  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.
