Fully differentiable optimization protocols for non-equilibrium steady states

TL;DR

This paper introduces a novel automatic differentiation method for quantum steady states, enabling efficient inverse design and optimization of quantum heat transfer devices and energy transfer systems.

Contribution

A new automatic differentiation approach for steady states in quantum systems that reduces memory use and is compatible with various algorithms.

Findings

Successfully designed quantum heat transfer devices with optimized heat current and rectification.

Optimized parameters for Lindblad operators in energy transfer simulations.

Performed sensitivity analysis of steady states under incoherent light.

Abstract

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