Many-Qudit representation for the Travelling Salesman Problem Optimisation

Abstract

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 manyqudit system with a Hilbert space of dimension 2 N log 2 N , 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.

Noise Improvements in Quantum Simulations of sQED using Qutrits

“…Much work has been done on qubit based hardware since it is what is most widely available, however recent studies have shown that qudit (d-state quantum objects) based algorithms are frequently more efficient for quantum computing [50,[79][80][81][82][83][84][85][86][87]. In addition there have been recent proof of principle implementations of qutrits [88][89][90][91][92][93][94][95] and cavity QED for qubit-qudit couplings [96][97][98][99][100][101][102].…”