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

Natalia G. Berloff
2022 arXiv   pre-print
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
more » ... standard Ising formulation. At the same time, the amplitude dynamics escape from the local minima.
arXiv:2201.10595v1 fatcat:irpcg3mvcfh7fk3ryjlun6bj6e