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arXiv:2602.07483

Recursive QAOA for Interference-Aware Resource Allocation in Wireless Networks

Kuan-Cheng Chen, Hiromichi Matsuyama, Wei-hao Huang, Yu Yamashiro

quant-phcs.DCSubmitted Feb 7, 2026• Announced Feb 10, 2026• 0 citations
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Abstract

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.

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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.
Recursive QAOA (RQAOA) solves combinatorial optimization problems by using shallow quantum circuits to estimate pairwise correlations and recursively eliminate variables until a classical solver can handle the residual instance. Each elimination step requires measurement shots, and the total shot cost grows with the number of recursive stages. On near-term quantum devices, increasing shot counts can translate directly into greater exposure to hardware-level noise sources such as readout errors and decoherence, making shot-efficient execution not merely a cost-reduction measure but a factor with direct implications for solution reliability. While shot reduction has been studied broadly across NISQ algorithms, step-wise measurement control inside the recursive loop of RQAOA has received little attention. We formulate this step-wise allocation as a sequential decision problem and propose two strategies for depth-1 RQAOA on weighted Max-Cut instances. A hand-crafted heuristic assigns shots based on local indicators of step difficulty, and a tabular Double Q-learning agent learns a residual policy that adjusts this baseline under a Lagrangian-constrained objective. Both methods are evaluated under a fixed-cap fairness protocol that equalizes the per-step budget across all strategies, and the elimination rule itself is kept unchanged so that the contribution of adaptive measurement control can be isolated. On a diverse set of weighted graph instances spanning a range of sizes and structures, the heuristic reduces total shots by approximately 23% relative to uniform allocation, and the RL policy achieves a 36% reduction with a lower effective shots per success ratio than both baselines. The improvement persists on problem sizes not seen during training, suggesting that reinforcement learning can discover efficient, instance-adaptive measurement strategies in recursive quantum optimization.
Quantum repeater networks(QRN) require efficient resource allocation to maintain highentanglement fidelity under noise and interference. We formulate this problem as a physicsinformedquadratic unconstrained binary optimization (QUBO) and solve it using the QuantumApproximate Optimization Algorithm (QAOA). To enable scalability on Noisy Intermediate-Scale Quantum (NISQ) devices, we introduce a cluster-based variant (CLQAOA) that decomposesthe global problem into smaller subproblems. We compare CLQAOA with classicalmethods, including Greedy and Simulated Annealing, and observe that it achieves nearoptimalsolution quality with controlled runtime scaling. We further incorporate RecursiveQAOA (RQAOA), which improves solution quality through iterative variable reduction butincurs higher computational cost. These results demonstrate that hybrid, cluster-basedquantum optimization provides a practical pathway for scalable quantum repeater networkcontrol, balancing solution quality and computational efficiency.
Efficient spectrum sharing in the Citizens Broadband Radio Service (CBRS) band is essential for maximizing 5G network capacity, particularly when high-traffic base stations require simultaneous access to multiple channels. Standard formulations of the Quantum Approximate Optimization Algorithm (QAOA) impose such multi-channel constraints using penalty terms, so most of the explored Hilbert space corresponds to invalid assignments. We propose a subspace-confined QAOA tailored to CBRS multi-channel allocation, in which each node-wise channel register is initialized in a Generalized Dicke state and evolved under an intra-register XY mixer. This ansatz confines the dynamics to a tensor product of Johnson graphs that exactly encode per-node Hamming-weight constraints. For an 8-node CBRS interference graph with 24 qubits, the effective search space is reduced from the full Hilbert space of size 2242^{24}224 to 2916 feasible configurations. Within this subspace, the algorithm converges rapidly to low-conflict assignments without large penalty coefficients. Simulations on instances with up to eight nodes show that the proposed ansatz achieves near-optimal conflict levels and consistently outperforms standard penalty-based QAOA and a greedy classical heuristic in terms of feasibility. Noise simulations with depolarizing channels further indicate that the constraint-preserving structure maintains a high feasibility ratio in NISQ-relevant error regimes.
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.
Quantum annealing (QA) offers a physics-inspired approach for such subproblems by mapping them onto an Ising Hamiltonian, which is algebraically equivalent to a Quadratic Unconstrained Binary Optimization (QUBO) model executable on quantum annealers or hybrid solvers. However, their practical employment in wireless systems critically depends on the specific problem formulation, on the particular variable encoding, constraint handling, solver selection, hardware embedding, and fair benchmarking. This paper develops wireless-oriented QUBO modeling guidelines for QA-assisted resource allocation. We first present a beginner-friendly toy example in which a terrestrial-aerial resource-allocation problem with a fractional signal-to-interference-plus-noise ratio (SINR) maximization objective is reformulated into a two-bit QUBO via Boolean interpolation, converted into an Ising representation, and decoded back into a wireless scheduling decision. The same scheduling is applicable to UAV, aircraft, satellite, and terrestrial links in SAGIN systems. We then review the QA foundations and solver ecosystems, including binary quadratic, discrete quadratic, constrained quadratic, and hybrid models from the perspective of NG wireless optimization. Furthermore, we discuss both binary and discrete encoding, penalty-based constraint conversion, embedding overhead, solution decoding, and feasibility verification. A QUBO Compatibility Index is introduced as a lightweight diagnostic metric for assessing the associated QUBO formulation readiness, rather than a predictor of runtime or solution quality. Finally, a case study on max-min uplink power control in cell-free massive MIMO illustrates how a fairness-oriented wireless problem can be discretized, constrained, converted into the concept of a QUBO, and evaluated against classical baselines. A host of key challenges and future directions are also discussed.
Quantum optimization is expected to resolve many computationally hard problems, such as Radio Resource Allocation (RRA) in wireless communications and networking. However, given noisy intermediate-scale quantum (NISQ) computers that supply a very limited number of effective logical qubits after quantum error correction, computationally efficient algorithms are highly desirable to facilitate quantum advantages, particularly the required number of qubits. To achieve quantum advantageous optimization by small number of qubits, we formulate RRA as a Maximum Independent Set (MIS) on dense conflict graphs, which is challenging for the Quantum Approximate Optimization Algorithm (QAOA) using NISQ computing machines. We further propose a modified Quantum Local Search (QLS) framework that decomposes the global MIS into overlapping subgraphs defined by a tunable neighborhood radius. Hard (feasibility) constraints are enforced via partial mixers, while soft (adjacency) constraints are resolved in a classical post-processing step. Considering practical interference issues that are typically ignored in quantum computational research, we uniquely extend the method to accommodate minimal-adjacency scenarios by specifying shared boundaries causing limited interference. While complexity analysis shows polynomial scaling in the number of feasible placements, computational experiments demonstrate substantial savings on required qubits and simultaneously achieving optimal solutions across multiple adjacency configurations. Efficient quantum optimization of RRA by NISQ computers of significantly fewer qubits is therefore accomplished.