A Quantum Mechanical Travelling Salesman

TL;DR

This paper presents a quantum simulation approach to the travelling salesman problem, using quantum states and operators to represent tours, where the amplitude correlates with classical costs, potentially highlighting different optimal tours.

Contribution

It introduces a quantum framework for simulating the travelling salesman problem, linking quantum amplitudes to classical costs and exploring quantum advantages.

Findings

Quantum amplitudes depend on classical tour costs

Potential for different optimal tours in quantum vs classical solutions

Framework for quantum simulation of combinatorial optimization

Abstract

A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.