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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 [00:23<00:00, 4.52it/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 0x7f6436d22020>
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: 0.582 Simulating with theta = -0.785 zeta = 0.1 chi = 0 gamma = 0 phi = 0 Loss: 0.569 Simulating with theta = -0.785 zeta = 0 chi = 0.1 gamma = 0 phi = 0 Loss: 0.554 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0.1 phi = 0 Loss: 0.592 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0 phi = 0.1 Loss: 0.557 Simulating with theta = -0.745 zeta = 0.04 chi = 0.04 gamma = -0.1 phi = 0.04 Loss: 0.586 Simulating with theta = -0.755 zeta = 0.03 chi = 0.03 gamma = -0.05 phi = 0.03 Loss: 0.542 Simulating with theta = -0.873 zeta = 0.052 chi = 0.052 gamma = -0.02 phi = 0.052 Loss: 0.6 Simulating with theta = -0.732 zeta = 0.013 chi = 0.013 gamma = -0.005 phi = 0.013 Loss: 0.546 Simulating with theta = -0.752 zeta = -0.0828 chi = 0.0572 gamma = -0.022 phi = 0.0572 Loss: 0.566 Simulating with theta = -0.76 zeta = -0.0371 chi = 0.0429 gamma = -0.0165 phi = 0.0429 Loss: 0.534 Simulating with theta = -0.742 zeta = 0.00236 chi = 0.0744 gamma = -0.0286 phi = -0.0656 Loss: 0.57 Simulating with theta = -0.775 zeta = 0.00059 chi = 0.0186 gamma = -0.00715 phi = 0.0586 Loss: 0.534 Simulating with theta = -0.738 zeta = 0.0026 chi = -0.0582 gamma = -0.0315 phi = 0.0578 Loss: 0.555 Simulating with theta = -0.774 zeta = 0.000649 chi = 0.0604 gamma = -0.00787 phi = 0.0144 Loss: 0.528 Simulating with theta = -0.807 zeta = -0.0153 chi = 0.0478 gamma = -0.0276 phi = 0.0454 Loss: 0.536 Simulating with theta = -0.805 zeta = -0.0505 chi = 0.0379 gamma = 0.0264 phi = 0.0345 Loss: 0.557 Simulating with theta = -0.768 zeta = 0.00988 chi = 0.032 gamma = -0.0309 phi = 0.0311 Loss: 0.528 Simulating with theta = -0.737 zeta = 0.00495 chi = 0.0138 gamma = 0.00264 phi = 0.0135 Loss: 0.543 Simulating with theta = -0.79 zeta = -0.0103 chi = 0.0393 gamma = -0.02 phi = 0.0374 Loss: 0.526 Simulating with theta = -0.776 zeta = -0.0153 chi = 0.0512 gamma = -0.023 phi = -0.00824 Loss: 0.531 Simulating with theta = -0.797 zeta = 0.0311 chi = 0.0303 gamma = -0.0162 phi = -0.013 Loss: 0.536 Simulating with theta = -0.77 zeta = -0.0201 chi = 0.0397 gamma = -0.0164 phi = 0.0289 Loss: 0.526 Simulating with theta = -0.778 zeta = 0.00741 chi = 0.0173 gamma = -0.00712 phi = 0.053 Loss: 0.533 Simulating with theta = -0.777 zeta = -0.00964 chi = 0.0428 gamma = -0.019 phi = 0.00707 Loss: 0.525 Simulating with theta = -0.766 zeta = -0.0118 chi = 0.0857 gamma = -0.0377 phi = 0.0476 Loss: 0.548 Simulating with theta = -0.78 zeta = -0.00294 chi = 0.0214 gamma = -0.00943 phi = 0.0119 Loss: 0.525 Simulating with theta = -0.78 zeta = -0.0139 chi = 0.00963 gamma = -0.0305 phi = 0.0321 Loss: 0.528 Simulating with theta = -0.775 zeta = -0.00298 chi = 0.0477 gamma = -0.0135 phi = 0.0189 Loss: 0.525 Simulating with theta = -0.789 zeta = -0.0282 chi = 0.0444 gamma = -0.000461 phi = 0.0105 Loss: 0.53 Simulating with theta = -0.773 zeta = 0.00035 chi = 0.0351 gamma = -0.0233 phi = 0.026 Loss: 0.525 Simulating with theta = -0.76 zeta = -0.00384 chi = 0.0354 gamma = -0.0126 phi = -0.0003 Loss: 0.526 Simulating with theta = -0.777 zeta = 0.0124 chi = 0.0332 gamma = -0.0147 phi = -0.00352 Loss: 0.527 Simulating with theta = -0.771 zeta = -0.0119 chi = 0.0381 gamma = -0.016 phi = 0.0208 Loss: 0.525 Simulating with theta = -0.791 zeta = -0.00702 chi = 0.0386 gamma = -0.0199 phi = 0.0342 Loss: 0.526 Simulating with theta = -0.783 zeta = -0.00623 chi = 0.0378 gamma = -0.0181 phi = 0.0255 Loss: 0.525 Simulating with theta = -0.776 zeta = 0.00015 chi = 0.0293 gamma = -0.0131 phi = 0.0342 Loss: 0.526 Simulating with theta = -0.777 zeta = -0.00719 chi = 0.0394 gamma = -0.0175 phi = 0.0138 Loss: 0.524 Simulating with theta = -0.771 zeta = -0.00825 chi = 0.0578 gamma = -0.0259 phi = 0.0301 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00427 chi = 0.0305 gamma = -0.0136 phi = 0.0165 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.00873 chi = 0.0246 gamma = -0.0219 phi = 0.0222 Loss: 0.525 Simulating with theta = -0.776 zeta = -0.00442 chi = 0.042 gamma = -0.0156 phi = 0.0197 Loss: 0.524 Simulating with theta = -0.781 zeta = -0.014 chi = 0.0401 gamma = -0.00901 phi = 0.0126 Loss: 0.525 Simulating with theta = -0.775 zeta = -0.00323 chi = 0.0363 gamma = -0.0197 phi = 0.0226 Loss: 0.524 Simulating with theta = -0.784 zeta = 0.0018 chi = 0.0363 gamma = -0.0178 phi = 0.0184 Loss: 0.525 Simulating with theta = -0.773 zeta = -0.000699 chi = 0.036 gamma = -0.0156 phi = 0.0109 Loss: 0.524 Simulating with theta = -0.767 zeta = -0.00972 chi = 0.0374 gamma = -0.015 phi = 0.015 Loss: 0.525 Simulating with theta = -0.78 zeta = -0.00108 chi = 0.0366 gamma = -0.0171 phi = 0.0176 Loss: 0.524 Simulating with theta = -0.781 zeta = -0.00738 chi = 0.0379 gamma = -0.0178 phi = 0.0252 Loss: 0.524 Simulating with theta = -0.775 zeta = -0.00237 chi = 0.0365 gamma = -0.0162 phi = 0.0145 Loss: 0.524 Simulating with theta = -0.777 zeta = 0.00105 chi = 0.0333 gamma = -0.0153 phi = 0.0225 Loss: 0.524 Simulating with theta = -0.779 zeta = -0.00121 chi = 0.0352 gamma = -0.0114 phi = 0.0136 Loss: 0.524 Simulating with theta = -0.781 zeta = -0.000196 chi = 0.0347 gamma = -0.00719 phi = 0.00915 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.00639 chi = 0.039 gamma = -0.0142 phi = 0.0103 Loss: 0.524 Simulating with theta = -0.781 zeta = -0.00171 chi = 0.0291 gamma = -0.0134 phi = 0.00926 Loss: 0.524 Simulating with theta = -0.779 zeta = -0.00239 chi = 0.0323 gamma = -0.0139 phi = 0.0119 Loss: 0.524 Simulating with theta = -0.779 zeta = -0.0011 chi = 0.0413 gamma = -0.0155 phi = 0.0107 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.00348 chi = 0.0332 gamma = -0.0141 phi = 0.015 Loss: 0.524 Simulating with theta = -0.776 zeta = -0.00525 chi = 0.0339 gamma = -0.0108 phi = 0.00852 Loss: 0.524 Simulating with theta = -0.782 zeta = -0.00511 chi = 0.033 gamma = -0.00956 phi = 0.00925 Loss: 0.524 Simulating with theta = -0.779 zeta = -0.000587 chi = 0.0281 gamma = -0.00968 phi = 0.0131 Loss: 0.524 Simulating with theta = -0.779 zeta = -0.00494 chi = 0.0363 gamma = -0.0131 phi = 0.011 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.00561 chi = 0.0363 gamma = -0.00962 phi = 0.0111 Loss: 0.524 Simulating with theta = -0.775 zeta = -0.00308 chi = 0.037 gamma = -0.014 phi = 0.0144 Loss: 0.524 Simulating with theta = -0.776 zeta = -0.00359 chi = 0.036 gamma = -0.0129 phi = 0.0131 Loss: 0.524 Simulating with theta = -0.777 zeta = -0.00476 chi = 0.0379 gamma = -0.00904 phi = 0.00793 Loss: 0.524 Simulating with theta = -0.777 zeta = -0.0054 chi = 0.0402 gamma = -0.00653 phi = 0.00439 Loss: 0.524 Simulating with theta = -0.776 zeta = -0.00323 chi = 0.0355 gamma = -0.00841 phi = 0.0108 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.00451 chi = 0.0361 gamma = -0.0119 phi = 0.0109 Loss: 0.524 Simulating with theta = -0.78 zeta = -0.00262 chi = 0.0386 gamma = -0.0111 phi = 0.0142 Loss: 0.524 Simulating with theta = -0.777 zeta = -0.00459 chi = 0.0351 gamma = -0.0109 phi = 0.00993 Loss: 0.524 Simulating with theta = -0.78 zeta = -0.00468 chi = 0.0362 gamma = -0.00823 phi = 0.00826 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.00229 chi = 0.0359 gamma = -0.0109 phi = 0.00918 Loss: 0.524 Simulating with theta = -0.778 zeta = -0.000631 chi = 0.0357 gamma = -0.0116 phi = 0.00824 Loss: 0.524
characterization_result.final_params
{(cirq.GridQubit(4, 4), cirq.GridQubit(4, 5)): {'theta': -0.778232976741861,
'zeta': -0.0022901040111069438,
'chi': 0.03588533873863812,
'gamma': -0.010947609912514509,
'phi': 0.00918394807046469} }
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()
