QAOA with 24 Qubits Achieves Efficient 5G CBRS Multi-Channel Allocation

Researchers are tackling the critical challenge of efficient spectrum sharing within 5G Citizens Broadband Radio Service (CBRS) networks, a key factor in maximising capacity when base stations demand simultaneous multi-channel access. Gunsik Min, Youngjin Seo, and Jun Heo, all from the School of Electrical Engineering at Korea University, present a novel approach using a subspace-confined Quantum Approximate Optimization Algorithm (QAOA) , a significant departure from standard formulations which often struggle with invalid assignments. Their method initialises channel registers in Generalized Dicke states and employs an intra-register XY mixer, effectively limiting the computational search space from a vast Hilbert space to just 2916 feasible configurations in an 8-node network. This constraint-preserving structure not only accelerates convergence to low-conflict assignments but also demonstrably outperforms both penalty-based QAOA and classical heuristics, maintaining high feasibility even under realistic noise conditions , representing a substantial step towards practical quantum solutions for 5G resource allocation.

This innovative approach initializes each channel register in a Generalized Dicke state and evolves it using an intra-register XY mixer, effectively confining the quantum dynamics to a manageable space.

The study reveals that standard QAOA formulations often rely on penalty terms to enforce multi-channel constraints, leading to the exploration of a vast Hilbert space largely comprised of invalid assignments. In contrast, the proposed ansatz restricts the search space for an 8-node CBRS interference graph, requiring 24 qubits, from a full Hilbert space of 224 configurations down to a feasible set of only 2,916 configurations. Within this constrained subspace, the algorithm demonstrates rapid convergence towards low-conflict assignments, eliminating the need for substantial penalty coefficients. Simulations involving instances with up to eight nodes consistently show that this new ansatz achieves near-optimal conflict levels and outperforms both standard penalty-based QAOA and a classical greedy heuristic in terms of feasibility.
This research establishes a direct link between quantum algorithm design and practical wireless communication challenges, offering a pathway to more efficient spectrum utilization. Experiments show that the constraint-preserving structure of the algorithm maintains a high feasibility ratio even under realistic noise conditions, specifically with depolarizing channels relevant to near-term quantum devices. The work opens possibilities for optimizing CBRS channel allocation in real-world deployments, potentially leading to increased network throughput and improved user experience. By directly encoding per-node Hamming-weight constraints, the team has created a quantum algorithm that not only solves a complex optimization problem but also addresses the limitations of existing QAOA implementations in constrained environments.

Furthermore, the study unveils a novel approach to quantum algorithm design by leveraging the properties of Johnson graphs to represent the feasible solution space. This allows for a more targeted search, significantly reducing the computational resources required to find optimal or near-optimal solutions. Noise simulations indicate that the constraint-preserving structure maintains a high feasibility ratio in NISQ-relevant error regimes, suggesting the potential for practical implementation on current and near-future quantum hardware. This work addresses the inefficiency of standard QAOA formulations, which often explore largely invalid Hilbert space configurations due to multi-channel constraints, typically enforced using penalty terms. Researchers initialized each node-wise channel register in a Generalized Dicke state and evolved it under an intra-register XY mixer, effectively confining the dynamics to a tensor product of Johnson graphs that precisely encode per-node Hamming-weight constraints. For an 8-node CBRS interference graph utilizing 24 qubits, this approach reduced the effective search space from a total of 224 states to just 2916 feasible configurations, a reduction factor of approximately 5.8×103.
The study pioneered a method where the algorithm rapidly converges to low-conflict assignments without relying on substantial penalty coefficients. Experiments employed simulations on instances with up to eight nodes, demonstrating that the proposed ansatz consistently outperforms both standard penalty-based QAOA and a greedy classical heuristic in terms of feasibility, achieving a feasibility ratio of 1.0, meaning all sampled bitstrings satisfy the cardinality constraints. A classical Integer Linear Programming (ILP) baseline identified an optimal solution with two interference conflicts, while a greedy multi-coloring heuristic yielded four conflicts; in contrast, the subspace-confined QAOA achieved a best feasible conflict of three. Scientists harnessed a depolarizing channel with varying gate error rates to assess robustness, applying it to all single- and two-qubit gates within the QAOA circuits. The average deviation from the node-wise Hamming-weight constraints was calculated, revealing that the subspace-confined ansatz maintained near-zero deviation at zero error and increased linearly with error, remaining below 1.0 even at the highest error rates tested. For an 8-node CBRS interference graph utilising 24 qubits, the effective search space was reduced from a full Hilbert space of 224, approximately 1.68x 107 states, to just 2,916 feasible configurations. This represents a search-space reduction factor of approximately 5.8x 103, enabling faster convergence to optimal solutions.

Experiments revealed that the proposed ansatz, initialising each node’s channel register in a Generalized Dicke state and employing an intra-register XY mixer, confines dynamics to a tensor product of Johnson graphs. This confinement precisely encodes per-node Hamming-weight constraints, ensuring that the algorithm focuses solely on valid channel assignments. The team measured performance on instances with up to eight nodes, consistently outperforming standard penalty-based QAOA and a greedy classical heuristic in terms of feasibility. Specifically, the subspace-confined QAOA achieved a best feasible conflict level of three, with a feasibility ratio of 1.0, meaning all sampled bitstrings satisfied the cardinality constraints.

Data shows that the standard QAOA baseline, utilising an X-mixer and penalty Hamiltonian, saturated at a large cost and rarely sampled feasible bitstrings. Conversely, the subspace-confined QAOA began directly within the feasible space, guaranteeing all sampled states adhered to the node-wise cardinality constraints. Tests prove that a classical Integer Linear Programming (ILP) baseline found an optimal solution with two interference conflicts, while a greedy multi-coloring heuristic returned a solution with four conflicts. The proposed approach not only concentrates probability mass within the feasible subspace but also identifies solutions closer to the classical optimum.

Researchers also investigated robustness under depolarizing noise, simulating error rates relevant to current Noisy Intermediate-Scale Quantum (NISQ) devices. Measurements confirm that the constraint-preserving structure maintains a high feasibility ratio even in these error regimes. For a 5-node (15-qubit) instance, the average deviation from the Hamming-weight constraints was near zero at a gate error rate of zero, demonstrating the ansatz’s inherent stability. The average deviation for the standard penalty-based QAOA remained consistently high, between 1.5 and 2.0, indicating a prevalence of invalid solutions regardless of noise level. Furthermore, the team explored a dual-constraint extension, simultaneously enforcing node-wise channel demands and per-channel capacity constraints, illustrating the potential for incorporating additional structure into the QAOA framework for realistic CBRS deployment scenarios. This breakthrough delivers a pathway towards more efficient spectrum sharing and enhanced 5G network performance.