A Hybrid Classical-Quantum Annealing Algorithm for the TSP

TL;DR

This paper introduces a hybrid classical-quantum algorithm for solving the NP-hard Traveling Salesperson Problem by contracting the problem graph to fit quantum hardware capabilities.

Contribution

It presents a novel graph contraction method that reduces TSP complexity, enabling quantum annealing solutions on current hardware.

Findings

Successfully tested on classical simulations with Path Integral Monte Carlo.

Implemented on a D-Wave quantum annealer with promising results.

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.