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