Coherent control of a qubit is trap-free

TL;DR

This paper proves that for a broad class of control problems involving two-level quantum systems, all locally optimal controls are also globally optimal, indicating that such systems are free of traps in control landscapes.

Contribution

It demonstrates that two-level quantum systems, including qubits, are inherently trap-free for key control tasks, simplifying the search for optimal controls.

Findings

All locally optimal controls are globally optimal for these systems.

Two-level quantum systems are generally trap-free in control landscapes.

Implications for quantum computation and control optimization.

Abstract

There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal controls in numerical and laboratory experiments, and for this reason the analysis of traps attracts considerable attention. In this paper we prove that for a wide range of control problems for two-level quantum systems all locally optimal controls are also globally optimal. Hence we conclude that two-level systems in general are trap-free. In particular, manipulating qubits---two-level quantum systems forming a basic building block for quantum computation---is free of traps for fundamental problems such as the state preparation and gate generation.