Efficient algorithms for optimal control of quantum dynamics: The Krotov method unencumbered

Abstract

Efficient algorithms are of fundamental importance for the discovery of optimal control designs for coherent control of quantum processes. One important class of algorithms is 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, despite being necessary for regularizing 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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.