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arXiv:2502.08170 · IEEE Transactions on Cybernetics

Evolutionary Optimization-Based Design of LQG Controllers in Quantum Coherent Feedback

Chunxiang Song, Yanan Liu, Guofeng Zhang, Huadong Mo, Daoyi Dong

Published Jan 19, 2026• 2 citations

Abstract

In this article, we propose a differential evolution (DE) algorithm specifically tailored for the design of linear-quadratic-Gaussian (LQG) controllers in quantum systems. Building upon the foundational DE framework, the algorithm incorporates specialized modules, including relaxed feasibility rules, a scheduled penalty function, adaptive search range adjustment, and the "bet-and-run" initialization strategy. These enhancements improve the algorithm's exploration and exploitation capabilities while addressing the unique physical realizability requirements of quantum systems. The proposed method is applied to a quantum optical system, where three distinct controllers with varying configurations relative to the plant are designed. The resulting controllers demonstrate superior performance, achieving lower LQG performance indices compared to existing approaches. In addition, the algorithm ensures that the designs comply with physical realizability constraints, guaranteeing compatibility with practical quantum platforms. The proposed approach holds significant potential for application to other linear quantum systems in performance optimization tasks subject to physically feasible constraints.

DOI: 10.1109/tcyb.2026.3651242

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Mixed LQG and

H_\infty

Coherent Feedback Control for Linear Quantum Systems

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and

H_\infty

optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as "coherent feedback controller". A lower bound of the LQG control is proved. Then two different methods, rank constrained linear matrix inequality (LMI) method and genetic algorithm are proposed for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier, DPA) demonstrate the effectiveness of these two proposed algorithms.

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