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()

XRB Extended Randomized Benchmarking	Cliffords (0, 1) Key: labels: (0, 1) protocol: XRB twirl: (('C', 0, 1),)
${e}_{S}$ The probability of a stochastic error acting on the specified systems during a random gate.	3.7e-02 (4.0e-04) 0.037236770939636336, 0.00039557564101160724
${u}$ The unitarity of the noise, that is, the average decrease in the purity of an initial state.	9.2e-01 (8.1e-04) 0.9221391719517216, 0.0008103758595748585
${A}$ SPAM parameter of the exponential decay $Au^m$.	9.7e-01 (1.1e-02) 0.9707793955224528, 0.010956426308776685

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()

XRB Extended Randomized Benchmarking	Cliffords (0,) Key: labels: (0,) protocol: XRB twirl: (('C', 0), ('C', 3), ('C', 1, 2))	Cliffords (1, 2) Key: labels: (1, 2) protocol: XRB twirl: (('C', 0), ('C', 3), ('C', 1, 2))	Cliffords (3,) Key: labels: (3,) protocol: XRB twirl: (('C', 0), ('C', 3), ('C', 1, 2))
${e}_{S}$ The probability of a stochastic error acting on the specified systems during a random gate.	2.0e-02 (2.9e-04) 0.019968262333878772, 0.0002912673449135749	3.6e-02 (4.7e-04) 0.03634603033543741, 0.0004709618502467283	2.0e-02 (3.3e-04) 0.019731804787703727, 0.0003342421170458248
${u}$ The unitarity of the noise, that is, the average decrease in the purity of an initial state.	9.5e-01 (7.6e-04) 0.9474601564441181, 0.0007560334433161052	9.2e-01 (9.7e-04) 0.9239648449902357, 0.000965766578427236	9.5e-01 (8.7e-04) 0.9480740212242214, 0.0008678627113919699
${A}$ SPAM parameter of the exponential decay $Au^m$.	9.9e-01 (1.1e-02) 0.9900330374428721, 0.010748687222223148	9.7e-01 (1.3e-02) 0.9659866055048891, 0.01328854803274169	9.8e-01 (1.3e-02) 0.9775114146048323, 0.013117601625400679