Coherent feedback control for linear quantum systems and two-strategy evolutionary game theory

Chuanxin Bian

Z. W. Sun

A. Iqbal, A.H. Toor

Yulong Liu, Zhong-Peng Liu, Jing Zhang

Abstract It is well known that some nonlinear phenomena such as strong photon blockade are difficult to observe in optomechanical systems with current experimental technology. Here we present a coherent feedback control strategy in which a linear cavity is coherently controlled by an optomechanical controller in a feedback manner. The coherent feedback loop transfers quantum nonlinearity from the controller to the controlled cavity causing destructive quantum interference to occur, and making it possible to observe strong nonlinear effects. With the help of the coherent feedback loop, large and tunable bistability and strong photon blockade of the cavity modes can be achieved even in the optomechanical weak coupling regime. Additionally, the coherent feedback loop leads to two-photon and multiphoton tunnelings for the controlled linear cavity, which are also typical quantum nonlinear phenomena. We hope that our work can give new perspectives on engineering nonlinear interactions in quantum systems.

Chunxiang Song, Yanan Liu, Guofeng Zhang +2 more

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.

Hendra I. Nurdin, Naoki Yamamoto