Hybrid Quantum-Classical Detection for RIS-Assisted SC-FDE via Grover Adaptive Search

TL;DR

The paper addresses the challenge of achieving near-ML detection for RIS-assisted broadband SC-FDE with manageable complexity. It reformulates the ML detection as a QUBO and solves it with Grover adaptive search, augmented by a frequency-domain MMSE threshold to initialize the search, reducing quantum circuit depth. The authors quantify quantum resources (register widths, gate counts) and analyze query complexity, showing a quadratic speedup over exhaustive search and robustness to typical NISQ noise models. Through Qiskit simulations, the approach closely tracks ML performance in ideal scenarios and remains resilient to depolarizing and readout noise, highlighting its potential for practical 6G-level RIS-assisted detection. The work demonstrates algorithmic scalability and practical robustness, offering a viable path toward quantum-enhanced detection in wideband wireless systems.

Abstract

Wideband and low-latency requirements in sixth-generation (6G) networks demand detectors that approach maximum-likelihood (ML) performance without incurring exponential complexity. This work develops a hybrid quantum-classical detection framework for reconfigurable intelligent surface (RIS)-assisted single-carrier (SC) frequency-domain equalization (FDE) over frequency-selective channels. The ML detection objective is reformulated as a quadratic unconstrained binary optimization (QUBO) problem and solved via Grover adaptive search (GAS). To accelerate convergence, we introduce a frequency-domain MMSE threshold that exploits the circulant structure of SC-FDE channels, yielding low-complexity initialization. The framework is evaluated across varying channel lengths and RIS sizes, confirming robustness and scalability. In addition, GAS requirements are quantified through register widths and gate counts, and its query complexity is analyzed to characterize the algorithm's cost for block transmission in frequency-selective channels. Quantum circuit simulations are conducted in Qiskit under both ideal and noisy conditions. In the ideal case, the detector achieves near-optimal performance while benefiting from Grover's quadratic speedup, reducing the search cost from from O(M^N) exhaustive evaluations to O(SQRT(M^N)) oracle queries. Under noise, the shallow depth of the GAS circuits, aided by MMSE initialization, makes depolarizing errors negligible, while readout errors introduce moderate degradation yet still preserve performance close to the MMSE baseline. These results establish the feasibility of quantum-enhanced detection for RIS-assisted broadband communications, highlighting both algorithmic scalability and practical robustness for 6G networks.

Figures (8)

• Figure 1: RIS-assisted SC-FDE uplink SISO system with blocked direct UE–BS link. The BS controls the RIS via a dedicated controller.
• Figure 2: Quantum circuit of the GAS state-preparation stage. The example cost is $E(b) = 2b_0 + 3b_1 + 4b_0 b_1$ with threshold $\gamma_i = 2$. A value register of $m=3$ qubits encodes the cost in binary (weights $1,2,4$), while a key register of $n=2$ qubits holds candidate bitstrings $\mathbf b=(b_0,b_1)$. Controlled rotations implement the cost terms, unconditional rotations encode subtraction of $\gamma_i$ in two’s-complement form, and the final IQFT maps accumulated phases into measurable amplitudes.
• Figure 3: GAS circuit showing state preparation $A_{\gamma_{i}}$, oracle $O$, and diffusion operator $D$, iterated to amplify low-cost solutions based on threshold $\gamma_i$.
• Figure 4: BER versus SNR for MMSE, MLD, and Hybrid-GAS detectors with and without RIS, shown for $R \in \{2,4,8\}$.
• Figure 5: BER versus SNR for Hybrid-GAS and MLD with $L \in \{2,4,6\}$, $N=6$, and $R=4$.