Sliding Mode Control of Two-Level Quantum Systems

TL;DR

This paper introduces a robust sliding mode control approach for two-level quantum systems with uncertainties, ensuring system stability and robustness through Lyapunov-based design and periodic measurements.

Contribution

It presents a novel control law design method for quantum systems that guarantees robustness against bounded uncertainties using sliding mode control and Lyapunov techniques.

Findings

Guarantees robustness in quantum control with uncertainties

Provides conditions for control law design

Potential applications in quantum information processing

Abstract

This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system's state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We propose a controller design method using the Lyapunov methodology and periodic projective measurements. In particular, we give conditions for designing such a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.