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try:
import cirq
except ImportError:
print("installing cirq...")
!pip install 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 [00:18<00:00, 5.78it/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 0x7fbe89477d50>
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: 0.591 Simulating with theta = -0.785 zeta = 0.1 chi = 0 gamma = 0 phi = 0 Loss: 0.54 Simulating with theta = -0.785 zeta = 0 chi = 0.1 gamma = 0 phi = 0 Loss: 0.566 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0.1 phi = 0 Loss: 0.586 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0 phi = 0.1 Loss: 0.537 Simulating with theta = -0.885 zeta = 0.04 chi = 0.04 gamma = 0.04 phi = 0.04 Loss: 0.612 Simulating with theta = -0.735 zeta = 0.01 chi = 0.01 gamma = 0.01 phi = 0.01 Loss: 0.548 Simulating with theta = -0.765 zeta = 0.044 chi = 0.044 gamma = -0.096 phi = 0.044 Loss: 0.549 Simulating with theta = -0.757 zeta = 0.0616 chi = -0.0784 gamma = -0.0344 phi = 0.0616 Loss: 0.552 Simulating with theta = -0.764 zeta = 0.0462 chi = -0.0338 gamma = -0.0258 phi = 0.0462 Loss: 0.53 Simulating with theta = -0.777 zeta = 0.0185 chi = -0.0535 gamma = 0.0897 phi = 0.0185 Loss: 0.584 Simulating with theta = -0.768 zeta = 0.0376 chi = 0.0196 gamma = -0.0496 phi = 0.0376 Loss: 0.53 Simulating with theta = -0.82 zeta = 0.0635 chi = -0.0157 gamma = -0.0402 phi = 0.0635 Loss: 0.544 Simulating with theta = -0.799 zeta = 0.0501 chi = -0.00925 gamma = -0.0276 phi = 0.0501 Loss: 0.53 Simulating with theta = -0.776 zeta = -0.0464 chi = -0.00937 gamma = -0.0412 phi = 0.0936 Loss: 0.532 Simulating with theta = -0.772 zeta = 0.035 chi = -0.0131 gamma = -0.0577 phi = -0.00898 Loss: 0.553 Simulating with theta = -0.782 zeta = 0.00876 chi = -0.00328 gamma = -0.0144 phi = 0.0728 Loss: 0.524 Simulating with theta = -0.784 zeta = 0.104 chi = -0.00131 gamma = -0.00577 phi = -0.0109 Loss: 0.542 Simulating with theta = -0.778 zeta = -0.00893 chi = -0.00736 gamma = -0.0323 phi = 0.0675 Loss: 0.524 Simulating with theta = -0.795 zeta = 0.000847 chi = -0.0411 gamma = 0.00951 phi = 0.057 Loss: 0.531 Simulating with theta = -0.775 zeta = 0.0284 chi = 0.00444 gamma = -0.0348 phi = 0.0425 Loss: 0.526 Simulating with theta = -0.803 zeta = -0.0148 chi = 0.0276 gamma = -0.0179 phi = 0.0469 Loss: 0.535 Simulating with theta = -0.774 zeta = 0.0309 chi = -0.0184 gamma = -0.0238 phi = 0.0464 Loss: 0.525 Simulating with theta = -0.759 zeta = -0.0265 chi = -0.000603 gamma = -0.0145 phi = 0.0415 Loss: 0.533 Simulating with theta = -0.789 zeta = 0.031 chi = -0.00709 gamma = -0.0243 phi = 0.048 Loss: 0.525 Simulating with theta = -0.774 zeta = 0.0361 chi = -0.0127 gamma = -0.0519 phi = 0.111 Loss: 0.523 Simulating with theta = -0.768 zeta = 0.0541 chi = -0.019 gamma = -0.0778 phi = 0.166 Loss: 0.537 Simulating with theta = -0.784 zeta = 0.0107 chi = -0.024 gamma = -0.0239 phi = 0.0957 Loss: 0.524 Simulating with theta = -0.767 zeta = 2.18e-05 chi = -0.0192 gamma = -0.0342 phi = 0.109 Loss: 0.525 Simulating with theta = -0.784 zeta = 0.0232 chi = -0.0101 gamma = -0.0268 phi = 0.0633 Loss: 0.523 Simulating with theta = -0.786 zeta = -0.003 chi = -0.00453 gamma = -0.0359 phi = 0.118 Loss: 0.526 Simulating with theta = -0.777 zeta = 0.0225 chi = -0.015 gamma = -0.0268 phi = 0.0642 Loss: 0.522 Simulating with theta = -0.774 zeta = 0.0219 chi = 0.00462 gamma = -0.037 phi = 0.0557 Loss: 0.524 Simulating with theta = -0.781 zeta = 0.0135 chi = -0.0168 gamma = -0.0272 phi = 0.0857 Loss: 0.522 Simulating with theta = -0.781 zeta = 0.0506 chi = -0.0158 gamma = -0.0265 phi = 0.0912 Loss: 0.526 Simulating with theta = -0.779 zeta = 0.00594 chi = -0.00947 gamma = -0.0309 phi = 0.0734 Loss: 0.522 Simulating with theta = -0.776 zeta = 0.0317 chi = -0.0224 gamma = -0.051 phi = 0.0862 Loss: 0.524 Simulating with theta = -0.78 zeta = 0.0145 chi = -0.00805 gamma = -0.0236 phi = 0.0761 Loss: 0.522 Simulating with theta = -0.787 zeta = -0.00421 chi = -0.0111 gamma = -0.00223 phi = 0.0343 Loss: 0.525 Simulating with theta = -0.777 zeta = 0.026 chi = -0.0123 gamma = -0.0395 phi = 0.0917 Loss: 0.522 Simulating with theta = -0.774 zeta = 0.00971 chi = -0.0145 gamma = -0.0324 phi = 0.0931 Loss: 0.522 Simulating with theta = -0.779 zeta = 0.00541 chi = -0.0095 gamma = -0.0346 phi = 0.104 Loss: 0.523 Simulating with theta = -0.778 zeta = 0.0182 chi = -0.0136 gamma = -0.0288 phi = 0.0741 Loss: 0.522 Simulating with theta = -0.774 zeta = 0.0162 chi = -0.00634 gamma = -0.0348 phi = 0.0777 Loss: 0.522 Simulating with theta = -0.77 zeta = 0.0176 chi = -0.00109 gamma = -0.0387 phi = 0.0737 Loss: 0.523 Simulating with theta = -0.781 zeta = 0.0226 chi = -0.00538 gamma = -0.0306 phi = 0.0641 Loss: 0.523 Simulating with theta = -0.776 zeta = 0.0129 chi = -0.0122 gamma = -0.0319 phi = 0.0859 Loss: 0.522 Simulating with theta = -0.773 zeta = 0.0172 chi = -0.0135 gamma = -0.0428 phi = 0.085 Loss: 0.522 Simulating with theta = -0.778 zeta = 0.0152 chi = -0.00942 gamma = -0.0284 phi = 0.0783 Loss: 0.522 Simulating with theta = -0.775 zeta = 0.0295 chi = -0.0121 gamma = -0.0345 phi = 0.0897 Loss: 0.522 Simulating with theta = -0.778 zeta = 0.0118 chi = -0.0101 gamma = -0.0318 phi = 0.0775 Loss: 0.522 Simulating with theta = -0.775 zeta = 0.0147 chi = -0.00656 gamma = -0.0378 phi = 0.0903 Loss: 0.522 Simulating with theta = -0.774 zeta = 0.0129 chi = -0.00304 gamma = -0.0423 phi = 0.0984 Loss: 0.522 Simulating with theta = -0.776 zeta = 0.00234 chi = -0.00558 gamma = -0.0264 phi = 0.0722 Loss: 0.522 Simulating with theta = -0.777 zeta = 0.0201 chi = -0.0106 gamma = -0.0362 phi = 0.0868 Loss: 0.522 Simulating with theta = -0.78 zeta = 0.0137 chi = -0.0132 gamma = -0.0316 phi = 0.0898 Loss: 0.522 Simulating with theta = -0.775 zeta = 0.0156 chi = -0.00806 gamma = -0.034 phi = 0.0807 Loss: 0.522 Simulating with theta = -0.774 zeta = 0.0149 chi = -0.00962 gamma = -0.0403 phi = 0.0901 Loss: 0.522 Simulating with theta = -0.777 zeta = 0.0151 chi = -0.00947 gamma = -0.0314 phi = 0.0813 Loss: 0.522 Simulating with theta = -0.777 zeta = 0.018 chi = -0.0057 gamma = -0.0365 phi = 0.0808 Loss: 0.522 Simulating with theta = -0.775 zeta = 0.0215 chi = -0.00604 gamma = -0.0386 phi = 0.0905 Loss: 0.522 Simulating with theta = -0.776 zeta = 0.0191 chi = -0.00706 gamma = -0.0369 phi = 0.0872 Loss: 0.522 Simulating with theta = -0.777 zeta = 0.0205 chi = -0.0098 gamma = -0.0322 phi = 0.0764 Loss: 0.522 Simulating with theta = -0.776 zeta = 0.0161 chi = -0.00737 gamma = -0.0364 phi = 0.0868 Loss: 0.522 Simulating with theta = -0.775 zeta = 0.0164 chi = -0.0113 gamma = -0.0334 phi = 0.0884 Loss: 0.522 Simulating with theta = -0.777 zeta = 0.0176 chi = -0.00711 gamma = -0.0358 phi = 0.0827 Loss: 0.522
characterization_result.final_params
{(cirq.GridQubit(4, 4),
cirq.GridQubit(4, 5)): {'theta': np.float64(-0.7766190436351619), 'zeta': np.float64(0.017582753361376283), 'chi': np.float64(-0.0071055864609924635), 'gamma': np.float64(-0.03575806139006697), 'phi': np.float64(0.08267429314279195)} }
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()
