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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, 4.57it/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 0x7f09a8e09e10>

## 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: 0.531 Simulating with theta = -0.685 zeta = 0 chi = 0 gamma = 0 phi = 0 Loss: 0.611 Simulating with theta = -0.785 zeta = 0.1 chi = 0 gamma = 0 phi = 0 Loss: 0.571 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: 0.599 Simulating with theta = -0.785 zeta = 0 chi = 0 gamma = 0 phi = 0.1 Loss: 0.559 Simulating with theta = -0.885 zeta = 0.04 chi = 0.04 gamma = 0.04 phi = 0.04 Loss: 0.635 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: 0.578 Simulating with theta = -0.77 zeta = 0.033 chi = 0.033 gamma = -0.047 phi = 0.033 Loss: 0.549 Simulating with theta = -0.759 zeta = -0.0828 chi = 0.0572 gamma = -0.0148 phi = 0.0572 Loss: 0.562 Simulating with theta = -0.766 zeta = -0.0371 chi = 0.0429 gamma = -0.0111 phi = 0.0429 Loss: 0.536 Simulating with theta = -0.752 zeta = 0.00236 chi = 0.0744 gamma = -0.0192 phi = -0.0656 Loss: 0.573 Simulating with theta = -0.777 zeta = 0.00059 chi = 0.0186 gamma = -0.00481 phi = 0.0586 Loss: 0.535 Simulating with theta = -0.748 zeta = 0.0026 chi = -0.0582 gamma = -0.0212 phi = 0.0578 Loss: 0.549 Simulating with theta = -0.803 zeta = -0.0104 chi = 0.00451 gamma = -0.0436 phi = 0.0669 Loss: 0.542 Simulating with theta = -0.813 zeta = -0.00815 chi = 0.0978 gamma = -0.0215 phi = 0.0228 Loss: 0.574 Simulating with theta = -0.764 zeta = -8.96e-05 chi = -0.0192 gamma = -0.0212 phi = 0.049 Loss: 0.534 Simulating with theta = -0.788 zeta = -0.0518 chi = -0.0143 gamma = 0.0147 phi = 0.054 Loss: 0.558 Simulating with theta = -0.775 zeta = 0.0118 chi = 0.0212 gamma = -0.0316 phi = 0.0382 Loss: 0.536 Simulating with theta = -0.744 zeta = 0.000447 chi = 0.0209 gamma = 0.0161 phi = 0.00859 Loss: 0.542 Simulating with theta = -0.788 zeta = -0.00766 chi = 0.0086 gamma = -0.0287 phi = 0.0523 Loss: 0.533 Simulating with theta = -0.778 zeta = -0.0295 chi = -0.000823 gamma = 0.00524 phi = 0.0429 Loss: 0.538 Simulating with theta = -0.775 zeta = 0.00148 chi = 0.0157 gamma = -0.0224 phi = 0.0394 Loss: 0.532 Simulating with theta = -0.79 zeta = 0.0348 chi = -0.0334 gamma = -0.0197 phi = 0.0368 Loss: 0.542 Simulating with theta = -0.772 zeta = -0.0191 chi = 0.0238 gamma = -0.0133 phi = 0.0414 Loss: 0.531 Simulating with theta = -0.777 zeta = -0.0107 chi = -0.00703 gamma = -0.0294 phi = 0.0143 Loss: 0.535 Simulating with theta = -0.777 zeta = -0.00791 chi = -0.000625 gamma = -0.0233 phi = 0.0254 Loss: 0.532 Simulating with theta = -0.795 zeta = -0.0132 chi = 0.0382 gamma = -0.0138 phi = 0.0144 Loss: 0.541 Simulating with theta = -0.772 zeta = -0.00337 chi = -0.00485 gamma = -0.0194 phi = 0.0404 Loss: 0.531 Simulating with theta = -0.764 zeta = -0.00391 chi = 0.005 gamma = -0.00262 phi = 0.00627 Loss: 0.531 Simulating with theta = -0.773 zeta = -0.0152 chi = -0.00634 gamma = -0.00104 phi = 0.00594 Loss: 0.53 Simulating with theta = -0.772 zeta = -0.0235 chi = -0.0174 gamma = 0.00963 phi = -0.0108 Loss: 0.534 Simulating with theta = -0.77 zeta = -0.00872 chi = 0.00768 gamma = 0.00874 phi = 0.0122 Loss: 0.53 Simulating with theta = -0.766 zeta = -0.00913 chi = 0.0118 gamma = 0.0247 phi = 0.00567 Loss: 0.534 Simulating with theta = -0.784 zeta = -0.0147 chi = 0.00312 gamma = -0.00735 phi = 0.0337 Loss: 0.532 Simulating with theta = -0.769 zeta = -0.00659 chi = 0.00453 gamma = -0.0038 phi = 0.0131 Loss: 0.53 Simulating with theta = -0.776 zeta = -0.0165 chi = 0.0167 gamma = 0.0156 phi = -0.0113 Loss: 0.53 Simulating with theta = -0.777 zeta = 0.000318 chi = -0.0148 gamma = 0.0211 phi = -0.0334 Loss: 0.532 Simulating with theta = -0.773 zeta = -0.0143 chi = 0.0142 gamma = -0.00468 phi = 0.0227 Loss: 0.53 Simulating with theta = -0.759 zeta = -0.0245 chi = 0.0147 gamma = 0.00595 phi = 0.0171 Loss: 0.533 Simulating with theta = -0.779 zeta = -0.00613 chi = 0.00368 gamma = 0.00149 phi = 0.00427 Loss: 0.529 Simulating with theta = -0.774 zeta = -0.00568 chi = 0.0251 gamma = 0.00799 phi = 0.0105 Loss: 0.53 Simulating with theta = -0.779 zeta = -0.0109 chi = 0.018 gamma = -0.00209 phi = 0.00348 Loss: 0.53 Simulating with theta = -0.772 zeta = -0.00928 chi = 0.0103 gamma = 0.00604 phi = 0.01 Loss: 0.529 Simulating with theta = -0.771 zeta = -0.000287 chi = 0.00635 gamma = -0.0128 phi = 0.0355 Loss: 0.531 Simulating with theta = -0.775 zeta = -0.0124 chi = 0.0141 gamma = 0.00852 phi = 0.000417 Loss: 0.529 Simulating with theta = -0.779 zeta = -0.0125 chi = 0.0224 gamma = 0.0115 phi = 0.00603 Loss: 0.53 Simulating with theta = -0.772 zeta = -0.00807 chi = 0.00899 gamma = 3.39e-05 phi = 0.0114 Loss: 0.529 Simulating with theta = -0.775 zeta = -0.00238 chi = 0.0107 gamma = 0.0143 phi = -0.00807 Loss: 0.529 Simulating with theta = -0.776 zeta = 0.00356 chi = 0.00893 gamma = 0.0238 phi = -0.0235 Loss: 0.529 Simulating with theta = -0.775 zeta = -0.00964 chi = -0.00596 gamma = 0.00416 phi = -0.00327 Loss: 0.53 Simulating with theta = -0.774 zeta = -0.00667 chi = 0.0173 gamma = 0.00703 phi = 0.00704 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.005 chi = 0.0117 gamma = 0.00651 phi = -0.00404 Loss: 0.529 Simulating with theta = -0.771 zeta = -0.00769 chi = 0.0214 gamma = 0.0131 phi = -0.00159 Loss: 0.53 Simulating with theta = -0.777 zeta = -0.00652 chi = 0.00811 gamma = 0.00438 phi = 0.00281 Loss: 0.529 Simulating with theta = -0.776 zeta = 0.000983 chi = 0.00856 gamma = 0.00439 phi = 0.00322 Loss: 0.529 Simulating with theta = -0.78 zeta = 0.000244 chi = 0.0135 gamma = 0.0146 phi = -0.011 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00911 chi = 0.0159 gamma = 0.0144 phi = -0.00852 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.00659 chi = 0.0141 gamma = 0.0119 phi = -0.00558 Loss: 0.529 Simulating with theta = -0.781 zeta = -0.00143 chi = 0.00593 gamma = 0.0136 phi = -0.0174 Loss: 0.529 Simulating with theta = -0.776 zeta = -0.00536 chi = 0.0145 gamma = 0.00868 phi = 0.000932 Loss: 0.529 Simulating with theta = -0.776 zeta = -0.00324 chi = 0.0127 gamma = 0.015 phi = -0.00432 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.000409 chi = 0.0181 gamma = 0.0214 phi = -0.014 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.00499 chi = 0.0106 gamma = 0.00864 phi = -0.0014 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00439 chi = 0.0127 gamma = 0.00822 phi = -0.00572 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.0041 chi = 0.0127 gamma = 0.00992 phi = -0.00537 Loss: 0.529 Simulating with theta = -0.773 zeta = -0.00961 chi = 0.0115 gamma = 0.00675 phi = 0.00318 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00222 chi = 0.013 gamma = 0.0126 phi = -0.00744 Loss: 0.529 Simulating with theta = -0.779 zeta = -0.00692 chi = 0.0153 gamma = 0.0064 phi = 0.000529 Loss: 0.529 Simulating with theta = -0.776 zeta = -0.00351 chi = 0.0118 gamma = 0.0123 phi = -0.00592 Loss: 0.529 Simulating with theta = -0.779 zeta = -0.00321 chi = 0.0104 gamma = 0.0135 phi = -0.0112 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.000626 chi = 0.00931 gamma = 0.0109 phi = -0.00696 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.0051 chi = 0.0129 gamma = 0.0116 phi = -0.00593 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00226 chi = 0.0137 gamma = 0.0154 phi = -0.013 Loss: 0.529 Simulating with theta = -0.779 zeta = -0.000899 chi = 0.0153 gamma = 0.0187 phi = -0.0187 Loss: 0.529 Simulating with theta = -0.776 zeta = -0.00367 chi = 0.0152 gamma = 0.0113 phi = -0.00383 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.00261 chi = 0.014 gamma = 0.0154 phi = -0.00905 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.000613 chi = 0.0142 gamma = 0.0152 phi = -0.00975 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.000815 chi = 0.0115 gamma = 0.0171 phi = -0.0142 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00395 chi = 0.0114 gamma = 0.0139 phi = -0.0101 Loss: 0.529 Simulating with theta = -0.78 zeta = -0.00123 chi = 0.0136 gamma = 0.0174 phi = -0.0156 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.00294 chi = 0.0123 gamma = 0.0136 phi = -0.00834 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.000384 chi = 0.0144 gamma = 0.0157 phi = -0.0107 Loss: 0.529 Simulating with theta = -0.778 zeta = -0.00306 chi = 0.0122 gamma = 0.0144 phi = -0.0102 Loss: 0.529 Simulating with theta = -0.777 zeta = -0.00246 chi = 0.0125 gamma = 0.0177 phi = -0.0145 Loss: 0.529

```
characterization_result.final_params
```

{(cirq.GridQubit(4, 4), cirq.GridQubit(4, 5)): {'theta': -0.778225012034631, 'zeta': -0.00226323301143552, 'chi': 0.013727090788150039, 'gamma': 0.015359082663484815, 'phi': -0.012950433459515836} }

```
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()
```