Sliding mode control of quantum systems

TL;DR

This paper introduces a sliding mode control approach for quantum systems, enabling robust control despite uncertainties, by combining unitary control and measurements, demonstrated on two- and three-level systems.

Contribution

It presents a novel quantum sliding mode control method that guarantees performance under Hamiltonian uncertainties, extending classical SMC to quantum systems.

Findings

Successfully applied to two-level and three-level quantum systems.

Guarantees control performance despite system uncertainties.

Provides a new tool for robust quantum information processing.

Abstract

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.