Lyapunov-Based Stabilization and Control of Closed Quantum Systems

TL;DR

This paper introduces a Lyapunov-based control method for stabilizing closed quantum systems, utilizing a novel quantum Lyapunov function that enhances control design and improves stabilization performance.

Contribution

It proposes a new quantum Lyapunov function with additional degrees of freedom and analyzes stabilization under different operator commutation scenarios, advancing quantum control techniques.

Findings

Enhanced stabilization of quantum systems demonstrated.

Significant improvement in invariant state trajectories.

Potential applications in high-fidelity quantum computing.

Abstract

A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite operator in the Lyapunov function provides additional degrees of freedom for the designer. The stabilization process is analyzed regarding two distinct cases for this operator in terms of its vanishing or non-vanishing commutation with the Hamiltonian operator of the undriven quantum system. To cope with the global phase invariance of quantum states as a result of the quantum projective measurement postulate, equivalence classes of quantum states are defined and used in the proposed Lyapunov-based analysis and design. Results show significant improvement in both the set of stabilizable quantum systems and their invariant sets of state trajectories generated by designed control signals. The proposed method can potentially be applied for high-fidelity quantum control purposes in quantum computing frameworks.