Ground-state Stabilization of Open Quantum Systems by Dissipation

TL;DR

This paper develops an algebraic Lyapunov stability framework for engineering dissipation in open quantum systems, enabling robust ground-state stabilization and scalable quantum control.

Contribution

It introduces algebraic conditions for ground-state stability using operator inequalities, linking quantum dissipation engineering to classical control theory methods.

Findings

Derived Lyapunov stability conditions as operator inequalities.

Established a connection between quantum dissipation engineering and classical control techniques.

Discussed implications for dissipative quantum computing and state engineering.

Abstract

Control by dissipation, or environment engineering, constitutes an important methodology within quantum coherent control which was proposed to improve the robustness and scalability of quantum control systems. The system-environment coupling, often considered to be detrimental to quantum coherence, also provides the means to steer the system to desired states. This paper aims to develop the theory for engineering of the dissipation, based on a ground-state Lyapunov stability analysis of open quantum systems via a Heisenberg-picture approach. Algebraic conditions concerning the ground-state stability and scalability of quantum systems are obtained. In particular, Lyapunov stability conditions expressed as operator inequalities allow a purely algebraic treatment of the environment engineering problem, which facilitates the integration of quantum components into a large-scale quantum system and draws an explicit connection to the classical theory of vector Lyapunov functions and decomposition-aggregation methods for control of complex systems. The implications of the results in relation to dissipative quantum computing and state engineering are also discussed in this paper.