Quantum Trajectory Approach to Error Mitigation

TL;DR

This paper links quantum trajectory theory with error mitigation techniques, showing how classical post-processing of quantum trajectories can effectively invert noise maps in NISQ devices, potentially avoiding the need for engineered reservoirs.

Contribution

It introduces a novel approach connecting quantum trajectory theory with error mitigation, enabling inverse noise map realization via classical post-processing of quantum trajectories.

Findings

Inverse noise maps realized through classical post-processing

Quantum trajectories can be simulated with an ancillary qubit

Model demonstrated on a NISQ-relevant system

Abstract

Quantum Error Mitigation (EM) is a collection of strategies to reduce errors on noisy intermediate scale quantum (NISQ) devices on which proper quantum error correction is not feasible. One of such strategies aimed at mitigating noise effects of a known environment is to realise the inverse map of the noise using a set of completely positive maps weighted by a quasi-probability distribution, i.e. a probability distribution with positive and negative values. This quasi-probability distribution is realised using classical post-processing after final measurements of the desired observables have been made. Here we make a connection with quasi-probability EM and recent results from quantum trajectory theory for open quantum systems. We show that the inverse of noise maps can be realised by performing classical post-processing on the quantum trajectories generated by an additional reservoir with a quasi-probability measure called the influence martingale. We demonstrate our result on a model relevant for current NISQ devices. Finally, we show the quantum trajectories required for error correction can themselves be simulated by coupling an ancillary qubit to the system. In this way, we can avoid the introduction of the engineered reservoir.