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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 [00:22<00:00, 4.88it/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 0x7f0b075bdf60>
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: 0.528 Simulating with theta = -0.685 zeta = 0 chi = 0 gamma = 0 phi = 0 Loss: 0.6 Simulating with theta = -0.785 zeta = 0.1 chi = 0 gamma = 0 phi = 0 Loss: 0.563 Simulating with theta = -0.785 zeta = 0 chi = 0.1 gamma = 0 phi = 0 Loss: 0.568 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0.1 phi = 0 Loss: 0.582 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0 phi = 0.1 Loss: 0.549 Simulating with theta = -0.885 zeta = 0.04 chi = 0.04 gamma = 0.04 phi = 0.04 Loss: 0.625 Simulating with theta = -0.735 zeta = 0.01 chi = 0.01 gamma = 0.01 phi = 0.01 Loss: 0.557 Simulating with theta = -0.765 zeta = 0.044 chi = 0.044 gamma = -0.096 phi = 0.044 Loss: 0.571 Simulating with theta = -0.77 zeta = 0.033 chi = 0.033 gamma = -0.047 phi = 0.033 Loss: 0.54 Simulating with theta = -0.759 zeta = 0.0572 chi = -0.0828 gamma = -0.0148 phi = 0.0572 Loss: 0.57 Simulating with theta = -0.779 zeta = 0.0143 chi = 0.0543 gamma = -0.0037 phi = 0.0143 Loss: 0.535 Simulating with theta = -0.757 zeta = -0.0771 chi = 0.0389 gamma = -0.0163 phi = 0.0629 Loss: 0.577 Simulating with theta = -0.778 zeta = 0.0557 chi = 0.00973 gamma = -0.00407 phi = 0.0157 Loss: 0.537 Simulating with theta = -0.824 zeta = 0.0312 chi = 0.0288 gamma = -0.0319 phi = 0.0552 Loss: 0.54 Simulating with theta = -0.789 zeta = 0.0537 chi = 0.0503 gamma = -0.0347 phi = -0.0527 Loss: 0.572 Simulating with theta = -0.786 zeta = 0.0134 chi = 0.0126 gamma = -0.00867 phi = 0.0618 Loss: 0.529 Simulating with theta = -0.811 zeta = 0.0129 chi = 0.00917 gamma = 0.0277 phi = 0.0258 Loss: 0.535 Simulating with theta = -0.752 zeta = 0.00732 chi = 0.0055 gamma = 0.0364 phi = -0.00814 Loss: 0.547 Simulating with theta = -0.806 zeta = 0.0252 chi = 0.023 gamma = -0.0148 phi = 0.0394 Loss: 0.529 Simulating with theta = -0.809 zeta = -0.0294 chi = 0.0299 gamma = 0.00425 phi = 0.0408 Loss: 0.54 Simulating with theta = -0.786 zeta = 0.0344 chi = 0.0148 gamma = -0.00199 phi = 0.022 Loss: 0.529 Simulating with theta = -0.811 zeta = 0.0201 chi = -0.0305 gamma = 0.00457 phi = 0.0453 Loss: 0.536 Simulating with theta = -0.787 zeta = 0.0157 chi = 0.0331 gamma = -0.00163 phi = 0.0221 Loss: 0.527 Simulating with theta = -0.769 zeta = 0.0227 chi = 0.0242 gamma = -0.0385 phi = 0.0323 Loss: 0.536 Simulating with theta = -0.8 zeta = 0.0153 chi = 0.0129 gamma = 0.0111 phi = 0.0274 Loss: 0.527 Simulating with theta = -0.8 zeta = -0.00656 chi = 0.0179 gamma = -0.00362 phi = 0.0383 Loss: 0.526 Simulating with theta = -0.807 zeta = -0.0271 chi = 0.0194 gamma = -0.00443 phi = 0.0464 Loss: 0.534 Simulating with theta = -0.778 zeta = -0.0101 chi = 0.00761 gamma = 0.0137 phi = 0.0205 Loss: 0.532 Simulating with theta = -0.799 zeta = 0.0164 chi = 0.0191 gamma = -0.0077 phi = 0.0346 Loss: 0.525 Simulating with theta = -0.802 zeta = 0.00294 chi = 0.0206 gamma = 0.00794 phi = -0.0129 Loss: 0.529 Simulating with theta = -0.79 zeta = 0.0108 chi = 0.0146 gamma = -0.00452 phi = 0.0432 Loss: 0.526 Simulating with theta = -0.805 zeta = 0.0207 chi = 0.0391 gamma = -0.00254 phi = 0.0662 Loss: 0.535 Simulating with theta = -0.79 zeta = 0.00517 chi = 0.00976 gamma = -0.000634 phi = 0.0166 Loss: 0.525 Simulating with theta = -0.805 zeta = 0.000713 chi = -0.00338 gamma = -0.000505 phi = 0.042 Loss: 0.527 Simulating with theta = -0.794 zeta = -0.0047 chi = 0.0103 gamma = -0.0179 phi = 0.0424 Loss: 0.525 Simulating with theta = -0.784 zeta = 0.00774 chi = 0.032 gamma = -0.0132 phi = 0.028 Loss: 0.528 Simulating with theta = -0.8 zeta = 0.00247 chi = 0.00547 gamma = -0.00369 phi = 0.0385 Loss: 0.525 Simulating with theta = -0.789 zeta = 0.0186 chi = 0.00583 gamma = -0.0102 phi = 0.0318 Loss: 0.526 Simulating with theta = -0.792 zeta = 0.0123 chi = 0.00884 gamma = -0.00852 phi = 0.0334 Loss: 0.525 Simulating with theta = -0.799 zeta = 0.00187 chi = 0.0068 gamma = -0.0109 phi = 0.0231 Loss: 0.525 Simulating with theta = -0.791 zeta = -0.00956 chi = -0.00269 gamma = -0.00895 phi = 0.0269 Loss: 0.526 Simulating with theta = -0.797 zeta = 0.00992 chi = 0.0137 gamma = -0.00801 phi = 0.0327 Loss: 0.525 Simulating with theta = -0.79 zeta = 0.00821 chi = 0.0124 gamma = -0.00464 phi = 0.0424 Loss: 0.526 Simulating with theta = -0.797 zeta = 0.00345 chi = 0.0082 gamma = -0.00931 phi = 0.0279 Loss: 0.525 Simulating with theta = -0.788 zeta = 0.008 chi = 0.0148 gamma = -0.0141 phi = 0.0227 Loss: 0.526 Simulating with theta = -0.797 zeta = 0.00385 chi = 0.00781 gamma = -0.00628 phi = 0.0345 Loss: 0.525 Simulating with theta = -0.796 zeta = 0.0186 chi = 0.00905 gamma = 0.0048 phi = 0.0157 Loss: 0.526 Simulating with theta = -0.794 zeta = 0.00112 chi = 0.00996 gamma = -0.0122 phi = 0.0357 Loss: 0.525 Simulating with theta = -0.8 zeta = 0.0071 chi = 0.00964 gamma = -0.0171 phi = 0.0492 Loss: 0.525 Simulating with theta = -0.793 zeta = 0.00565 chi = 0.00973 gamma = -0.00475 phi = 0.0247 Loss: 0.525 Simulating with theta = -0.799 zeta = -0.00273 chi = 0.0109 gamma = -0.00771 phi = 0.0288 Loss: 0.525 Simulating with theta = -0.797 zeta = 0.00104 chi = 0.0104 gamma = -0.00791 phi = 0.03 Loss: 0.524 Simulating with theta = -0.794 zeta = -0.00387 chi = 0.00476 gamma = -0.00818 phi = 0.0284 Loss: 0.525 Simulating with theta = -0.796 zeta = 0.00647 chi = 0.0115 gamma = -0.00805 phi = 0.0316 Loss: 0.524 Simulating with theta = -0.794 zeta = 0.0038 chi = 0.0115 gamma = -0.00638 phi = 0.0347 Loss: 0.525 Simulating with theta = -0.799 zeta = 0.00086 chi = 0.0107 gamma = -0.0116 phi = 0.0419 Loss: 0.525 Simulating with theta = -0.794 zeta = 0.00446 chi = 0.00998 gamma = -0.00646 phi = 0.029 Loss: 0.524 Simulating with theta = -0.798 zeta = 0.00673 chi = 0.0105 gamma = -0.00181 phi = 0.0282 Loss: 0.525 Simulating with theta = -0.795 zeta = 0.00252 chi = 0.0101 gamma = -0.00962 phi = 0.0338 Loss: 0.524
characterization_result.final_params
{(cirq.GridQubit(4, 4), cirq.GridQubit(4, 5)): {'theta': -0.7949597090484766,
'zeta': 0.002522882039776196,
'chi': 0.010100591038089794,
'gamma': -0.009623918466707756,
'phi': 0.03384923972295669} }
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()
