Quantum Local Search for Traveling Salesman Problem with Path-Slicing Strategy

Abstract: We present novel path-slicing strategies integrated with quantum local search to optimize solutions for the Traveling Salesman Problem (TSP), addressing the limitations of current Noisy Intermediate-Scale Quantum (NISQ) technologies. Our hybrid quantum-classical approach leverages classical path initialization and quantum optimization to effectively manage the computational challenges posed by the TSP. We explore various path slicing methods, including k-means and anti-k-means clustering, to divide the TSP into manageable subproblems. These are then solved using quantum or classical solvers. Our analysis, performed on multiple TSP instances from the TSPlib, demonstrates the ability of our strategies to achieve near-optimal solutions efficiently, highlighting significant improvements in solving efficiency and resource utilization. This approach paves the way for future applications in larger combinatorial optimization scenarios, advancing the field of quantum optimization.