Recursive QAOA for Interference-Aware Resource Allocation in Wireless Networks

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.

💡 Research Summary

This paper addresses the challenging problem of interference‑aware channel assignment in dense wireless networks by formulating it as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solving it with a recursive variant of the Quantum Approximate Optimization Algorithm (RQAOA). The authors first map the channel‑allocation task to a QUBO: binary variables x_{u,c} indicate whether user u uses channel c, pairwise interference weights w_{c}^{u,v} generate quadratic terms x_{u,c}x_{v,c}, and constraints (exactly one channel per user and optional per‑channel capacity limits) are enforced either through quadratic penalty terms with coefficients A and B or via constraint‑preserving mixers such as one‑hot or ring‑exchange mixers. After converting the QUBO to an Ising Hamiltonian H_C, the algorithm proceeds as follows.

1. Pre‑processing – Classical reductions (isolated spins, dominance tests, wireless‑specific pruning) are applied to fix obvious variables and shrink the problem before any quantum computation.
2. Shallow QAOA Execution – A low‑depth QAOA circuit (typically p = 1 or 2) is run on the current Ising instance. Expectation values ⟨Z_i⟩ and ⟨Z_i Z_j⟩ are estimated from a modest number of measurement shots.
3. Variable Elimination – High‑confidence single‑spin signs (|⟨Z_i⟩|) and strong pairwise correlations (|⟨Z_i Z_j⟩|) are scored. The highest‑scoring spin or spin pair exceeding a threshold τ is fixed: a single spin is set to sign(⟨Z_i⟩), while a correlated pair is merged via z_j = σ z_i with σ = sign(⟨Z_i Z_j⟩). The Ising parameters (h, J, const) are updated analytically, effectively reducing the number of qubits.
4. Recursion – Steps 2–3 repeat until the active variable set size falls below a predefined cutoff n_cutoff, at which point a classical exact solver (brute‑force or ILP) solves the remaining tiny instance.
5. Back‑substitution – The recorded elimination decisions are reversed to reconstruct a full assignment for all original variables.

The recursive reduction yields several practical benefits. First, each QAOA call operates on fewer qubits, allowing shallower circuits that are more tolerant to noise on near‑term devices. Second, the number of variational parameters grows only modestly, avoiding the parameter explosion typical of plain QAOA on large problems. Third, by fixing variables that are already strongly biased, the algorithm naturally respects the one‑hot constraints, especially when constraint‑preserving mixers are employed, reducing the need for large penalty coefficients.

Experimental evaluation is performed on synthetic wireless topologies, including a detailed four‑user, four‑channel case. In these simulations, RQAOA consistently identifies high‑confidence variables, shrinking the problem to ≤ 6 binary variables after one or two recursion levels. The shallow QAOA layers already achieve low expected energy, and the final exact solve recovers the global optimum in every trial. Compared against integer linear programming (exact for small instances) and greedy/graph‑coloring heuristics, RQAOA attains zero or near‑zero infeasibility rates and improves the interference cost by 2–5 % on average. Moreover, the total number of variational parameters required is reduced to roughly 30 % of that needed by a non‑recursive QAOA of comparable depth.

The authors also release an end‑to‑end software pipeline built on the open‑source Qamomile framework, which automates instance generation, QUBO construction, circuit compilation, expectation estimation, recursive elimination, and final decoding.

Limitations are acknowledged: (i) the reliability of correlation estimates depends on the number of measurement shots; (ii) penalty coefficients A and B must be tuned to balance feasibility and solution quality; (iii) all results are obtained on noiseless simulators, so the impact of realistic hardware noise remains to be quantified. Future work is outlined to incorporate error mitigation, adaptive thresholding, multi‑objective extensions (e.g., power and latency), and broader applications such as joint user‑AP association or time‑frequency scheduling.

Overall, the paper demonstrates that recursive QAOA can effectively mitigate scaling challenges of plain QAOA, maintain feasibility for constrained wireless resource allocation, and deliver high‑quality solutions on problem sizes that are already relevant for near‑term quantum hardware.