How do I use TREX?#

As with all techniques, TREX is compatible with any frontend supported by Mitiq:

import mitiq

mitiq.SUPPORTED_PROGRAM_TYPES.keys()

['braket', 'cirq', 'pennylane', 'pyquil', 'qibo', 'qiskit', 'openqasm']

Problem setup#

In this example we will simulate a noisy device to demonstrate the capabilities of TREX. This method requires an observable to be defined, and we use \(Z_0 + Z_1\) as an example. Since the circuit includes an \(X\) gate on each qubit, the noiseless expectation value should be \(-2\).

from cirq import LineQubit, Circuit, X

from mitiq.observable.observable import Observable
from mitiq.observable.pauli import PauliString

qreg = [LineQubit(i) for i in range(2)]
circuit = Circuit(X.on_each(*qreg))
observable = Observable(PauliString("ZI"), PauliString("IZ"))

print(circuit)

───X───

───X───

Next we define a simple noisy readout executor function which takes a circuit as input, executes the circuit on a noisy simulator, and returns the raw measurement results. See the Executors section for more information on how to define more advanced executors.

Warning

TREX executors require bitstrings as output since the technique applies to raw measurement results.

from functools import partial

import numpy as np
from cirq.experiments.single_qubit_readout_calibration_test import (
    NoisySingleQubitReadoutSampler,
)

from mitiq import MeasurementResult

def noisy_readout_executor(circuit, p0, p1, shots=8192) -> MeasurementResult:
    # Replace with code based on your frontend and backend.
    simulator = NoisySingleQubitReadoutSampler(p0, p1)
    result = simulator.run(circuit, repetitions=shots)
    bitstrings = np.column_stack(list(result.measurements.values()))
    return MeasurementResult(bitstrings, qubit_indices=(0, 1))

The executor can be used to evaluate noisy (unmitigated) expectation values.

from mitiq.raw import execute as raw_execute

# Compute the expectation value of the observable.
# Use a noisy executor that has a 15% chance of bit flipping
p_flip = 0.15
noisy_executor = partial(noisy_readout_executor, p0=p_flip, p1=p_flip)
noisy_value = raw_execute(circuit, noisy_executor, observable)

ideal_executor = partial(noisy_readout_executor, p0=0, p1=0)
ideal_value = raw_execute(circuit, ideal_executor, observable)
error = abs((ideal_value - noisy_value) / ideal_value)
print(f"Error without mitigation: {error:.3}")

Error without mitigation: 0.298

Apply TREX#

TREX can be easily applied with the function execute_with_trex(). Unlike REM, TREX does not require an explicit inverse confusion matrix. It automatically runs calibration circuits to estimate and correct readout errors.

from mitiq.experimental.trex import execute_with_trex

mitigated_result = execute_with_trex(
    circuit,
    noisy_executor,
    observable,
    num_randomizations=32,
    random_state=42,
)

error = abs((ideal_value - mitigated_result) / ideal_value)
print(f"Error with mitigation (TREX): {error:.3}")

Error with mitigation (TREX): 0.0008

Here we observe that the application of TREX reduces the readout error when compared to the unmitigated result.

The section What additional options are available when using TREX? contains more information on configuring TREX parameters.

How do I use TREX?#

Problem setup#

Apply TREX#

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