  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.
