# On exponential stabilization of two-qubit systems

## TL;DR

This paper develops feedback control laws for two-qubit systems under continuous measurements, ensuring exponential convergence to Bell states, with explicit formulas and numerical validation.

## Contribution

It introduces explicit feedback control laws for stabilizing two-qubit systems to Bell states under continuous measurement, with conditions for exponential convergence.

## Key findings

- Explicit feedback laws ensure almost sure exponential stabilization.
- Single-channel case achieves asymptotic convergence.
- Numerical simulations validate the control strategies.

## Abstract

In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to a predetermined Bell state. This is obtained by applying stochastic tools, Lyapunov methods and geometric control tools. With one channel, we establish asymptotic convergence towards a predetermined Bell state. In both cases, we provide explicit expressions of feedback control laws satisfying the above-mentioned conditions. Finally, we demonstrate the effectiveness of our methodology through numerical simulations.