Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control

TL;DR

This paper introduces a new continuous-time feedback control method for stabilizing a two-level quantum system's eigenstate, achieving exponential convergence with a simple, low-complexity controller based on Lyapunov functions.

Contribution

It presents a novel Lyapunov-based control strategy that guarantees exponential stabilization of a quantum eigenstate, improving upon previous probabilistic methods.

Findings

Achieves global exponential convergence to the eigenstate.

Controller depends only on a single measurement coordinate.

Potential for replacing full state observers with simpler filters.

Abstract

This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the measurement operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous measurement output, our controller only depends on the single coordinate along the measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.