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

TL;DR

BD-RIS is proposed to overcome the diagonality limitations of conventional RIS by enabling a non-diagonal beamforming matrix $\boldsymbol{\Theta}$ that provides richer wave manipulation for 6G networks. The paper systematically introduces BD-RIS, covering architectural design, functional classifications, advantages, and the principal challenges and opportunities, and includes a case study contrasting four beamforming algorithms and a hybrid quantum-classical ML approach for beam prediction on DeepSense 6G Scenario 8. It demonstrates that BD-RIS can improve coverage and sum-rate while enabling advanced applications such as ISCC, NTN, and spectrum sharing, with quantum ML models offering notable gains in beam forecasting. The results highlight a practical path toward BD-RIS deployment in 6G, including the integration of hybrid quantum-classical ML to enhance beam prediction and network adaptability, under realistic mobility and radio environments.

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 machine learning (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.

Figures (4)

• Figure 1: BD-RIS for 6G networks.
• Figure 2: Beamforming design performance. (a) The sum rate and (b) the average computation time are plotted as a function of the number of BD-RIS elements for RZF, FP, AO, and QNM.
• Figure 3: Beam prediction performance: (a) The training and (b) validation results of distance-based accuracy and cross-entropy loss are plotted as a function of epochs for hybrid quantum-classical ML models---i.e., quantum-ResNet (Q-ResNet34) and quantum-vision transformer (Q-ViT)---and a standalone classical ML model---i.e., vision transformer (ViT).
• Figure 4: Confusion matrices for hybrid Q-ResNet34, hybrid Q-ViT, and standalone ViT. For Scenario 8 from the DeepSense 6G dataset, the frequency of each beam index and the variations in the distribution of the maximum normalized power are also demonstrated to identify any data bias that may lead to the deteriorated performance of these ML models.