Stabilization via feedback switching for quantum stochastic dynamics

Abstract

We propose a new method for pure-state and subspace preparation in quantum systems, which employs the output of a continuous measurement process and switching dissipative control to improve convergence speed, as well as robustness with respect to the initial conditions. In particular, we prove that the proposed closed-loop strategy makes the desired target globally asymptotically stable both in mean and almost surely, and we show it compares favorably against a time-based and a state-based switching control law, with significant improvements in the case of faulty initialization.

Figures (3)

• Figure 1: Results of the two simulations scenarios described in paragraphs \ref{['par:sim_1']} and \ref{['par:sim_2']}. Only the trajectories of the true state of the system are here reported (not the estimated one).
• Figure 2: Graph configuration used in the simulations.
• Figure 3: Evolution of the measurement-based trajectory in Simulation 1. In solid blue the average trajectory over 1000 realizations is shown, the light-blue area shows the average plus or minus one standard deviation while the dashed lines represent five typical realizations of the quantum trajectories.

Theorems & Definitions (10)

• Theorem \oldthetheorem
• Proposition 1
• proof
• Definition 1: Cyclic switching control law
• Definition 2: State-based switching control law
• Definition 3: Measurement-based switching control law
• Theorem \oldthetheorem
• proof
• Theorem \oldthetheorem
• proof