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. We
present a simulation scheme for open qubit dynamics described by a larger class
of maps: the general dynamical maps which are linear, hermitian preserving and
trace preserving but not necessarily positivity preserving. The latter suggests
an underlying system-reservoir model where both are entangled and thus
non-Markovian qubit dynamics. Such maps also come about as the inverse of CP
maps. We illustrate our simulation scheme on an IBM quantum processor by
showing that we can 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.
Mirko Rossini Dominik Maile Joachim Ankerhold Brecht I. C Donvil