Stochastic optimal control formalism for an open quantum system

TL;DR

This paper introduces a stochastic control method for open quantum systems that simplifies optimal control calculations by using wave functions instead of density matrices, enhancing efficiency for large systems.

Contribution

It develops a stochastic formalism for quantum control based on Pontryagin's principle, avoiding density matrix computations and enabling efficient control of dissipative quantum systems.

Findings

Method matches results from Lindbladian dynamics control

Formalism is time and memory efficient for large systems

Can be extended to non-Markovian dynamics

Abstract

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing the density matrix. Specifically, the proper dynamical update rules are presented for the stochastic costate variables introduced by Pontryagin's maximum principle and restrictions on the form of the terminal cost function are discussed. The proposed procedure is confirmed by comparing the results to those obtained from optimal control on Lindbladian dynamics. Numerically, the proposed formalism becomes time and memory efficient for large systems, and it can be generalized to describe non-Markovian dynamics.