Relationship between costs for quantum error mitigation and non-Markovian measures

TL;DR

This paper explores how quantum error mitigation costs relate to non-Markovian noise measures, providing insights for improving error correction strategies in realistic quantum systems affected by complex noise environments.

Contribution

It establishes a theoretical relationship between QEM costs and non-Markovian measures, supported by models relevant to physical quantum systems.

Findings

QEM costs are quantitatively linked to non-Markovian measures.

Several non-Markovian noise models demonstrate this relationship.

The results can inform better QEM strategies for real quantum devices.

Abstract

Quantum error mitigation (QEM) has been proposed as an alternative method of quantum error correction to compensate errors in quantum systems without qubit overhead. While Markovian gate errors on digital quantum computers have been mainly considered previously, it is indispensable to discuss a relationship between QEM and non-Markovian errors because non-Markovian noise effects inevitably exist in most of the solid-state systems. In this work, we investigate the QEM for non-Markovian noise, and show that there is a clear relationship between costs for QEM and non-Markovian measures. As examples, we show several non-Markovian noise models to bridge a gap between our theoretical framework and concrete physical systems. This discovery may help in designing better QEM strategies for realistic quantum devices with non-Markovian environments.