Fully differentiable optimization protocols for non-equilibrium steady states

Abstract In the case of quantum systems interacting with multiple environments, time-evolution reduced density matrix is described by Liouvillian. For a variety physical observables, long-time limit or steady state (SS) solution needed for computation desired observables. inverse design optimal control such systems, common approaches are based on brute-force search strategies. Here, we present novel methodology, automatic differentiation, capable differentiating SS respect to any parameter Our approach has low memory cost, and agnostic exact algorithm computing SS. We illustrate advantage this method designing parameters heat transfer device that maximizes current rectification coefficient. Additionally, optimize various Lindblad operators used in simulation energy under natural incoherent light. also sensitivity analysis light as function incoherent-light pumping rate.