Global controllability with a single local actuator

TL;DR

This paper demonstrates that most N-dimensional quantum systems can be globally controlled using a single local actuator, with controllability depending on the actuator's position and system symmetries.

Contribution

It introduces a method to achieve global controllability in quantum systems with a single local actuator, expanding control possibilities with minimal intervention.

Findings

Controllability depends on actuator position and system symmetries.

Explicit control sequences are constructed for spin-chain systems.

Most N-dimensional systems can be controlled with a single actuator.

Abstract

We show that we can achieve global density-operator controllability for most N-dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally-acting actuator that modulates one energy-level transition. Controllability depends upon the position of the actuator and relies on the absence of either decompositions into non-interacting subgroups or symmetries restricting the dynamics to a subgroup of SU(N). These results are applied to spin-chain systems and used to explicitly construct control sequences for a single binary-valued switch actuator.