Non-Markovian Noise Mitigation: Practical Implementation, Error Analysis, and the Role of Environment Spectral Properties

TL;DR

This paper introduces a non-Markovian noise mitigation method for quantum error mitigation that extends probabilistic error cancellation to environment-aware scenarios, validated through numerical simulations on a spin-boson model.

Contribution

It develops a non-Markovian noise mitigation technique by linking environment spectral properties to error analysis, extending existing methods to non-Markovian environments.

Findings

Effective error mitigation in non-Markovian environments demonstrated

Error bounds linked to environment spectral properties established

Numerical validation confirms approach's efficacy

Abstract

Quantum error mitigation(QEM), an error suppression strategy without the need for additional ancilla qubits for noisy intermediate-scale quantum~(NISQ) devices, presents a promising avenue for realizing quantum speedups of quantum computing algorithms on current quantum devices. However, prior investigations have predominantly been focused on Markovian noise. In this paper, we propose a non-Markovian Noise Mitigation(NMNM) method by extending the probabilistic error cancellation (PEC) method in the QEM framework to treat non-Markovian noise. We present the derivation of a time-local quantum master equation where the decoherence coefficients are directly obtained from bath correlation functions(BCFs), key properties of a non-Markovian environment that will make the error mitigation algorithms environment-aware. We further establish a direct connection between the overall approximation error and sampling overhead of QEM and the spectral property of the environment. Numerical simulations performed on a spin-boson model further validate the efficacy of our approach.