Exploring the Robustness of stabilizing controls for stochastic quantum evolutions

TL;DR

This paper investigates how modeling errors impact the stabilization of quantum states in stochastic evolutions, providing bounds and conditions for robustness in open-loop and feedback control protocols.

Contribution

It introduces bounds on the effects of perturbations on quantum stabilization, emphasizing the importance of invariance and analyzing both open-loop and feedback strategies.

Findings

Invariance preservation ensures stability under perturbations.

Bounded mean solutions for open-loop protocols.

Explicit bounds for feedback control in quantum systems.

Abstract

In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we highlight the key role of dynamical invariance of the target: if the perturbation preserves invariance, it is possible to prove that it also preserves its attractivity, under some additional assumptions. In addition, we prove boundedness in mean of the solutions of perturbed systems under open-loop protocols. For the feedback strategies, in the general case without assumptions on invariance, we provide bounds on the perturbation effect in expectation and in probability, as well as specific bounds for non-demolition nominal systems.