Mitigating measurement errors in multiqubit experiments

TLDR

Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. The authors demonstrate a classical postprocessing method to mitigate measurement errors in multiqubit quantum devices. They propose two schemes—tensor‑product and correlated Markovian noise models—extracting error rates from calibration data, applying the inverse noise matrix to the outcome probability vector, with overhead exponential in εn. The methods, applicable to any observable‑expectation calculation, were experimentally validated on IBM Quantum devices for graph states up to 12 qubits and 20‑qubit entangled states from low‑depth random Clifford circuits.

Abstract

Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and $n$ is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.