Noise and Controllability: suppression of controllability in large quantum systems

TL;DR

This paper investigates how noise in control fields affects the ability to manipulate large quantum systems, showing that noise generally destroys controllability as system size increases.

Contribution

It demonstrates that for large quantum systems, noise in control fields prevents achieving complete controllability, highlighting a fundamental limitation in quantum control scalability.

Findings

Noise dominates in large systems, destroying controllability.

Control noise effects grow with system size.

Complete controllability is unachievable in the presence of generic noise for large systems.

Abstract

A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? Complete controllability in practice requires that the effect of noise can be suppressed for an arbitrary transformation. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases, determined by the dimension of the Hilbert space representation of the algebra. We show that for large quantum systems, generic noise in the controls dominates for a typical class of target transformations i.e., complete controllability is destroyed by the noise.