Two-step feedback preparation of entanglement for qubit systems with time delay

TL;DR

This paper introduces two Lyapunov-based feedback control strategies to generate entangled states in qubit systems with constant time delay, improving robustness and compensating for computational delays.

Contribution

It proposes novel two-step feedback control methods, including bang-bang and switching Lyapunov controls, specifically designed for systems with inherent time delays.

Findings

Both control strategies effectively generate entanglement in two-qubit systems.

The stability of the bang-bang control is theoretically proven.

Numerical simulations demonstrate the effectiveness of the proposed methods.

Abstract

Quantum entanglement plays a fundamental role in quantum computation and quantum communication. Feedback control has been widely used in stochastic quantum systems to generate given entangled states since it has good robustness, where the time required to compute filter states and conduct filter based control usually cannot be ignored in many practical applications. This paper designed two control strategies based on the Lyapunov method to prepare a class of entangled states for qubit systems with a constant delay time. The first one is bang bang like control strategy, which has a simple form with switching between a constant value and zero, the stability of which is proved. Another control strategy is switching Lyapunov control, where a constant delay time is introduced in the filter-based feedback control law to compensate for the computation time. Numerical results on a two qubit system illustrate the effectiveness of these two proposed control strategies.