Quantum Approaches to the Minimum Edge Multiway Cut Problem

TL;DR

The paper tackles the Minimum Edge Multiway Cut (MEMC) problem in the context of telecom resilience, comparing three quantum optimization paradigms—quantum annealing on a D-Wave QPU, gate-based QAOA, and photonic variational circuits—through a unified QUBO formulation. It demonstrates that, for small instances, all approaches can recover optimal solutions, but Quantum Annealing offers the most scalable performance as instance size grows, while QAOA and photonic approaches are hindered by circuit depth, optimization ruggedness, and hardware limitations. The study provides actionable insights into embedding overheads, model expressiveness, and hardware compatibility, guiding the design of quantum workflows for combinatorial telecom optimization. The results suggest a practical takeaway: quantum annealing is the most mature option among the tested modalities for MEMC today, with future work needed to enhance encodings, noise resilience, and photonic scalability.

Abstract

We investigate the minimum edge multiway cut problem, a fundamental task in evaluating the resilience of telecommunication networks. This study benchmarks the problem across three quantum computing paradigms: quantum annealing on a D-Wave quantum processing unit, photonic variational quantum circuits simulated on Quandela s Perceval platform, and IBM s gate-based Quantum Approximate Optimization Algorithm (QAOA). We assess the comparative feasibility of these approaches for early-stage quantum optimization, highlighting trade-offs in circuit constraints, encoding overhead, and scalability. Our findings suggest that quantum annealing currently offers the most scalable performance for this class of problems, while photonic and gate-based approaches remain limited by hardware and simulation depth. These results provide actionable insights for designing quantum workflows targeting combinatorial optimization in telecom security and resilience analysis.

Figures (6)

• Figure 1: Hybrid vs Quantum Annealing Cut Cost
• Figure 2: D-Wave Runtime vs Instance Size
• Figure 3: QAOA Circuit Structure ($p = 1$)
• Figure 4: QAOA Training Convergence
• Figure 5: Photonic Energy Convergence