Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered

TL;DR

This paper introduces a comprehensive framework for Krotov-type algorithms in quantum control, improving their efficiency, convergence, and robustness by addressing discretization effects and eliminating the need for ad-hoc penalties.

Contribution

It provides a general, practical framework for sequential update algorithms in quantum control, enhancing their theoretical understanding and computational performance.

Findings

The framework ensures monotonic convergence without ad-hoc penalties.

Efficient update rules with dynamic search length control are proposed.

Numerical examples demonstrate improved performance and broader applicability.

Abstract

Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad-hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad-hoc penalty terms. The latter, while necessary to regularize the problem in the limit of infinite time resolution, i.e., the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.