Unified analysis of terminal-time control in classical and quantum systems

TL;DR

This paper demonstrates that, under certain conditions, optimal control objectives at a terminal time for open classical and quantum systems are free of sub-optimal maxima, simplifying the control discovery process across regimes.

Contribution

It provides a unified theoretical framework showing the absence of sub-optimal maxima for terminal-time control objectives in open classical and quantum systems.

Findings

Control objectives are inherently free of sub-optimal maxima under specified conditions.

The framework applies to a wide range of classical and quantum phenomena.

Facilitates seamless control discovery across classical and quantum regimes.

Abstract

Many phenomena in physics, chemistry, and biology involve seeking an optimal control to maximize an objective for a classical or quantum system which is open and interacting with its environment. The complexity of finding an optimal control for maximizing an objective is strongly affected by the possible existence of sub-optimal maxima. Within a unified framework under specified conditions, control objectives for maximizing at a terminal time physical observables of open classical and quantum systems are shown to be inherently free of sub-optimal maxima. This attractive feature is of central importance for enabling the discovery of controls in a seamless fashion in a wide range of phenomena transcending the quantum and classical regimes.