Complex matter field universal models with optimal scaling for solving combinatorial optimization problems

TL;DR

This paper introduces a universal complex matter field model that optimally maps NP-hard combinatorial problems into spin Hamiltonian minimization, significantly improving global minimum search efficiency and avoiding local minima.

Contribution

The authors propose a novel complex matter field-based model that provides optimal problem mappings and enhances solution search for combinatorial optimization.

Findings

Significant improvement in global minimum search efficiency.

Explicit mappings for graph coloring, TSP, and N-queens.

Amplitude dynamics escape from local minima.

Abstract

We develop a universal model based on the classical complex matter fields that allow the optimal mapping of many real-life NP-hard combinatorial optimisation problems into the problem of minimising a spin Hamiltonian. We explicitly formulate one-to-one mapping for three famous problems: graph colouring, the travelling salesman, and the modular N-queens problem. We show that such a formulation allows for several orders of magnitude improvement in the search for the global minimum compared to the standard Ising formulation. At the same time, the amplitude dynamics escape from the local minima.