Fully differentiable optimization protocols for non-equilibrium steady states

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.

Main work 10 pages and 5 Figures. Supplemental Material 12 pages, 1 Figure, 3 Tables

References in corpus (11)

• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Constructing neural stationary states for open quantum many-body systems
• Time-optimal control of a two-level dissipative quantum system
• Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
• Long-lived quasi-stationary coherences in V-type system driven by incoherent light
• Linked cluster expansions for open quantum systems on a lattice
• Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems
• Stochastic optimal control formalism for an open quantum system