Hybrid Classical--Quantum Optimization of Wireless Routing Using QAOA and Quantum Walks

Abstract

Routing in wireless communication networks is shaped by mobility, interference, congestion, and competing service requirements, making route selection a high-dimensional constrained optimization problem rather than a simple shortest-path task. This paper investigates the use of hybrid classical--quantum methods for wireless routing, focusing on the Quantum Approximate Optimization Algorithm (QAOA) and quantum walks as candidate mechanisms for exploring complex routing spaces. The paper examines how wireless routing can be expressed as a constrained graph optimization problem in which routing objectives, flow constraints, connectivity requirements, and interference effects are mapped into quantum-compatible Hamiltonian representations. It then discusses how these approaches can be integrated into a hybrid architecture in which classical systems perform network monitoring, graph construction, pre-processing, and deployment, while quantum subroutines are used for selected optimization components. The analysis shows that the potential value of quantum routing lies primarily in the treatment of difficult combinatorial subproblems rather than end-to-end replacement of classical routing frameworks. The paper also highlights practical limitations arising from state preparation, constraint encoding, oracle construction, hardware noise, limited qubit resources, and hybrid execution overhead. It is argued that any meaningful near-term advantage will depend on careful problem decomposition, compact encoding, and tight classical--quantum integration.

Figures (3)

• Figure 1: Classical formulation of wireless routing in dynamic networks. The figure illustrates the time-varying graph model, the multi-objective routing cost function, and the combinatorial binary optimization structure with flow conservation constraints that motivate subsequent quantum representations.
• Figure 2: Quantum encoding strategies for wireless graph optimization. The figure presents a conceptual framework for mapping classical wireless network structures into quantum representations suitable for routing optimization. It illustrates edge-based encoding, path-based encoding, adjacency matrix encoding, constraint Hamiltonians, amplitude encoding, interference modelling, and hardware-aware qubit optimization.
• Figure 3: Hybrid classical--quantum routing architecture illustrating the integration of a classical network management and preprocessing pipeline with a quantum optimization pipeline through a central hybrid router. The figure highlights how link measurements, node states, traffic demands, graph representation, and interference-related constraints from the classical domain are transformed into routing optimization inputs, while quantum processing is used to evaluate cost and constraint Hamiltonians, generate candidate routing solutions, and return optimized decisions through a feedback loop.