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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 0x7f81575414b0>

## 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: 0.588 Simulating with theta = -0.785 zeta = 0.1 chi = 0 gamma = 0 phi = 0 Loss: 0.556 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: 0.579 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0 phi = 0.1 Loss: 0.556 Simulating with theta = -0.885 zeta = 0.04 chi = 0.04 gamma = 0.04 phi = 0.04 Loss: 0.59 Simulating with theta = -0.735 zeta = 0.01 chi = 0.01 gamma = 0.01 phi = 0.01 Loss: 0.551 Simulating with theta = -0.765 zeta = 0.044 chi = 0.044 gamma = -0.096 phi = 0.044 Loss: 0.566 Simulating with theta = -0.77 zeta = 0.033 chi = 0.033 gamma = -0.047 phi = 0.033 Loss: 0.541 Simulating with theta = -0.759 zeta = -0.0828 chi = 0.0572 gamma = -0.0148 phi = 0.0572 Loss: 0.563 Simulating with theta = -0.779 zeta = 0.0543 chi = 0.0143 gamma = -0.0037 phi = 0.0143 Loss: 0.542 Simulating with theta = -0.757 zeta = 0.0389 chi = 0.0629 gamma = -0.0163 phi = -0.0771 Loss: 0.565 Simulating with theta = -0.778 zeta = 0.00973 chi = 0.0157 gamma = -0.00407 phi = 0.0557 Loss: 0.544 Simulating with theta = -0.754 zeta = 0.0428 chi = -0.0708 gamma = -0.0179 phi = 0.0452 Loss: 0.546 Simulating with theta = -0.811 zeta = 0.0459 chi = -0.0131 gamma = -0.0391 phi = 0.0493 Loss: 0.535 Simulating with theta = -0.816 zeta = 0.0144 chi = 0.0908 gamma = -0.0196 phi = 0.0157 Loss: 0.552 Simulating with theta = -0.769 zeta = 0.0357 chi = -0.0304 gamma = -0.0183 phi = 0.0378 Loss: 0.534 Simulating with theta = -0.788 zeta = 0.0578 chi = -0.0142 gamma = -0.0392 phi = -0.00196 Loss: 0.534 Simulating with theta = -0.791 zeta = 0.0147 chi = -0.0242 gamma = -0.0537 phi = 0.033 Loss: 0.531 Simulating with theta = -0.808 zeta = 0.0287 chi = -0.0658 gamma = -0.0131 phi = 0.0143 Loss: 0.53 Simulating with theta = -0.826 zeta = 0.0265 chi = -0.115 gamma = 0.00381 phi = 0.00489 Loss: 0.541 Simulating with theta = -0.765 zeta = 0.00883 chi = -0.0407 gamma = -0.0107 phi = -0.0161 Loss: 0.533 Simulating with theta = -0.805 zeta = 0.00831 chi = -0.0276 gamma = -0.0283 phi = -0.0261 Loss: 0.536 Simulating with theta = -0.778 zeta = 0.0289 chi = -0.0297 gamma = -0.0208 phi = 0.0218 Loss: 0.528 Simulating with theta = -0.783 zeta = -0.0254 chi = -0.0499 gamma = -0.000177 phi = 0.0232 Loss: 0.533 Simulating with theta = -0.813 zeta = 0.00989 chi = -0.0271 gamma = -0.0245 phi = 0.0529 Loss: 0.53 Simulating with theta = -0.807 zeta = 0.0583 chi = -0.00877 gamma = -0.0447 phi = 0.0256 Loss: 0.534 Simulating with theta = -0.789 zeta = -0.0045 chi = -0.0396 gamma = -0.0113 phi = 0.0238 Loss: 0.527 Simulating with theta = -0.798 zeta = 0.0105 chi = -0.0407 gamma = 0.0258 phi = 0.0122 Loss: 0.537 Simulating with theta = -0.793 zeta = 0.0136 chi = -0.0283 gamma = -0.0338 phi = 0.0278 Loss: 0.525 Simulating with theta = -0.768 zeta = 0.0168 chi = -0.0383 gamma = -0.00717 phi = -0.0179 Loss: 0.531 Simulating with theta = -0.802 zeta = 0.0116 chi = -0.0299 gamma = -0.0201 phi = 0.0352 Loss: 0.526 Simulating with theta = -0.802 zeta = 0.0313 chi = -0.0773 gamma = -0.0397 phi = 0.0492 Loss: 0.533 Simulating with theta = -0.79 zeta = 0.00783 chi = -0.0193 gamma = -0.00993 phi = 0.0123 Loss: 0.526 Simulating with theta = -0.773 zeta = -0.0057 chi = 0.00702 gamma = -0.0253 phi = 0.0341 Loss: 0.532 Simulating with theta = -0.799 zeta = 0.0201 chi = -0.0476 gamma = -0.0162 phi = 0.0192 Loss: 0.526 Simulating with theta = -0.811 zeta = -0.00939 chi = -0.0362 gamma = -0.0157 phi = 0.0255 Loss: 0.526 Simulating with theta = -0.808 zeta = 0.022 chi = -0.0249 gamma = -0.027 phi = 0.0242 Loss: 0.526 Simulating with theta = -0.786 zeta = 0.0395 chi = -0.0238 gamma = -0.0271 phi = 0.022 Loss: 0.528 Simulating with theta = -0.804 zeta = 0.00282 chi = -0.0331 gamma = -0.0186 phi = 0.0246 Loss: 0.525 Simulating with theta = -0.787 zeta = 0.000383 chi = -0.0384 gamma = -0.0124 phi = 0.0234 Loss: 0.527 Simulating with theta = -0.803 zeta = 0.0166 chi = -0.0283 gamma = -0.0234 phi = 0.024 Loss: 0.525 Simulating with theta = -0.811 zeta = 0.0181 chi = -0.0475 gamma = -0.0349 phi = 0.0401 Loss: 0.528 Simulating with theta = -0.795 zeta = 0.0104 chi = -0.0264 gamma = -0.0162 phi = 0.0192 Loss: 0.525 Simulating with theta = -0.796 zeta = 0.0138 chi = -0.0356 gamma = -0.0231 phi = 0.0107 Loss: 0.525 Simulating with theta = -0.793 zeta = 0.0149 chi = -0.0384 gamma = -0.0246 phi = -0.00156 Loss: 0.527 Simulating with theta = -0.797 zeta = 0.00282 chi = -0.0131 gamma = -0.0299 phi = 0.0233 Loss: 0.526 Simulating with theta = -0.798 zeta = 0.00713 chi = -0.0217 gamma = -0.0264 phi = 0.0223 Loss: 0.525 Simulating with theta = -0.791 zeta = 0.00251 chi = -0.0298 gamma = -0.0239 phi = 0.0178 Loss: 0.525 Simulating with theta = -0.801 zeta = 0.00102 chi = -0.0303 gamma = -0.00942 phi = 0.0101 Loss: 0.525 Simulating with theta = -0.806 zeta = 0.0116 chi = -0.0291 gamma = -0.0136 phi = 0.017 Loss: 0.526 Simulating with theta = -0.795 zeta = 0.00477 chi = -0.0296 gamma = -0.0213 phi = 0.0176 Loss: 0.525 Simulating with theta = -0.803 zeta = 0.00143 chi = -0.0337 gamma = -0.0234 phi = 0.0149 Loss: 0.525 Simulating with theta = -0.797 zeta = 0.00815 chi = -0.0282 gamma = -0.018 phi = 0.0181 Loss: 0.525 Simulating with theta = -0.795 zeta = 0.0136 chi = -0.029 gamma = -0.0335 phi = 0.0272 Loss: 0.525 Simulating with theta = -0.799 zeta = 0.00418 chi = -0.03 gamma = -0.0154 phi = 0.0144 Loss: 0.525 Simulating with theta = -0.79 zeta = 0.0124 chi = -0.0249 gamma = -0.0231 phi = 0.00864 Loss: 0.525 Simulating with theta = -0.801 zeta = 0.00521 chi = -0.0311 gamma = -0.0197 phi = 0.0206 Loss: 0.525 Simulating with theta = -0.8 zeta = -0.00202 chi = -0.0206 gamma = -0.0172 phi = 0.0265 Loss: 0.526 Simulating with theta = -0.797 zeta = 0.00984 chi = -0.0318 gamma = -0.0216 phi = 0.0147 Loss: 0.525 Simulating with theta = -0.798 zeta = 0.00573 chi = -0.0386 gamma = -0.012 phi = 0.0119 Loss: 0.525 Simulating with theta = -0.798 zeta = 0.00678 chi = -0.0259 gamma = -0.0228 phi = 0.0197 Loss: 0.525 Simulating with theta = -0.799 zeta = 0.00417 chi = -0.0311 gamma = -0.0224 phi = 0.0166 Loss: 0.525 Simulating with theta = -0.797 zeta = 0.00715 chi = -0.0289 gamma = -0.0191 phi = 0.0178 Loss: 0.525 Simulating with theta = -0.796 zeta = 0.00933 chi = -0.029 gamma = -0.0264 phi = 0.0218 Loss: 0.525 Simulating with theta = -0.8 zeta = 0.0106 chi = -0.0291 gamma = -0.0225 phi = 0.0202 Loss: 0.525 Simulating with theta = -0.802 zeta = 0.00649 chi = -0.0298 gamma = -0.0159 phi = 0.0154 Loss: 0.525 Simulating with theta = -0.797 zeta = 0.00862 chi = -0.0292 gamma = -0.0238 phi = 0.0202 Loss: 0.525 Simulating with theta = -0.795 zeta = 0.012 chi = -0.0269 gamma = -0.0242 phi = 0.0164 Loss: 0.525 Simulating with theta = -0.799 zeta = 0.0069 chi = -0.03 gamma = -0.0208 phi = 0.0196 Loss: 0.525 Simulating with theta = -0.795 zeta = 0.00516 chi = -0.0292 gamma = -0.0207 phi = 0.0165 Loss: 0.525 Simulating with theta = -0.799 zeta = 0.00921 chi = -0.0291 gamma = -0.0221 phi = 0.0193 Loss: 0.525

```
characterization_result.final_params
```

{(cirq.GridQubit(4, 4), cirq.GridQubit(4, 5)): {'theta': -0.7990482518698238, 'zeta': 0.009208657582893263, 'chi': -0.029136675661585624, 'gamma': -0.0220853288225957, 'phi': 0.019277642086914897} }

```
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()
```