Many-Qudit Representation for the Travelling Salesman Problem Optimisation

We present a map from the travelling salesman problem (TSP), prototypical NP-complete combinatorial optimisation task, to ground state associated with system of many-qudits. Conventionally, TSP is cast into quadratic unconstrained binary (QUBO) problem, that can be solved on an Ising machine. The size corresponding physical system's Hilbert space $2^{N^2}$, where $N$ number cities considered in TSP. Our proposal provides many-qudit dimension $2^{N\log_2N}$, which considerably smaller than resulting usual QUBO map. This reduction yield significant speedup quantum and classical computers. simulate validate our using variational Monte Carlo neural state, solving linear layout for up almost 100 cities.