Switching Quantum Dynamics for Fast Stabilization

TL;DR

This paper introduces switching control strategies for quantum state stabilization, demonstrating faster convergence and robustness by switching between generators in the coherence-vector space.

Contribution

It recasts quantum control as a switched-stabilization problem and compares time-based and state-based switching methods for improved entangled state preparation.

Findings

State-based switching achieves faster convergence.

Switching methods retain robustness to initialization.

Reformulation enables control-theoretic analysis of quantum stabilization.

Abstract

Control strategies for dissipative preparation of target quantum states, both pure and mixed, and subspaces are obtained by switching between a set of available semigroup generators. We show that the class of problems of interest can be recast, from a control--theoretic perspective, into a switched-stabilization problem for linear dynamics. This is attained by a suitable affine transformation of the coherence-vector representation. In particular, we propose and compare stabilizing time-based and state-based switching rules for entangled state preparation, showing that the latter not only ensure faster convergence with respect to non-switching methods, but can designed so that they retain robustness with respect to initialization, as long as the target is a pure state or a subspace.