The Role of Bases in Quantum Optimal Control

TL;DR

This paper investigates how the choice of basis functions impacts the efficiency of quantum optimal control optimization, demonstrating that selecting a problem-specific basis can significantly speed up convergence.

Contribution

It introduces and compares sinc and sigmoid bases with Fourier basis in quantum control, providing strategies for choosing the most effective basis for different problems.

Findings

Basis choice affects convergence rates in quantum control optimization

Problem-dependent basis selection can speed up optimization by up to a factor of 10

Different bases perform variably depending on problem complexity

Abstract

Quantum Optimal Control (QOC) supports the advance of quantum technologies by tackling its problems at the pulse level: Numerical approaches iteratively work towards a given target by parametrising the applied time-dependent fields with a finite set of variables. The effectiveness of the resulting optimisation depends on the complexity of the problem and the number of variables. We consider different parametrisations in terms of basis functions, asking whether the choice of the applied basis affects the quality of the optimisation. Furthermore, we consider strategies to choose the most suitable basis. For the comparison, we test three different randomisable bases - introducing the sinc and sigmoid bases as alternatives to the Fourier basis - on QOC problems of varying complexity. For each problem, the basis-specific convergence rates result in a unique ranking. Especially for expensive evaluations, e.g., in closed-loop, a potential speed-up by a factor of up to 10 may be crucial for the optimisation's feasibility. We conclude that a problem-dependent basis choice is an influential factor for QOC efficiency and provide advice for its approach.