Non-Markovian noise mitigation: Practical implementation, error analysis, and the role of spectral properties of the environment

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, which only occurs when the separation between the system and environment is sufficiently large. 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 incoherent 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.