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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
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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 0x7f652521b8d0>
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: 0.527 Simulating with theta = -0.685 zeta = 0 chi = 0 gamma = 0 phi = 0 Loss: 0.596 Simulating with theta = -0.785 zeta = 0.1 chi = 0 gamma = 0 phi = 0 Loss: 0.562 Simulating with theta = -0.785 zeta = 0 chi = 0.1 gamma = 0 phi = 0 Loss: 0.557 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0.1 phi = 0 Loss: 0.589 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0 phi = 0.1 Loss: 0.547 Simulating with theta = -0.885 zeta = 0.04 chi = 0.04 gamma = 0.04 phi = 0.04 Loss: 0.618 Simulating with theta = -0.735 zeta = 0.01 chi = 0.01 gamma = 0.01 phi = 0.01 Loss: 0.546 Simulating with theta = -0.765 zeta = 0.044 chi = 0.044 gamma = -0.096 phi = 0.044 Loss: 0.582 Simulating with theta = -0.77 zeta = 0.033 chi = 0.033 gamma = -0.047 phi = 0.033 Loss: 0.546 Simulating with theta = -0.759 zeta = -0.0828 chi = 0.0572 gamma = -0.0148 phi = 0.0572 Loss: 0.555 Simulating with theta = -0.749 zeta = -0.0159 chi = -0.0599 gamma = -0.0207 phi = 0.0801 Loss: 0.571 Simulating with theta = -0.776 zeta = -0.00398 chi = 0.06 gamma = -0.00518 phi = 0.02 Loss: 0.528 Simulating with theta = -0.782 zeta = 0.0984 chi = -0.016 gamma = -0.00207 phi = 0.00801 Loss: 0.559 Simulating with theta = -0.765 zeta = -0.0375 chi = 0.0389 gamma = -0.0116 phi = 0.0449 Loss: 0.525 Simulating with theta = -0.748 zeta = 0.000609 chi = 0.0568 gamma = -0.0215 phi = -0.0568 Loss: 0.571 Simulating with theta = -0.776 zeta = 0.000152 chi = 0.0142 gamma = -0.00538 phi = 0.0608 Loss: 0.527 Simulating with theta = -0.814 zeta = -0.0133 chi = 0.0484 gamma = -0.0377 phi = 0.0535 Loss: 0.54 Simulating with theta = -0.796 zeta = -0.0549 chi = 0.0316 gamma = 0.0231 phi = 0.0387 Loss: 0.536 Simulating with theta = -0.746 zeta = -0.0251 chi = 0.00945 gamma = 0.038 phi = 0.0123 Loss: 0.539 Simulating with theta = -0.763 zeta = -0.0222 chi = 0.0192 gamma = 0.0191 phi = 0.0226 Loss: 0.527 Simulating with theta = -0.75 zeta = 0.0295 chi = 0.0213 gamma = -0.0243 phi = 0.0206 Loss: 0.543 Simulating with theta = -0.785 zeta = -0.0338 chi = 0.029 gamma = 0.0112 phi = 0.0342 Loss: 0.523 Simulating with theta = -0.773 zeta = -0.0333 chi = -0.0195 gamma = 0.0105 phi = 0.045 Loss: 0.541 Simulating with theta = -0.776 zeta = -0.0113 chi = 0.0401 gamma = -0.00126 phi = 0.0263 Loss: 0.521 Simulating with theta = -0.76 zeta = -0.0419 chi = 0.0566 gamma = 0.00483 phi = 0.0755 Loss: 0.541 Simulating with theta = -0.779 zeta = -0.0105 chi = 0.0141 gamma = 0.00121 phi = 0.0189 Loss: 0.523 Simulating with theta = -0.771 zeta = -0.0463 chi = 0.0424 gamma = 0.0128 phi = -0.00208 Loss: 0.526 Simulating with theta = -0.787 zeta = -0.0335 chi = 0.0466 gamma = -0.0141 phi = 0.0263 Loss: 0.525 Simulating with theta = -0.786 zeta = -0.00439 chi = 0.0252 gamma = -0.0187 phi = 0.0623 Loss: 0.522 Simulating with theta = -0.8 zeta = 0.000101 chi = 0.0232 gamma = 0.00296 phi = 0.0222 Loss: 0.525 Simulating with theta = -0.783 zeta = 0.0096 chi = 0.00602 gamma = 0.0123 phi = 0.0392 Loss: 0.529 Simulating with theta = -0.786 zeta = -0.0228 chi = 0.0365 gamma = -0.00753 phi = 0.0295 Loss: 0.521 Simulating with theta = -0.765 zeta = -0.0332 chi = 0.0348 gamma = -0.00897 phi = 0.0462 Loss: 0.525 Simulating with theta = -0.791 zeta = -0.00822 chi = 0.0261 gamma = -2.36e-05 phi = 0.0282 Loss: 0.521 Simulating with theta = -0.782 zeta = 0.0109 chi = 0.0278 gamma = -0.0217 phi = 0.0319 Loss: 0.528 Simulating with theta = -0.784 zeta = -0.0226 chi = 0.0287 gamma = 0.00298 phi = 0.0336 Loss: 0.52 Simulating with theta = -0.79 zeta = -0.0173 chi = 0.0485 gamma = -0.011 phi = 0.0531 Loss: 0.521 Simulating with theta = -0.785 zeta = -0.0285 chi = 0.0468 gamma = 0.0119 phi = 0.00599 Loss: 0.522 Simulating with theta = -0.786 zeta = -0.0104 chi = 0.0306 gamma = -0.011 phi = 0.0482 Loss: 0.52 Simulating with theta = -0.777 zeta = -0.0255 chi = 0.0477 gamma = -0.0111 phi = 0.048 Loss: 0.52 Simulating with theta = -0.771 zeta = -0.0342 chi = 0.0585 gamma = -0.0166 phi = 0.0579 Loss: 0.525 Simulating with theta = -0.774 zeta = -0.0198 chi = 0.025 gamma = -0.000165 phi = 0.0212 Loss: 0.522 Simulating with theta = -0.786 zeta = -0.0179 chi = 0.0426 gamma = -0.0083 phi = 0.0451 Loss: 0.52 Simulating with theta = -0.777 zeta = -0.0123 chi = 0.0394 gamma = -0.00395 phi = 0.051 Loss: 0.521 Simulating with theta = -0.789 zeta = -0.0242 chi = 0.0355 gamma = -0.0113 phi = 0.0641 Loss: 0.521 Simulating with theta = -0.785 zeta = -0.021 chi = 0.0366 gamma = -0.00879 phi = 0.0546 Loss: 0.52 Simulating with theta = -0.79 zeta = -0.0266 chi = 0.0351 gamma = -0.0105 phi = 0.0409 Loss: 0.521 Simulating with theta = -0.78 zeta = -0.0159 chi = 0.0383 gamma = -0.0056 phi = 0.0484 Loss: 0.52 Simulating with theta = -0.78 zeta = -0.0307 chi = 0.047 gamma = -0.0013 phi = 0.0437 Loss: 0.52 Simulating with theta = -0.779 zeta = -0.0218 chi = 0.0562 gamma = -0.017 phi = 0.0624 Loss: 0.522 Simulating with theta = -0.783 zeta = -0.0224 chi = 0.0356 gamma = -0.00202 phi = 0.0408 Loss: 0.519 Simulating with theta = -0.788 zeta = -0.0176 chi = 0.0324 gamma = 0.000705 phi = 0.045 Loss: 0.52 Simulating with theta = -0.78 zeta = -0.0235 chi = 0.0439 gamma = -0.00815 phi = 0.0473 Loss: 0.519 Simulating with theta = -0.786 zeta = -0.00954 chi = 0.0318 gamma = -0.0118 phi = 0.0508 Loss: 0.52 Simulating with theta = -0.781 zeta = -0.0254 chi = 0.0432 gamma = -0.00394 phi = 0.0455 Loss: 0.519 Simulating with theta = -0.778 zeta = -0.0254 chi = 0.0364 gamma = -0.0031 phi = 0.0496 Loss: 0.52 Simulating with theta = -0.784 zeta = -0.0198 chi = 0.0411 gamma = -0.007 phi = 0.0462 Loss: 0.519 Simulating with theta = -0.778 zeta = -0.0219 chi = 0.0442 gamma = -0.00189 phi = 0.0366 Loss: 0.52 Simulating with theta = -0.782 zeta = -0.0293 chi = 0.0448 gamma = -0.0036 phi = 0.0381 Loss: 0.52 Simulating with theta = -0.781 zeta = -0.0193 chi = 0.04 gamma = -0.0051 phi = 0.0459 Loss: 0.519 Simulating with theta = -0.785 zeta = -0.0223 chi = 0.0373 gamma = -0.00859 phi = 0.0536 Loss: 0.52 Simulating with theta = -0.78 zeta = -0.022 chi = 0.0425 gamma = -0.00357 phi = 0.0409 Loss: 0.519 Simulating with theta = -0.783 zeta = -0.02 chi = 0.0371 gamma = -0.000494 phi = 0.0404 Loss: 0.519 Simulating with theta = -0.781 zeta = -0.0202 chi = 0.0459 gamma = -0.00602 phi = 0.0467 Loss: 0.52 Simulating with theta = -0.782 zeta = -0.0218 chi = 0.0382 gamma = -0.00302 phi = 0.0423 Loss: 0.519 Simulating with theta = -0.783 zeta = -0.0157 chi = 0.0363 gamma = -0.00373 phi = 0.0408 Loss: 0.519 Simulating with theta = -0.782 zeta = -0.023 chi = 0.0415 gamma = -0.00389 phi = 0.0443 Loss: 0.519
characterization_result.final_params
{(cirq.GridQubit(4, 4),
cirq.GridQubit(4, 5)): {'theta': np.float64(-0.7824010738176892), 'zeta': np.float64(-0.021846951021398952), 'chi': np.float64(0.03817187711394892), 'gamma': np.float64(-0.0030186313800510695), 'phi': np.float64(0.04228060788532288)} }
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()
