Ancilla-train quantum algorithm for simulating non-Markovian open quantum systems

Abstract

We present a quantum algorithm for simulating open quantum systems coupled to Gaussian environments valid for any configuration and coupling strength. The algorithm is applicable to problems with strongly coupled, or non-Markovian, environments, problems with multiple environments out of mutual equilibrium, and problems with time-dependent Hamiltonians. We show that the algorithm can reproduce the true dynamics of such problems at arbitrary accuracy and, for a broad range of problems, only adds a minor resource cost relative to Trotterized time evolution; the cost is low-degree polynomial in the inverse target accuracy. The algorithm is based on the insight that any Gaussian environment can be represented as a train of ancillary qubits that sequentially interact with the system through a time-local coupling, given by the convolution square root of the bath correlation function; this is a secondary result of our work. Our results open up new applications of quantum computers for efficient simulation of non-equilibrium and open quantum systems.