Quantum hobbit routing: Annealer implementation of generalized Travelling Salesperson Problem

TL;DR

This paper demonstrates the implementation of a generalized TSP on a quantum annealer using fewer qubits than traditional algorithms, but hardware limitations prevent quantum advantage.

Contribution

It introduces a quantum annealer implementation of a generalized TSP with linear qubit scaling, contrasting with quadratic scaling in existing quantum algorithms.

Findings

Quantum approach successfully finds solutions to the generalized TSP.

Hardware limitations prevent quantum advantage over classical methods.

Implementation uses fewer qubits than previous quantum algorithms.

Abstract

In this paper, we present an implementation of a Job Selection Problem (JSP) -- a generalization of the well-known Travelling Salesperson Problem (TSP) -- of $N=9$ jobs on its Quadratic Unconstrained Binary Optimization (QUBO) form, using $\mathcal{O}(N)$ qubits on DWave's Advantage$\_$system4.1 quantum annealing device. The best known quantum algorithm for TSP to date uses $\mathcal{O}(N^2)$ qubits. A solution is found using the quantum method. However, since hardware is not yet able to compensate the increase in search-space size, no present overall advantage is achieved when comparing the quantum results with either exhaustive or equiprobably sampled classical solutions of the problem.