Calibration

The mitiq.Calibrator class provides a workflow for users to run a set of experiments to automatically determine an error mitigation strategy. This gives the user freedom to work on more important parts of their algorithm/quantum program, and allows them to spend less time tuning error mitigation parameters.

Workflow

To begin, we will need to define an executor which tells Mitiq how to run circuits. In order to use the calibration capabilities of Mitiq, we will need to define an executor which returns all the measured bitstrings, rather than an expectation value. This allows the calibration experiment to extract more fine-grained data from each circuit experiment it will run

import cirq
import numpy as np
from mitiq import MeasurementResult

def execute(circuit, noise_level=0.001):
    circuit = circuit.with_noise(cirq.amplitude_damp(noise_level))
    result = cirq.DensityMatrixSimulator().run(circuit, repetitions=100)
    bitstrings = np.column_stack(list(result.measurements.values()))
    return MeasurementResult(bitstrings)

We can now import the required objects and functions required for calibration.

from mitiq import Calibrator

To instantiate a Calibrator we need to pass it an executor (as defined above), and a Settings object. You are free to define your own Settings, but as a simple starting point, we provide ZNE_SETTINGS based on different zero-noise extrapolation strategies and PEC_SETTINGS based on different quasiprobability representations of ideal gates. Finally, the execute_with_mitigation function allows us to pass the calibration results directly to Mitiq and have it pick the strategy that performed best of those supplied in the Settings object.

Calibration Experiments

Before running any experiments, we can call the get_cost function to ensure the experiments will not be too costly. Once instantiated, we call the run method to run the set of experiments, and the results of such experiments are stored internal to the class in cal.results.

cal = Calibrator(execute, frontend="cirq")
print(cal.get_cost())
cal.run()

{'noisy_executions': 100, 'ideal_executions': 0}

Applying the optimal error mitigation strategy

We first define randomized benchmarking circuit to test the effect of error mitigation.

from mitiq.benchmarks import generate_rb_circuits

circuit = generate_rb_circuits(2, 10)[0]
# circuits passed to an executor returning bitstrings must contain measurements
circuit.append(cirq.measure(circuit.all_qubits()))

Instead of deciding what error mitigation technique and what options to use, we can ask Mitiq to determine the optimal error mitigation strategy based on the previously performed calibration. We can obtain this by calling the execute_with_mitigation function and passing the circuit, Calibrator object, and a new expectation value executor.

def execute(circuit, noise_level=0.001):
    circuit = circuit.with_noise(cirq.amplitude_damp(noise_level))

    rho = (
        cirq.DensityMatrixSimulator()
        .simulate(circuit)
        .final_density_matrix
    )
    return rho[0, 0].real

cal.execute_with_mitigation(circuit, execute)

0.9999995827674864

Tutorial

You can find an example on quantum error mitigation calibration in the Examples section of the documentation. This example illustrates functionalities from the calibration module using ZNE on a simulated IBM Quantum backend using Qiskit, defining a new settings object.