The role of controllability in optimizing quantum dynamics

TL;DR

This paper explores how the controllability of quantum systems influences the complexity of optimizing quantum control, showing that limited controllability increases landscape ruggedness and false traps, affecting search efficiency.

Contribution

It provides a topology analysis linking controllability to control landscape ruggedness and demonstrates the impact of controllability restrictions on false traps in quantum control.

Findings

Limited controllability increases false traps.

Controllable systems lack false traps.

Ruggedness of landscape correlates with controllability.

Abstract

This paper discusses the important role of controllability played on the complexity of optimizing quantum mechanical control systems. The study is based on a topology analysis of the corresponding quantum control landscape, which is referred to as the optimization objective as a functional of control fields. We find that the degree of controllability is closely relevant with the ruggedness of the landscape, which determines the search efficiency for global optima. This effect is demonstrated via the gate fidelity control landscape of a system whose controllability is restricted on a SU(2) dynamic symmetry group. We show that multiple local false traps (i.e., non-global suboptima) exist even if the target gate is realizable and that the number of these traps is increased by the loss of controllability, while the controllable systems are always devoid of false traps.