Role of control constraints in quantum optimal control

TL;DR

This paper investigates how control constraints affect the optimization landscape in quantum control of two-level systems, revealing that constraints can introduce traps but may be mitigated by fixing control time.

Contribution

It provides a comprehensive analysis of optimal control policies and the impact of inequality-type control constraints on the control landscape in quantum systems.

Findings

Control constraints can introduce traps in the control landscape.

Fixing the control time can prevent the emergence of traps.

Theoretically, the landscape is always trap-free, but practical conditions vary.

Abstract

The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive analysis of globally optimal control policies and traps (i.e. policies which are locally but not globally optimal) is presented. The central question addressed is whether the control landscape remains trap-free if control constraints of the inequality type are imposed. The answer is astonishingly controversial, namely, although formally it is always negative, in practice it is positive provided that the control time is fixed and chosen long enough.