Searching for quantum optimal controls under severe constraints

TL;DR

This paper explores how severe constraints on control parameters in quantum optimal control can create artificial traps, hindering the success of gradient-based optimization, and emphasizes the importance of managing these constraints for effective control.

Contribution

It provides a systematic analysis of how specific control constraints impact the landscape topology and optimization success in quantum control, offering practical guidelines for parameter selection.

Findings

Constraints on control variables can prevent reaching global optima.

Exceeding certain limits introduces artificial traps in the control landscape.

Proper management of constraints improves the success rate of gradient searches.

Abstract

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.