Quantum hobbit routing: Annealer implementation of generalized Travelling Salesperson Problem
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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 $\mathrm{O}(N)$ 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.