Dissipative Feedback Switching for Quantum Stabilization

TL;DR

This paper introduces a novel dissipative feedback switching method for quantum stabilization that enhances control flexibility and convergence speed without requiring strict invariance assumptions.

Contribution

It extends switching control techniques to dissipative quantum systems without invariance constraints and avoids chattering through control modulation.

Findings

Switching strategies outperform open-loop dissipation in convergence speed

The method avoids undesired chattering and Zeno effects

Exponential convergence can be achieved without modulation when target invariance is broken

Abstract

Switching controlled dynamics allows for fast, flexible control design methods for quantum stabilization of pure states and subspaces, which naturally include both Hamiltonian and dissipative control actions. A novel approach to measurement-based, dissipative feedback design is introduced, and extends the applicability of switching techniques with respect to previously proposed ones, as it does not need stringent invariance assumptions, while it still avoids undesired chattering or Zeno effects by modulating the control intensity. When the switching dynamics do leave the target invariant, on the other hand, we show that exponential convergence to the target can be enforced without modulation, and switching times that can be either fixed or stochastic with hysteresis to avoid chattering. The effectiveness of the proposed methods is illustrated via numerical simulations of simple yet paradigmatic examples, demonstrating how switching strategies converge faster than open-loop engineered dissipation.