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

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