Variational quantum algorithms for simulation of Lindblad dynamics

Abstract

We introduce variational hybrid classical-quantum algorithms to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our methods are based on a direct representation of density matrices and quantum observables as quantum superstates. We design and optimize low-depth variational quantum circuits that efficiently capture the unitary and non-unitary dynamics of the solutions. We benchmark and test the algorithms on different models and system sizes, showing their potential for utility with near-future hardware.