A Quantum N-Queens Solver

Abstract

The $N$-queens problem is to find the position of $N$ queens on an $N$ by $N$ chess board such that no queens attack each other. The excluded diagonals $N$-queens problem is a variation where queens cannot be placed on some predefined fields along diagonals. This variation is proven NP-complete and the parameter regime to generate hard instances that are intractable with current classical algorithms is known. We propose a special purpose quantum simulator that implements the excluded diagonals $N$-queens completion problem using atoms in an optical lattice and cavity-mediated long-range interactions. Our implementation has no overhead from the embedding allowing to directly probe for a possible quantum advantage in near term devices for optimization problems.