A Hybrid Classical-Quantum Annealing Algorithm for the TSP

2026-05-10

AI Summary

This work addresses the classic NP-hard Traveling Salesman Problem (TSP) by proposing a hybrid classical-quantum optimization framework designed to overcome the limitations of current noisy intermediate-scale quantum (NISQ) devices, particularly their constrained qubit counts and connectivity topologies. The core innovation lies in an efficient graph contraction algorithm that reduces large-scale TSP instances to smaller subproblems amenable to quantum annealing. The framework integrates path-integral Monte Carlo simulation with end-to-end execution on D-Wave quantum annealing hardware. Experimental validation on both classical simulators and real quantum processors demonstrates the method’s efficacy, significantly enhancing the scalability and practical applicability of contemporary quantum hardware for real-world combinatorial optimization problems.

Abstract

Hybrid quantum-classical algorithms can help mitigating the physical limitations of current quantum devices, particularly the low qubit count and the reduced topological connectivity. In this paper, we propose a hybrid technique to solve a well-known NP-hard optimization problem: the Traveling Salesperson Problem (TSP). Our approach is based on a graph contraction technique that removes most of the dimensionality of the original problem instance, producing a sub-TSP of a size suitable to be efficiently solved by a quantum device. The performance of our approach is first demonstrated on classical quantum simulation using Path Integral Monte Carlo, and then run on a D-Wave quantum annealer.

Problem

• Traveling Salesperson Problem
• quantum annealing
• hybrid algorithm
• NP-hard optimization
• quantum hardware limitations

Innovation

• hybrid quantum-classical algorithm
• graph contraction
• quantum annealing
• Traveling Salesperson Problem
• dimensionality reduction