Tackling Traveling Salesman Problems with a Cluster-Based Quantum-Classical Optimization

초록

Resource requirements for direct quantum computation impose a critical barrier to solving NP-hard combinatorial optimization problems such as the Traveling Salesperson Problem (TSP), in the current Noisy Intermediate-Scale Quantum (NISQ) devices. For example, computation of Grover's Search Algorithm (GSA) requires a substantial cost, requiring 56 qubits to tackle just 5-city problems. While the Quantum Approximate Optimization Algorithm (QAOA) has been known as a candidate that can exploit the NISQ device, it still requires N-2 qubits to solve N-city problems and, more importantly, it may suffer from convergence issues as the problem includes more cities. To circumvent these constraints, here we propose and validate a hybrid cluster-based QAOA framework, which decomposes large TSP instances into small-sized subproblems, solves each sub-problem using QAOA with reasonable budgets of qubits, and then subsequently integrates solutions of sub-problems with a classical stitching strategy to secure the final global Hamiltonian cycle. Through a set of extensive benchmark test, we demonstrate this cluster-based hybrid approach scales well in computing environments that are commonly interactable these days, producing solutions of up to 24-city problems. Comparative analysis against classical heuristics is also conducted to confirm that the hybrid QAOA algorithm can achieve competitive performance, while offering a resource-efficient pathway for leveraging NISQ hardware for large-scale combinatorial optimization.

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