Beyond-Diagonal Reconfigurable Intelligent Surfaces for 6G Networks: Principles, Challenges, and Quantum Horizons

Abstract: A beyond-diagonal reconfigurable intelligent surface (BD-RIS) is an innovative type of reconfigurable intelligent surface (RIS) that has recently been proposed and is considered a revolutionary advancement in wave manipulation. Unlike the mutually disconnected arrangement of elements in traditional RISs, BD-RIS creates cost-effective and simple inter-element connections, allowing for greater freedom in configuring the amplitude and phase of impinging waves. However, there are numerous underlying challenges in realizing the advantages associated with BD-RIS, prompting the research community to actively investigate cutting-edge schemes and algorithms in this direction. Particularly, the passive beamforming design for BD-RIS under specific environmental conditions has become a major focus in this research area. In this article, we provide a systematic introduction to BD-RIS, elaborating on its functional principles concerning architectural design, promising advantages, and classification. Subsequently, we present recent advances and identify a series of challenges and opportunities. Additionally, we consider a specific case study where beamforming is designed using four different algorithms, and we analyze their performance with respect to sum rate and computation cost. To augment the beamforming capabilities in 6G BD-RIS with quantum enhancement, we analyze various hybrid quantum-classical ML models to improve beam prediction performance, employing real-world communication Scenario 8 from the DeepSense 6G dataset. Consequently, we derive useful insights about the practical implications of BD-RIS.