A Quantum N-Queens Solver

TL;DR

This paper introduces a quantum simulator for the NP-complete excluded diagonals N-queens problem, enabling direct testing of quantum advantage in solving complex optimization problems with atoms in optical lattices.

Contribution

It presents a specialized quantum simulator using atoms in optical lattices to directly implement the excluded diagonals N-queens problem without embedding overhead.

Findings

Proposes a quantum simulator for a hard NP-complete problem.

Enables direct testing of quantum advantage in near-term devices.

Utilizes cavity-mediated long-range interactions in optical lattices.

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.