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IEEE International Conference on Quantum Computing and Engineering (QCE)

Exploring Beamforming Solutions Using Recursive Quantum Approximate Optimization Algorithm

Bidisha Dhara, Monika Agrawal, Sumantra Dutta Roy

Published Aug 30, 2025• 0 citations
Publisher

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum algorithm for solving combinatorial optimization problems. In this work, we explore the Recursive QAOA (RQAOA) approach, which improves upon the standard QAOA by successively reducing the problem size, to optimize sensor configuration for beamforming with the objective of maximizing the Signal-to-Interference-plus-Noise Ratio (SINR). We present a series of experiments across various setups, including different numbers of sensors and a range of optimizers. Additionally, we compare the obtained SINR with the maximum achievable SINR to assess the efficiency of the algorithm.

DOI
10.1109/qce65121.2025.00014

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The Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum algorithm for solving combinatorial optimization problems. In this work, we explore the Recursive QAOA (RQAOA) approach, which improves upon the standard QAOA by successively reducing the problem size, to optimize sensor configuration for beamforming with the objective of maximizing the Signal-to-Interference-plus-Noise Ratio (SINR). We present a series of experiments across various setups, including different numbers of sensors and a range of optimizers. Additionally, we compare the obtained SINR with the maximum achievable SINR to assess the efficiency of the algorithm.
Abstract This study investigates the application of quantum algorithms, specifically the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), to design optimal sensor configurations for beamforming, enhancing signal quality and overall system performance. We propose two distinct optimization formulations: one aimed at maximising array gain while the other aimed at maximising signal‐to‐noise‐interference ratio (SINR). Our findings show that the outputs obtained from quantum algorithms are consistent with those derived from classical methods.
Among quantum algorithms, the quantum approximation optimization algorithm (QAOA) is an algorithm that finds approximate solutions. Recursive QAOA is proposed to overcome the limitation that QAOA has lower performance than Goemans-Williamson algorithm in the MAX-CUT problem [Physical Review Letter, 125, 260504, 2020]. In this paper, we introduce a method with lower complexity than RQAOA and compare its numerical results in the MAX-CUT problem. At the same level, the performance of the proposed method is lower than that of RQAOA, but the number of computations of quantum and classical parts is very small.
Discrete radio resource management problems in dense wireless networks are naturally cast as quadratic unconstrained binary optimization (QUBO) programs but are difficult to solve at scale. We investigate a quantum-classical approach based on the Recursive Quantum Approximate Optimization Algorithm (RQAOA), which interleaves shallow QAOA layers with variable elimination guided by measured single- and two-qubit correlators. For interference-aware channel assignment, we give a compact QUBO/Ising formulation in which pairwise interference induces same-channel couplings and one-hot constraints are enforced via quadratic penalties (or, optionally, constraint-preserving mixers). Within RQAOA, fixing high-confidence variables or relations reduces the problem dimension, stabilizes training, and concentrates measurement effort on a shrinking instance that is solved exactly once below a cutoff. On simulated instances of modest size, including a four-user, four-channel example, the method consistently returns feasible assignments and, for the demonstrated case, attains the global optimum. These results indicate that recursion can mitigate parameter growth and feasibility issues that affect plain QAOA, and suggest a viable pathway for near-term quantum heuristics in wireless resource allocation.
Recent results on the Quantum Approximate Optimization Algorithm (QAOA) have cast pessimism on its potential to exhibit practical quantum speedups. For instance, QAOA’s locality limits its performance on tasks such as coloring bipartite graphs—which is easy for classical methods. Motivated by these limitations, the Recursive QAOA was introduced to overcome the locality and symmetry of QAOA. Despite being more powerful than QAOA, RQAOA is fully classically simulable at level-1 depth (p = 1). We report results on RQAOA in this classically simulable regime, benchmarked on random Quantum Unconstrainted Binary Optimization (QUBO) problems with up to 100 variables. We find that RQAOA generally matches the performance of classical simulated annealing and significantly outperforms ordinary QAOA.
This work explores the application of a Quantum algorithm, namely Weighted Subspace-Search-Variational-Quantum-Eigensolver (SSVQE), a variant of the traditional VQE algorithm, to predict optimal as well as sub-optimal sparse array configurations for the problem of beamforming. The optimization formulation is designed to maximize the Signal-to-Interference-plus-Noise Ratio (SINR), which is then reformulated into Quadratic Unconstrained Binary Optimization (QUBO) representation to serve as the Hamiltonian for the weighted SSVQE algorithm. The results obtained are presented along with classically obtained SINR plots to facilitate a comparison of the sparse array configurations. Our findings indicate that the output from the quantum algorithm precisely match with the results obtained from the classical method.
Abstract Quantum approximate optimization algorithm (QAOA) is a quantum–classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the noisy intermediate-scale quantum era and has been extensively studied. However, the performance limitations of low-level QAOA have also been demonstrated across various instances. In this work, we first analytically prove the performance limitations of the standard level-1 QAOA in solving the MAX-CUT problem on bipartite graphs. To this end, we derive an upper bound for the approximation ratio based on the average degree of bipartite graphs. Second, we demonstrate that recursive QAOA (RQAOA), which recursively reduces graph size using QAOA as a subroutine, outperforms the standard level-1 QAOA. However, the performance of RQAOA exhibits limitations as the graph size increases. Finally, we show that RQAOA with a restricted parameter regime can fully address these limitations. Surprisingly, this modified RQAOA always finds the exact maximum cut for any bipartite graphs and even for a more general graph with parity-signed weights.