e-16, 0.25, 0.25, 0.50000006][0.007, 0.2479, 0.2526, 0.4925]0.375000.250.3713750.1213750.125000.0151720.015625
4413[0.12499999, 0.12499999, 0.021446615, 0.7285534][0.1276, 0.1371, 0.0283, 0.707]0.562500.250.5487820.2987820.312500.0933690.097656
\n", "
" ], "text/plain": [ " circuit_i cycle_depth circuit_depth \\\n", "0 0 1 3 \n", "1 1 1 3 \n", "2 2 1 3 \n", "3 3 1 3 \n", "4 4 1 3 \n", "\n", " pure_probs \\\n", "0 [0.12499999, 0.12499999, 0.12499999, 0.625] \n", "1 [0.12499998, 0.12499998, 0.02144662, 0.72855335] \n", "2 [0.21338837, 0.64016503, 0.03661165, 0.10983497] \n", "3 [2.2204466e-16, 0.25, 0.25, 0.50000006] \n", "4 [0.12499999, 0.12499999, 0.021446615, 0.7285534] \n", "\n", " sampled_probs e_u u_u m_u y \\\n", "0 [0.1238, 0.126, 0.1265, 0.6237] 0.43750 0.25 0.436850 0.186850 \n", "1 [0.1222, 0.1303, 0.0318, 0.7157] 0.56250 0.25 0.553670 0.303670 \n", "2 [0.215, 0.6296, 0.0407, 0.1147] 0.46875 0.25 0.463015 0.213015 \n", "3 [0.007, 0.2479, 0.2526, 0.4925] 0.37500 0.25 0.371375 0.121375 \n", "4 [0.1276, 0.1371, 0.0283, 0.707] 0.56250 0.25 0.548782 0.298782 \n", "\n", " x numerator denominator \n", "0 0.18750 0.035034 0.035156 \n", "1 0.31250 0.094897 0.097656 \n", "2 0.21875 0.046597 0.047852 \n", "3 0.12500 0.015172 0.015625 \n", "4 0.31250 0.093369 0.097656 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.DataFrame(records)\n", "df['y'] = df['m_u'] - df['u_u']\n", "df['x'] = df['e_u'] - df['u_u']\n", "\n", "df['numerator'] = df['x'] * df['y']\n", "df['denominator'] = df['x'] ** 2\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": { "id": "f526271c8364" }, "source": [ "### Fit\n", "\n", "We'll plot the linear relationship and least-squares fit while we transform the raw DataFrame into one containing fidelities." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:40.788311Z", "iopub.status.busy": "2025-05-30T10:31:40.787735Z", "iopub.status.idle": "2025-05-30T10:31:41.476534Z", "shell.execute_reply": "2025-05-30T10:31:41.475799Z" }, "id": "705fe27d592f" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmpfs/tmp/ipykernel_88462/1866723132.py:26: DeprecationWarning: DataFrameGroupBy.apply operated on the grouping columns. This behavior is deprecated, and in a future version of pandas the grouping columns will be excluded from the operation. Either pass `include_groups=False` to exclude the groupings or explicitly select the grouping columns after groupby to silence this warning.\n", " fids = df.groupby('cycle_depth').apply(per_cycle_depth).reset_index()\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "# Color by cycle depth\n", "import seaborn as sns\n", "\n", "colors = sns.cubehelix_palette(n_colors=len(cycle_depths))\n", "colors = {k: colors[i] for i, k in enumerate(cycle_depths)}\n", "\n", "_lines = []\n", "\n", "\n", "def per_cycle_depth(df):\n", " fid_lsq = df['numerator'].sum() / df['denominator'].sum()\n", "\n", " cycle_depth = df.name\n", " xx = np.linspace(0, df['x'].max())\n", " (l,) = plt.plot(xx, fid_lsq * xx, color=colors[cycle_depth])\n", " plt.scatter(df['x'], df['y'], color=colors[cycle_depth])\n", "\n", " global _lines\n", " _lines += [l] # for legend\n", " return pd.Series({'fidelity': fid_lsq})\n", "\n", "\n", "fids = df.groupby('cycle_depth').apply(per_cycle_depth).reset_index()\n", "plt.xlabel(r'$e_U - u_U$', fontsize=18)\n", "plt.ylabel(r'$m_U - u_U$', fontsize=18)\n", "_lines = np.asarray(_lines)\n", "plt.legend(_lines[[0, -1]], cycle_depths[[0, -1]], loc='best', title='Cycle depth')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "9703fbf361fd" }, "source": [ "### Fidelities" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:41.480394Z", "iopub.status.busy": "2025-05-30T10:31:41.479396Z", "iopub.status.idle": "2025-05-30T10:31:41.737211Z", "shell.execute_reply": "2025-05-30T10:31:41.736553Z" }, "id": "dcb216997aeb" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(fids['cycle_depth'], fids['fidelity'], marker='o', label='Least Squares')\n", "\n", "xx = np.linspace(0, fids['cycle_depth'].max())\n", "\n", "# In XEB, we extract the depolarizing fidelity, which is\n", "# related to (but not equal to) the Pauli error.\n", "# For the latter, an error involves doing X, Y, or Z with E_PAULI/3\n", "# but for the former, an error involves doing I, X, Y, or Z with e_depol/4\n", "e_depol = E_PAULI / (1 - 1 / DIM**2)\n", "\n", "# The additional factor of four in the exponent is because each layer\n", "# involves two moments of two qubits (so each layer has four applications\n", "# of a single-qubit single-moment depolarizing channel).\n", "plt.plot(xx, (1 - e_depol) ** (4 * xx), label=r'$(1-\\mathrm{e\\_depol})^{4d}$')\n", "\n", "plt.ylabel('Circuit fidelity', fontsize=18)\n", "plt.xlabel('Cycle Depth $d$', fontsize=18)\n", "plt.legend(loc='best')\n", "plt.yscale('log')\n", "plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2025-05-30T10:31:41.740120Z", "iopub.status.busy": "2025-05-30T10:31:41.739453Z", "iopub.status.idle": "2025-05-30T10:31:41.750429Z", "shell.execute_reply": "2025-05-30T10:31:41.749835Z" }, "id": "e931726da2af" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Noise model fidelity: 9.788e-01\n", "XEB layer fidelity: 9.786e-01 +- 2.34e-04\n" ] } ], "source": [ "from cirq.experiments.xeb_fitting import fit_exponential_decays\n", "\n", "# Ordinarily, we'd use this function to fit curves for multiple pairs.\n", "# We add our qubit pair as a column.\n", "fids['pair'] = [(q0, q1)] * len(fids)\n", "\n", "fit_df = fit_exponential_decays(fids)\n", "fit_row = fit_df.iloc[0]\n", "print(f\"Noise model fidelity: {(1-e_depol)**4:.3e}\")\n", "print(f\"XEB layer fidelity: {fit_row['layer_fid']:.3e} +- {fit_row['layer_fid_std']:.2e}\")" ] } ], "metadata": { "colab": { "name": "xeb_theory.ipynb", "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "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": "3.10.17" } }, "nbformat": 4, "nbformat_minor": 0 }