Isolated XEB

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try:
    import cirq
except ImportError:
    print("installing cirq...")
    !pip install --quiet cirq
    print("installed cirq.")

This notebook demonstrates how to use the functionality in cirq.experiments to run Isolated XEB end-to-end. "Isolated" means we do one pair of qubits at a time.

import cirq
import numpy as np

Set up Random Circuits

We create a library of 20 random, two-qubit circuits using the sqrt(ISWAP) gate on the two qubits we've chosen.

from cirq.experiments import random_quantum_circuit_generation as rqcg

circuits = rqcg.generate_library_of_2q_circuits(
    n_library_circuits=20,
    two_qubit_gate=cirq.ISWAP**0.5,
    q0=cirq.GridQubit(4,4),
    q1=cirq.GridQubit(4,5),
)
print(len(circuits))
20
# We will truncate to these lengths
max_depth = 100
cycle_depths = np.arange(3, max_depth, 20)
cycle_depths
array([ 3, 23, 43, 63, 83])

Set up a Sampler.

For demonstration, we'll use a density matrix simulator to sample noisy samples. However, input a device_name (and have an authenticated Google Cloud project name set as your GOOGLE_CLOUD_PROJECT environment variable) to run on a real device.

device_name = None  # change me!

if device_name is None:
    sampler = cirq.DensityMatrixSimulator(noise=cirq.depolarize(5e-3))
else:
    import cirq_google as cg
    sampler = cg.get_engine_sampler(device_name, gate_set_name='sqrt_iswap')
    device = cg.get_engine_device(device_name)

    import cirq.contrib.routing as ccr
    graph = ccr.gridqubits_to_graph_device(device.qubits)
    pos = {q: (q.row, q.col) for q in graph.nodes}
    import networkx as nx
    nx.draw_networkx(graph, pos=pos)

Take Data

from cirq.experiments.xeb_sampling import sample_2q_xeb_circuits
sampled_df = sample_2q_xeb_circuits(
    sampler=sampler,
    circuits=circuits,
    cycle_depths=cycle_depths,
    repetitions=10_000,
)
sampled_df
100%|██████████| 108/108 [00:21<00:00,  5.13it/s]

Benchmark fidelities

from cirq.experiments.xeb_fitting import benchmark_2q_xeb_fidelities
fids = benchmark_2q_xeb_fidelities(
    sampled_df=sampled_df,
    circuits=circuits,
    cycle_depths=cycle_depths,
)
fids
%matplotlib inline
from matplotlib import pyplot as plt

# Exponential reference
xx = np.linspace(0, fids['cycle_depth'].max())
plt.plot(xx, (1-5e-3)**(4*xx), label=r'Exponential Reference')

def _p(fids):
    plt.plot(fids['cycle_depth'], fids['fidelity'], 'o-', label=fids.name)

fids.name = 'Sampled'
_p(fids)

plt.ylabel('Circuit fidelity')
plt.xlabel('Cycle Depth $d$')
plt.legend(loc='best')
<matplotlib.legend.Legend at 0x7f3db0c56ca0>

png

Optimize PhasedFSimGate parameters

We know what circuits we requested, and in this simulated example, we know what coherent error has happened. But in a real experiment, there is likely unknown coherent error that you would like to characterize. Therefore, we make the five angles in PhasedFSimGate free parameters and use a classical optimizer to find which set of parameters best describes the data we collected from the noisy simulator (or device, if this was a real experiment).

import multiprocessing
pool = multiprocessing.get_context('spawn').Pool()
from cirq.experiments.xeb_fitting import (
    parameterize_circuit, 
    characterize_phased_fsim_parameters_with_xeb, 
    SqrtISwapXEBOptions,
)

# Set which angles we want to characterize (all)
options = SqrtISwapXEBOptions(
    characterize_theta = True,
    characterize_zeta = True,
    characterize_chi = True,
    characterize_gamma = True,
    characterize_phi = True
)
# Parameterize the sqrt(iswap)s in our circuit library
pcircuits = [parameterize_circuit(circuit, options) for circuit in circuits]

# Run the characterization loop
characterization_result = characterize_phased_fsim_parameters_with_xeb(
    sampled_df,
    pcircuits,
    cycle_depths,
    options,
    pool=pool,
    # ease tolerance so it converges faster:
    fatol=5e-3, 
    xatol=5e-3
)
Simulating with theta =  -0.785 zeta  =       0 chi   =       0 gamma =       0 phi   =       0 
Loss:    0.53
Simulating with theta =  -0.685 zeta  =       0 chi   =       0 gamma =       0 phi   =       0 
Loss:   0.579
Simulating with theta =  -0.785 zeta  =     0.1 chi   =       0 gamma =       0 phi   =       0 
Loss:   0.552
Simulating with theta =  -0.785 zeta  =       0 chi   =     0.1 gamma =       0 phi   =       0 
Loss:   0.549
Simulating with theta =  -0.785 zeta  =       0 chi   =       0 gamma =     0.1 phi   =       0 
Loss:   0.577
Simulating with theta =  -0.785 zeta  =       0 chi   =       0 gamma =       0 phi   =     0.1 
Loss:   0.546
Simulating with theta =  -0.885 zeta  =    0.04 chi   =    0.04 gamma =    0.04 phi   =    0.04 
Loss:   0.598
Simulating with theta =  -0.735 zeta  =    0.01 chi   =    0.01 gamma =    0.01 phi   =    0.01 
Loss:   0.541
Simulating with theta =  -0.765 zeta  =   0.044 chi   =   0.044 gamma =  -0.096 phi   =   0.044 
Loss:   0.568
Simulating with theta =   -0.77 zeta  =   0.033 chi   =   0.033 gamma =  -0.047 phi   =   0.033 
Loss:   0.537
Simulating with theta =  -0.759 zeta  = -0.0828 chi   =  0.0572 gamma = -0.0148 phi   =  0.0572 
Loss:   0.555
Simulating with theta =  -0.779 zeta  =  0.0543 chi   =  0.0143 gamma = -0.0037 phi   =  0.0143 
Loss:   0.536
Simulating with theta =  -0.757 zeta  =  0.0389 chi   = -0.0771 gamma = -0.0163 phi   =  0.0629 
Loss:   0.551
Simulating with theta =  -0.778 zeta  = 0.00973 chi   =  0.0557 gamma = -0.00407 phi   =  0.0157 
Loss:   0.537
Simulating with theta =  -0.754 zeta  =  0.0428 chi   =  0.0452 gamma = -0.0179 phi   = -0.0708 
Loss:   0.555
Simulating with theta =  -0.778 zeta  =  0.0107 chi   =  0.0113 gamma = -0.00448 phi   =  0.0573 
Loss:   0.536
Simulating with theta =  -0.821 zeta  =  0.0331 chi   =  0.0357 gamma = -0.0337 phi   =  0.0381 
Loss:   0.539
Simulating with theta =  -0.799 zeta  =  0.0273 chi   =  0.0293 gamma = -0.0228 phi   =  0.0311 
Loss:   0.533
Simulating with theta =  -0.786 zeta  =  0.0404 chi   = -0.0206 gamma = -0.0271 phi   =  0.0386 
Loss:   0.529
Simulating with theta =  -0.791 zeta  =  0.0557 chi   = -0.0587 gamma = -0.0386 phi   =    0.05 
Loss:   0.536
Simulating with theta =  -0.801 zeta  =  0.0201 chi   = -0.0193 gamma =  0.0238 phi   =  0.0235 
Loss:    0.54
Simulating with theta =  -0.778 zeta  =  0.0298 chi   =  0.0199 gamma = -0.0293 phi   =  0.0306 
Loss:   0.531
Simulating with theta =  -0.794 zeta  =    0.05 chi   = 0.00588 gamma = -0.0287 phi   = -0.0115 
Loss:   0.532
Simulating with theta =  -0.798 zeta  =  0.0047 chi   = -0.000481 gamma = -0.0394 phi   =  0.0212 
Loss:    0.53
Simulating with theta =  -0.777 zeta  =  0.0226 chi   = -0.0274 gamma =  -0.027 phi   = 0.00047 
Loss:   0.528
Simulating with theta =  -0.766 zeta  =  0.0203 chi   = -0.0557 gamma = -0.0292 phi   = -0.0148 
Loss:   0.535
Simulating with theta =  -0.776 zeta  =  -0.011 chi   = -0.0173 gamma = -0.0205 phi   =  0.0478 
Loss:   0.531
Simulating with theta =  -0.781 zeta  = 0.00425 chi   = -0.0115 gamma = -0.0225 phi   =   0.033 
Loss:   0.529
Simulating with theta =  -0.793 zeta  = -0.00098 chi   = -0.0439 gamma = -0.0171 phi   = 0.00667 
Loss:    0.53
Simulating with theta =  -0.789 zeta  = 0.00671 chi   = -0.0279 gamma = -0.0202 phi   =  0.0127 
Loss:   0.528
Simulating with theta =  -0.769 zeta  =  0.0249 chi   = -0.0345 gamma = 0.000698 phi   =  0.0126 
Loss:   0.534
Simulating with theta =  -0.791 zeta  = 0.00975 chi   = -0.00898 gamma = -0.0294 phi   =  0.0191 
Loss:   0.528
Simulating with theta =  -0.785 zeta  =  0.0335 chi   = -0.0386 gamma = -0.0505 phi   =  0.0415 
Loss:   0.529
Simulating with theta =  -0.785 zeta  =  0.0251 chi   = -0.0289 gamma = -0.0379 phi   =  0.0311 
Loss:   0.528
Simulating with theta =  -0.783 zeta  =  -0.013 chi   = -0.0213 gamma = -0.0277 phi   = -1.84e-05 
Loss:   0.529
Simulating with theta =  -0.789 zeta  =  0.0162 chi   = -0.0343 gamma = -0.0344 phi   = -0.00767 
Loss:    0.53
Simulating with theta =  -0.783 zeta  = 0.00724 chi   = -0.0172 gamma = -0.0255 phi   =  0.0228 
Loss:   0.528
Simulating with theta =  -0.787 zeta  =  0.0416 chi   = -0.0229 gamma = -0.0283 phi   =  0.0345 
Loss:   0.529
Simulating with theta =  -0.784 zeta  = 0.000638 chi   = -0.0217 gamma = -0.0279 phi   = 0.00861 
Loss:   0.528
Simulating with theta =  -0.779 zeta  =  0.0194 chi   = -0.0137 gamma = -0.0389 phi   =  0.0202 
Loss:   0.528
Simulating with theta =  -0.781 zeta  =  0.0163 chi   = -0.0173 gamma = -0.0342 phi   =  0.0183 
Loss:   0.528
Simulating with theta =  -0.792 zeta  = 0.000971 chi   = -0.0102 gamma = -0.0349 phi   =  0.0395 
Loss:   0.529
Simulating with theta =  -0.781 zeta  =  0.0172 chi   = -0.0231 gamma =  -0.029 phi   =  0.0102 
Loss:   0.527
Simulating with theta =  -0.775 zeta  =  0.0168 chi   = -0.0343 gamma = -0.0324 phi   =  0.0174 
Loss:   0.528
Simulating with theta =  -0.787 zeta  =  0.0115 chi   = -0.0153 gamma = -0.0302 phi   =  0.0186 
Loss:   0.527
Simulating with theta =  -0.784 zeta  =  0.0211 chi   = -0.0253 gamma = -0.0382 phi   =  0.0119 
Loss:   0.528
Simulating with theta =  -0.783 zeta  =  0.0107 chi   = -0.0192 gamma = -0.0287 phi   =  0.0201 
Loss:   0.528
Simulating with theta =  -0.783 zeta  =  0.0317 chi   = -0.0198 gamma = -0.0361 phi   =  0.0308 
Loss:   0.528
Simulating with theta =  -0.781 zeta  = 0.00984 chi   = -0.00899 gamma = -0.0254 phi   = 0.00809 
Loss:   0.528
Simulating with theta =  -0.783 zeta  = -0.00548 chi   = -0.0137 gamma = -0.0229 phi   = -0.000606 
Loss:   0.528
Simulating with theta =  -0.783 zeta  =  0.0224 chi   = -0.0183 gamma = -0.0328 phi   =  0.0229 
Loss:   0.527
Simulating with theta =  -0.785 zeta  =  0.0124 chi   = -0.0167 gamma = -0.0242 phi   =  0.0137 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0199 chi   = -0.0281 gamma = -0.0325 phi   =  0.0261 
Loss:   0.528
Simulating with theta =  -0.783 zeta  =  0.0123 chi   = -0.0138 gamma = -0.0272 phi   =  0.0126 
Loss:   0.527
Simulating with theta =  -0.784 zeta  =  0.0197 chi   = -0.0156 gamma = -0.0287 phi   =  0.0111 
Loss:   0.527
Simulating with theta =  -0.784 zeta  =  0.0241 chi   = -0.0138 gamma = -0.0287 phi   = 0.00665 
Loss:   0.527
Simulating with theta =  -0.779 zeta  =  0.0221 chi   = -0.0197 gamma = -0.0266 phi   = 0.00958 
Loss:   0.527
Simulating with theta =  -0.781 zeta  =  0.0194 chi   = -0.0186 gamma = -0.0275 phi   =  0.0118 
Loss:   0.527
Simulating with theta =  -0.785 zeta  =  0.0173 chi   = -0.0101 gamma = -0.0271 phi   =  0.0187 
Loss:   0.527
Simulating with theta =  -0.782 zeta  =  0.0172 chi   = -0.0199 gamma = -0.0285 phi   =  0.0123 
Loss:   0.527
Simulating with theta =   -0.78 zeta  =   0.024 chi   = -0.0178 gamma = -0.0337 phi   =  0.0146 
Loss:   0.528
Simulating with theta =  -0.784 zeta  =  0.0153 chi   =  -0.017 gamma = -0.0266 phi   =  0.0139 
Loss:   0.527
Simulating with theta =  -0.783 zeta  =  0.0253 chi   =  -0.022 gamma = -0.0304 phi   =  0.0163 
Loss:   0.527
Simulating with theta =  -0.783 zeta  =  0.0164 chi   = -0.0189 gamma = -0.0239 phi   = 0.00329 
Loss:   0.527
Simulating with theta =  -0.783 zeta  =  0.0134 chi   = -0.0192 gamma = -0.0194 phi   = -0.00653 
Loss:   0.527
Simulating with theta =  -0.783 zeta  = 0.00993 chi   =  -0.014 gamma = -0.0236 phi   = 0.00475 
Loss:   0.527
Simulating with theta =  -0.783 zeta  =  0.0214 chi   =   -0.02 gamma = -0.0287 phi   =  0.0134 
Loss:   0.527
Simulating with theta =  -0.784 zeta  =  0.0197 chi   = -0.0162 gamma = -0.0256 phi   =  0.0091 
Loss:   0.527
Simulating with theta =  -0.785 zeta  =  0.0209 chi   = -0.0144 gamma = -0.0241 phi   = 0.00748 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =   0.018 chi   = -0.0157 gamma = -0.0253 phi   = 0.00784 
Loss:   0.527
Simulating with theta =  -0.784 zeta  =  0.0232 chi   = -0.0169 gamma = -0.0257 phi   = 0.00332 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0178 chi   = -0.0126 gamma = -0.0223 phi   = -0.000165 
Loss:   0.527
Simulating with theta =  -0.785 zeta  =  0.0189 chi   = -0.0158 gamma = -0.0199 phi   = -0.00243 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0185 chi   = -0.0158 gamma = -0.0155 phi   = -0.00921 
Loss:   0.527
Simulating with theta =  -0.788 zeta  =  0.0231 chi   = -0.0112 gamma =  -0.023 phi   = 0.00313 
Loss:   0.527
Simulating with theta =  -0.787 zeta  =  0.0163 chi   =  -0.011 gamma = -0.0201 phi   = 0.00302 
Loss:   0.527
Simulating with theta =  -0.785 zeta  =  0.0215 chi   = -0.0154 gamma = -0.0243 phi   = 0.00324 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0231 chi   = -0.0164 gamma = -0.0243 phi   = 0.00787 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0258 chi   = -0.0183 gamma = -0.0253 phi   =  0.0119 
Loss:   0.527
Simulating with theta =  -0.783 zeta  =  0.0178 chi   = -0.0198 gamma = -0.0241 phi   = 0.00647 
Loss:   0.527
Simulating with theta =  -0.787 zeta  =  0.0218 chi   = -0.0134 gamma = -0.0233 phi   = 0.00396 
Loss:   0.527
Simulating with theta =  -0.785 zeta  =  0.0245 chi   = -0.0144 gamma = -0.0211 phi   = 0.000212 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0196 chi   = -0.0154 gamma = -0.0242 phi   = 0.00593 
Loss:   0.527
Simulating with theta =  -0.787 zeta  =  0.0211 chi   = -0.0162 gamma = -0.0223 phi   = -5.25e-05 
Loss:   0.527
Simulating with theta =  -0.788 zeta  =  0.0212 chi   = -0.0171 gamma = -0.0214 phi   = -0.00382 
Loss:   0.527
Simulating with theta =  -0.787 zeta  =  0.0203 chi   = -0.0154 gamma = -0.0213 phi   = 0.00287 
Loss:   0.527
Simulating with theta =  -0.787 zeta  =  0.0235 chi   =  -0.015 gamma = -0.0263 phi   =  0.0107 
Loss:   0.527
Simulating with theta =  -0.788 zeta  =  0.0243 chi   = -0.0151 gamma = -0.0228 phi   = 0.00419 
Loss:   0.527
Simulating with theta =  -0.789 zeta  =  0.0267 chi   =  -0.015 gamma = -0.0221 phi   = 0.00332 
Loss:   0.527
Simulating with theta =  -0.786 zeta  =  0.0207 chi   = -0.0157 gamma = -0.0193 phi   = -0.00313 
Loss:   0.527
Simulating with theta =  -0.787 zeta  =  0.0228 chi   = -0.0151 gamma = -0.0246 phi   = 0.00721 
Loss:   0.527
characterization_result.final_params
{(cirq.GridQubit(4, 4), cirq.GridQubit(4, 5)): {'theta': -0.7875996188349357,
  'zeta': 0.024337612097931387,
  'chi': -0.015137949185273395,
  'gamma': -0.02279913410514104,
  'phi': 0.004192234177185471} }
characterization_result.fidelities_df
from cirq.experiments.xeb_fitting import before_and_after_characterization
before_after_df = before_and_after_characterization(fids, characterization_result)
before_after_df
from cirq.experiments.xeb_fitting import exponential_decay

for i, row in before_after_df.iterrows():
    plt.axhline(1, color='grey', ls='--')
    plt.plot(row['cycle_depths_0'], row['fidelities_0'], '*', color='red')
    plt.plot(row['cycle_depths_c'], row['fidelities_c'], 'o', color='blue')

    xx = np.linspace(0, np.max(row['cycle_depths_0']))
    plt.plot(xx, exponential_decay(xx, a=row['a_0'], layer_fid=row['layer_fid_0']), color='red')
    plt.plot(xx, exponential_decay(xx, a=row['a_c'], layer_fid=row['layer_fid_c']), color='blue')

    plt.show()

png