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Hybrid Quantum-Classical Maximum-Likelihood Detection via Grover-based Adaptive Search for RIS-assisted Broadband Wireless Systems

Maryam Tariq, Raneem Abdelrahim, Omar Alhussein, Sami Muhaidat

TL;DR

The paper addresses the high computational burden of maximum-likelihood detection (MLD) in RIS-assisted broadband wireless systems with frequency-selective channels by formulating MLD as a quadratic unconstrained binary optimization (QUBO) problem and solving it with Grover Adaptive Search (GAS). A classical MMSE-based threshold initialization accelerates convergence, effectively reducing the necessary quantum queries from $O(M^N)$ to $O(\sqrt{M^N})$. It introduces two real-valued cost encodings for GAS—integer approximation and direct encoding via Fejér distribution—and employs an adaptive threshold initialization to tighten the search. Simulation on a noiseless quantum statevector backend shows near-optimal BER performance close to classical MLD, with substantial reductions in query complexity and clear gains from RIS deployment, illustrating the practicality of quantum-enhanced detection in RIS-aided broadband systems.

Abstract

The escalating complexity and stringent performance demands of sixth-generation wireless systems necessitate advanced signal processing methods capable of simultaneously achieving high spectral efficiency and low computational complexity, especially under frequency-selective propagation conditions. In this paper, we propose a hybrid quantum-classical detection framework for broadband systems enhanced by reconfigurable intelligent surfaces (RISs). We address the maximum likelihood detection (MLD) problem for RIS-aided broadband wireless communications by formulating it as a quadratic unconstrained binary optimization problem, that is then solved using Grover adaptive search (GAS). To accelerate convergence, we initialize the GAS algorithm with a threshold based on a classical minimum mean-squared error detector. The simulation results show that the proposed hybrid classical-quantum detection scheme achieves near-optimal MLD performance while substantially reducing query complexity. These findings highlight the potential of quantum-enhanced detection strategies combined with RIS technology, offering efficient and near-optimal solutions for broadband wireless communications.

Hybrid Quantum-Classical Maximum-Likelihood Detection via Grover-based Adaptive Search for RIS-assisted Broadband Wireless Systems

TL;DR

The paper addresses the high computational burden of maximum-likelihood detection (MLD) in RIS-assisted broadband wireless systems with frequency-selective channels by formulating MLD as a quadratic unconstrained binary optimization (QUBO) problem and solving it with Grover Adaptive Search (GAS). A classical MMSE-based threshold initialization accelerates convergence, effectively reducing the necessary quantum queries from to . It introduces two real-valued cost encodings for GAS—integer approximation and direct encoding via Fejér distribution—and employs an adaptive threshold initialization to tighten the search. Simulation on a noiseless quantum statevector backend shows near-optimal BER performance close to classical MLD, with substantial reductions in query complexity and clear gains from RIS deployment, illustrating the practicality of quantum-enhanced detection in RIS-aided broadband systems.

Abstract

The escalating complexity and stringent performance demands of sixth-generation wireless systems necessitate advanced signal processing methods capable of simultaneously achieving high spectral efficiency and low computational complexity, especially under frequency-selective propagation conditions. In this paper, we propose a hybrid quantum-classical detection framework for broadband systems enhanced by reconfigurable intelligent surfaces (RISs). We address the maximum likelihood detection (MLD) problem for RIS-aided broadband wireless communications by formulating it as a quadratic unconstrained binary optimization problem, that is then solved using Grover adaptive search (GAS). To accelerate convergence, we initialize the GAS algorithm with a threshold based on a classical minimum mean-squared error detector. The simulation results show that the proposed hybrid classical-quantum detection scheme achieves near-optimal MLD performance while substantially reducing query complexity. These findings highlight the potential of quantum-enhanced detection strategies combined with RIS technology, offering efficient and near-optimal solutions for broadband wireless communications.
Paper Structure (14 sections, 24 equations, 3 figures, 1 algorithm)

This paper contains 14 sections, 24 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Quantum Preliminaries
  3. Qubits and Superposition
  4. Quantum Gates and Circuits
  5. Grover Search
  6. System Model and Problem Description
  7. MLD via Grover-based Adaptive Search
  8. Casting MLD as QUBO
  9. Grover Adaptive Search
  10. Integer Approximation
  11. Direct Encoding
  12. Adaptive Threshold Initialization
  13. Simulation Results
  14. Conclusion

Figures (3)

  • Figure 1: Grover adaptive search circuit showing state preparation $A_{y_i}$, oracle $O$, and diffusion operator $D$, iterated to amplify low-cost solutions based on threshold $y_i$.
  • Figure 2: Comparison between the proposed hybrid detector, conventional GAS, and classical MLD for three RIS configurations: no RIS, $R = 4$, and $R = 8$, with $N = 3$ symbols.
  • Figure 3: BER comparison of the proposed hybrid quantum-classical detector, MLD, and MMSE detector for varying RIS sizes ($R = 0, 4, 8$) with BPSK and $N = 3$.