{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Qubit Quality Metrics\n", "\n", "This tutorial covers benchmarks for measuring fundamental qubit properties." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from qcmet import T1, T2, IdleQubitOscillationFrequency\n", "from qcmet.devices import NoisySimulator\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The qubit quality metrics consist of:\n", "\n", "- Qubit relaxation time (T1)\n", "\n", "- Qubit dephasing time (T2)\n", "\n", "- Idle qubit purity oscillation frequency (IdleQubitOscillationFrequency)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## T1\n", "\n", "T1 (relaxation time) measures how long a qubit stays in the excited state before decaying to the ground state.\n", "\n", "The T1 benchmark can be executed using idle/identity gates or delay gates. Some QPU hardware will remove identity gates after circuit transpilation, so delay gates can be used instead.\n", "\n", "### How T1 Works\n", "\n", "1. Prepare qubit in excited state |1⟩ using X gate\n", "2. Wait for various durations (using idle/identity gates or delay gates)\n", "3. Measure the qubit\n", "4. Fit exponential decay: P(1) = A × exp(-t/T1)\n", "\n", "The decay rate gives us the T1 time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basic T1 Measurement (Idle Gates)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generated 10 circuits\n" ] } ], "source": [ "# Create noisy simulator\n", "device = NoisySimulator()\n", "\n", "# Setup T1 benchmark with range of idle gates\n", "num_idle_gates = np.arange(1, 3000, 300)\n", "t1_benchmark = T1(num_idle_gates_per_circ=num_idle_gates)\n", "\n", "# Generate circuits\n", "t1_benchmark.generate_circuits()\n", "print(f\"Generated {len(t1_benchmark.circuits)} circuits\")" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First T1 circuit (with 1 idle gate):\n", " ┌───┐ ░ ┌───┐ ░ ░ ┌─┐\n", " q: ┤ X ├─░─┤ I ├─░──░─┤M├\n", " └───┘ ░ └───┘ ░ ░ └╥┘\n", "meas: 1/════════════════════╩═\n", " 0 \n" ] } ], "source": [ "# Look at the first circuit structure\n", "print(\"First T1 circuit (with 1 idle gate):\")\n", "print(t1_benchmark.circuits[0])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T1 Results:\n", " success: True\n", " T1 (t/t_[1q_gate]): 4983.220514654325\n", " fit: {'popt': array([1.00068918e+00, 4.98322051e+03]), 'pcov': array([[ 4.94906776e-05, -7.17362085e-01],\n", " [-7.17362085e-01, 1.67935034e+04]])}\n" ] } ], "source": [ "# Run the benchmark\n", "t1_benchmark.run(device, num_shots=2048)\n", "\n", "# Analyze results\n", "results = t1_benchmark.analyze()\n", "print(\"T1 Results:\")\n", "for key, value in results.items():\n", " print(f\" {key}: {value}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing T1 Decay" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the decay\n", "fig, ax = t1_benchmark.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basic T1 Measurement (Delay Gates)\n", "\n", "This is how the T1 benchmark is initialised with delay gates instead of idle gates. All remaining steps to execute the benchmark are identical to the idle gates approach." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Setup T1 benchmark with range of delay gates\n", "delay = [1,2,5,10,15,20,25,30,35,45,55,70,100]\n", "t1_benchmark = T1(delay=delay)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## T2\n", "\n", "T2 (dephasing time) measures the timescale at which the phase information of a state in superposition is lost.\n", "\n", "The T2 benchmark can be executed using idle/identity gates or delay gates. Some QPU hardware will remove identity gates after circuit transpilation, so delay gates can be used instead.\n", "\n", "### How T2* (Ramsey) Works\n", "\n", "1. Prepare qubit in ground state |0⟩ \n", "2. Apply Rx($\\pi$/2) rotation gate\n", "3. Wait for various durations (using idle/identity gates or delay gates)\n", "4. Measure the qubit\n", "5. Fit exponential decay: P(1)R = A × exp(-t/T2*) cos(2 $\\pi$ ft + $\\phi$) + b\n", "\n", "### How T2 (Hahn) Works\n", "\n", "1. Prepare qubit in ground state |0⟩ \n", "2. Apply Rx($\\pi$/2) rotation gate\n", "3. Wait for half of total duration for various durations (using idle/identity gates or delay gates)\n", "4. Apply Rx($\\pi$) rotation gate\n", "5. Wait for half of total duration for various durations (using idle/identity gates or delay gates)\n", "6. Measure the qubit\n", "7. Fit exponential decay: P(1)E = A × exp(-t/T2) + B\n", "\n", "The decay rate gives us the T2 time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basic T2* (Ramsey) Measurement (Idle Gates)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generated 10 circuits\n" ] } ], "source": [ "# Create ideal simulator\n", "device = NoisySimulator()\n", "\n", "# Setup T1 benchmark with range of idle gates\n", "num_idle_gates = np.arange(1, 3000, 300)\n", "t2_benchmark = T2(method='ramsey',num_idle_gates_per_circ=num_idle_gates,detuning_phase=np.pi/200)\n", "\n", "# Generate circuits\n", "t2_benchmark.generate_circuits()\n", "print(f\"Generated {len(t2_benchmark.circuits)} circuits\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T2 Results:\n", " success: True\n", " T2* (t/t_[1q_gate]): 6841.646061120499\n", " method: ramsey\n", " fit: {'popt': array([4.98589725e-01, 6.84164606e+03, 2.49837117e-03, 1.75482321e-02,\n", " 5.01227008e-01]), 'pcov': array([[ 7.27604961e-05, -4.00419411e+00, -2.95256724e-10,\n", " 4.82740010e-06, -3.19695397e-06],\n", " [-4.00419411e+00, 3.77304969e+05, 1.51019183e-05,\n", " -1.98266560e-01, 4.52455786e-02],\n", " [-2.95256724e-10, 1.51019183e-05, 4.75659196e-12,\n", " -3.86961723e-08, 1.01502861e-10],\n", " [ 4.82740010e-06, -1.98266560e-01, -3.86961723e-08,\n", " 4.47411885e-04, -6.26974238e-06],\n", " [-3.19695397e-06, 4.52455786e-02, 1.01502861e-10,\n", " -6.26974238e-06, 1.12026707e-05]])}\n" ] } ], "source": [ "# Run the benchmark\n", "t2_benchmark.run(device, num_shots=2048)\n", "\n", "# Analyze results\n", "results = t2_benchmark.analyze()\n", "print(\"T2 Results:\")\n", "for key, value in results.items():\n", " print(f\" {key}: {value}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing T2* Decay" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the decay\n", "fig, ax = t2_benchmark.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Idle Qubit Oscillation Frequency\n", "\n", "An idle qubit periodically losing and regaining coherence can be a signature of non-Markovian noise.\n", "\n", "The oscillation frequency of the qubit purity can quantify the effect of non-Markovian noise induced coherence revivals, where a higher frequency indicates larger non-Markovianity of the noise.\n", "\n", "### How Idle Qubit Oscillation Frequency Works\n", "\n", "1. Select time step (dt) and max time (t_max) to leave qubit idle to get the set of idle times T = {0, dt, 2dt, ..., t_max} for which to run the circuits. \n", "2. For each initial state |i⟩ ∈ {|0⟩, |+⟩, |R⟩}, perform the following operations:\n", "\n", " a. For each idle time t ∈ T:\n", "\n", " i. For each measurement basis:\n", "\n", " - Prepare qubit in state |i⟩.\n", "\n", " - Leave qubit idle for time t.\n", "\n", " - Measure qubit in basis by applying the corresponding basis change gates and then\n", " measuring in the computational basis.\n", "\n", " ii. Calculate the purity ζ.\n", "\n", " b. For each initial state |i⟩, fit ζ(t) = a + b * exp(−λt) cos(ωt) to a decaying oscillation and store the estimated\n", " oscillation frequency ω_i.\n", "\n", "3. The largest oscillation frequency from all three initial states gives the single-qubit non-Markovian noise induced purity oscillation frequency, ω_max.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basic Idle Qubit Oscillation Frequency Measurements" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create noisy simulator\n", "device = NoisySimulator()\n", "\n", "# Setup IdleQubitOscillationFrequency benchmark\n", "idle_qubits_benchmark = IdleQubitOscillationFrequency(0.5, 15, 0.15)\n", "\n", "# Generate circuits\n", "idle_qubits_benchmark.generate_circuits()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Idle Qubits Oscillation Frequency Results:\n", " initial_state_0_purities: [1.002504, 1.00034, 1.00272, 1.0007300000000001, 1.0023440000000001, 1.000002, 1.000016, 1.00353, 1.0011700000000001, 1.000274, 1.0000900000000001, 1.001994, 1.000512, 1.00068, 1.0003279999999999, 1.002768, 1.000202, 1.000712, 1.000848, 1.0005, 1.001282, 1.000178, 1.00005, 1.000178, 1.000072, 1.00004, 1.000288, 1.000032, 1.001556, 1.001682]\n", " initial_state_0_fit_result: {'popt': array([1.00060176, 0.00128809, 0.12060744, 0.40391297]), 'pcov': array([[ 9.58550260e-08, -1.01789808e-07, 2.62613431e-05,\n", " -1.02436308e-06],\n", " [-1.01789808e-07, 5.15525661e-07, 1.90047929e-05,\n", " 6.31675770e-06],\n", " [ 2.62613431e-05, 1.90047929e-05, 2.19988658e-02,\n", " 1.07937086e-03],\n", " [-1.02436308e-06, 6.31675770e-06, 1.07937086e-03,\n", " 6.02190877e-03]])}\n", " initial_state_0_oscillation_frequency: 0.0\n", " initial_state_+_purities: [1.0001300000000002, 0.9804179999999999, 0.9479259999999999, 0.9122279999999999, 0.8316220000000001, 0.76145, 0.685226, 0.62095, 0.564342, 0.5142619999999999, 0.50504, 0.5030619999999999, 0.519282, 0.5800500000000001, 0.61118, 0.679202, 0.7696040000000001, 0.83434, 0.9052899999999999, 0.942866, 0.97077, 0.988658, 0.986458, 0.947748, 0.894348, 0.808722, 0.7575099999999999, 0.7076999999999999, 0.6352679999999999, 0.583732]\n", " initial_state_+_fit_result: {'popt': array([ 0.5006901 , 0.49424463, 0.00148934, -0.29871227]), 'pcov': array([[ 1.16050402e-05, -1.48579283e-05, 8.46001868e-08,\n", " -3.53809231e-07],\n", " [-1.48579283e-05, 4.53737988e-05, 5.23089132e-06,\n", " 8.53269442e-07],\n", " [ 8.46001868e-08, 5.23089132e-06, 1.57741212e-06,\n", " 1.92623114e-07],\n", " [-3.53809231e-07, 8.53269442e-07, 1.92623114e-07,\n", " 3.77383621e-07]])}\n", " initial_state_+_oscillation_frequency: 0.2987122699910167\n", " initial_state_R_purities: [1.00037, 0.997298, 0.94002, 0.8970499999999999, 0.829712, 0.7611699999999999, 0.7340499999999999, 0.621394, 0.568004, 0.5266359999999999, 0.5058779999999999, 0.503388, 0.5193559999999999, 0.564816, 0.630678, 0.69389, 0.7630579999999999, 0.82982, 0.8748499999999999, 0.9500259999999999, 0.9724759999999999, 0.9866320000000001, 0.986748, 0.93268, 0.885572, 0.843068, 0.7681399999999999, 0.695426, 0.616322, 0.566892]\n", " initial_state_R_fit_result: {'popt': array([ 0.5031087 , 0.49432227, 0.00256099, -0.29854841]), 'pcov': array([[ 1.47109075e-05, -1.88175378e-05, 1.55401620e-07,\n", " -4.48557068e-07],\n", " [-1.88175378e-05, 5.75226065e-05, 6.58008506e-06,\n", " 1.07726658e-06],\n", " [ 1.55401620e-07, 6.58008506e-06, 2.01517347e-06,\n", " 2.43569510e-07],\n", " [-4.48557068e-07, 1.07726658e-06, 2.43569510e-07,\n", " 4.88318324e-07]])}\n", " initial_state_R_oscillation_frequency: 0.29854841457971876\n", " idle_qubit_oscillation_frequency: 0.2987122699910167\n" ] } ], "source": [ "# Run the benchmark\n", "idle_qubits_benchmark.run(device, num_shots=1000)\n", "\n", "# Analyze results\n", "results = idle_qubits_benchmark.analyze()\n", "print(\"Idle Qubits Oscillation Frequency Results:\")\n", "for key, value in results.items():\n", " print(f\" {key}: {value}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing Oscillation Frequency" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the oscillation\n", "fig, ax = idle_qubits_benchmark.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interpreting Qubit Quality Results\n", "\n", "### What the Numbers Mean\n", "\n", "**T1 time** (in gate units/microseconds): How many idle gates/time passed before decay\n", "- If using idle gates approach, multiply T1 by gate duration to convert to physical time.\n", "- Longer T1 = better qubit quality\n", "\n", "**T2R time** (in gate units/microseconds): How many idle gates/time passed before decay\n", "- If using idle gates approach, multiply T2 by gate duration to convert to physical time.\n", "- Longer T2R = better qubit quality\n", "\n", "**T2E time** (in gate units/microseconds): How many idle gates/time passed before decay\n", "- If using idle gates approach, multiply T2 by gate duration to convert to physical time.\n", "- Longer T2E = better qubit quality\n", "\n", "**Oscillation frequency** : The largest rate of oscillation in qubit purity amongst the three measurement bases\n", "- Larger oscillation frequency = larger non-Markovianity of the noise.\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.12.10" } }, "nbformat": 4, "nbformat_minor": 4 }