Quantum annealing of the Traveling Salesman Problem

TL;DR

This paper introduces a quantum annealing approach using path-integral Monte Carlo for solving the symmetric Traveling Salesman Problem, demonstrating superior performance over classical simulated annealing on a large instance.

Contribution

It presents a novel quantum annealing scheme for TSP based on a constrained Ising-like model, showing improved results over classical methods.

Findings

Quantum annealing outperforms classical simulated annealing on large TSP instances.

The proposed method effectively restructures tours using simple Monte Carlo moves.

Performance tested on a 1002-city standard TSP benchmark.

Abstract

We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric Traveling Salesman Problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal Simulated Annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (2-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002 city instance of the standard TSPLIB.