Fully differentiable optimization protocols for non-equilibrium steady\n states

Abstract

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