Extended Randomized Benchmarking (XRB)

This example illustrates how to generate extended randomized benchmarking (XRB) circuits and use them to estimate the probability of a stochastic error acting on the specified system(s) during a random gate. While this example uses a simulator to execute the circuits, the same procedure can be followed for hardware applications.

Isolated XRB

This section illustrates how to generate XRB circuits to characterize a pair of qubits in isolation. Here, we are performing two-qubit XRB which learns the stochastic infidelity over the two-qubit Clifford gateset.

import trueq as tq

# generate XRB circuits to characterize a pair of qubits [0, 1]
# with 9 * 30 random circuits for each circuit depth [4, 32, 64]
circuits = tq.make_xrb([[0, 1]], [4, 32, 64], 30)

# initialize a noisy simulator with stochastic Pauli and overrotation
sim = tq.Simulator().add_stochastic_pauli(px=0.02).add_overrotation(0.04)

# run the circuits on the simulator to populate their results
sim.run(circuits, n_shots=1000)

# plot the exponential decay of the purities
circuits.plot.raw()

# print the fit summary
circuits.fit()

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XRB Extended Randomized Benchmarking	Cliffords (0, 1) Key: labels: (0, 1) protocol: XRB twirl: Cliffords on [(0, 1)]
${e}_{S}$ The probability of a stochastic error acting on the specified systems during a random gate.	3.6e-02 (4.0e-04) 0.036108853434251964, 0.0004027636691135585
${u}$ The unitarity of the noise, that is, the average decrease in the purity of an initial state.	9.2e-01 (8.3e-04) 0.9243585519230211, 0.0008282033809427102
${A}$ SPAM parameter of the exponential decay $Au^m$.	9.5e-01 (1.3e-02) 0.946837340193605, 0.013492156314188453

Simultaneous XRB

This section demonstrates how to generate XRB circuits that characterize the amount of stochastic noise while gates are applied simultaneously on a device.

# generate XRB circuits to simultaneously characterize a single qubit [0],
# a pair of qubits [1, 2], and another single qubit [3] with 9 * 30 random circuits
# for each circuit depth [4, 32, 64]
circuits = tq.make_xrb([[0], [1, 2], [3]], [4, 32, 64], 30)

# initialize a noisy simulator with stochastic Pauli and overrotation
sim = tq.Simulator().add_stochastic_pauli(px=0.02).add_overrotation(0.04)

# run the circuits on the simulator to populate their results
sim.run(circuits, n_shots=1000)

# plot the exponential decay of the purities
circuits.plot.raw()

# print the fit summary
circuits.fit()

True-Q formatting will not be loaded without trusting this notebook or rerunning the affected cells. Notebooks can be marked as trusted by clicking "File -> Trust Notebook".

XRB Extended Randomized Benchmarking	Cliffords (0,) Key: labels: (0,) protocol: XRB twirl: Cliffords on [0, (1, 2), 3]	Cliffords (1, 2) Key: labels: (1, 2) protocol: XRB twirl: Cliffords on [0, (1, 2), 3]	Cliffords (3,) Key: labels: (3,) protocol: XRB twirl: Cliffords on [0, (1, 2), 3]
${e}_{S}$ The probability of a stochastic error acting on the specified systems during a random gate.	1.9e-02 (2.9e-04) 0.01949968934907209, 0.0002948939277414213	3.6e-02 (4.5e-04) 0.03609633985778027, 0.0004451981380399996	2.0e-02 (2.6e-04) 0.019570178398109817, 0.0002600912033934169
${u}$ The unitarity of the noise, that is, the average decrease in the purity of an initial state.	9.5e-01 (7.7e-04) 0.9485078122487549, 0.0007710495673587623	9.2e-01 (9.2e-04) 0.9243842837712725, 0.0009154733114565479	9.5e-01 (6.8e-04) 0.9483235134484189, 0.0006800031257152766
${A}$ SPAM parameter of the exponential decay $Au^m$.	9.8e-01 (1.6e-02) 0.9848825628520131, 0.015861678110355253	9.4e-01 (1.2e-02) 0.9438411224741511, 0.01207048913202703	9.7e-01 (1.3e-02) 0.9697981670114009, 0.013333994888702683