Single-Qubit Error Mitigation by Simulating Non-Markovian Dynamics

Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by completely positive (CP) maps, for which several quantum simulation schemes exist. Such maps, however, represent only a subset of a larger class of maps: the general dynamical maps which are linear, Hermitian preserving, and trace-preserving but not necessarily positivity preserving. In this talk, I show a simulation scheme for these general dynamical maps, which occur when the underlying system-reservoir model undergoes entangling (and thus non-Markovian) dynamics. Such maps also arise as the inverse of CP maps, which are commonly used in error mitigation. Our simulation scheme is illustrated on an IBM quantum processor, demonstrating its ability to recover the initial state of a Lindblad evolution. This paves the way for a novel form of quantum error mitigation. Our scheme only requires one ancilla qubit as an overhead and a small number of one and two-qubit gates. Consequently, we expect it to be of practical use in near-term quantum devices.

Financial support through the Ministery of Economy of the State of Baden-Württemberg within the Quantum Computing Competence Network Baden-Württemberg (project SiQuRe), the BMBF within QSens (QComp), and QSolid (BMBF) is gratefully acknowledged.