Description and complexity of Non-markovian open quantum dynamics

Abstract

In open quantum system theory, unitary groups over system-environment Hilbert space corresponding to deltafunction memory kernels, and thus generating Markovian system dynamics, are specified as the solution of a quantum stochastic differential equation. In this paper, we identify a larger class of non-Markovian memory kernels, described by complex-valued radon measures, and rigorously define their dynamics by constructing system-environment unitary groups corresponding to the memory kernels. We then consider k−local manybody non-Markovian systems and show that under physically reasonable assumptions on the total variation and smoothness of the memory kernels, their dynamics can be efficiently approximated on quantum computers thus providing a rigorous verification of the Extended Church-Turing thesis for non-Markovian open quantum systems.