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.
Highlights
Quantum technology with its current rapid advances in number, quality and controllability of quantum bits is approaching a new era with computational quantum advantage for numerical tasks in reach [1,2,3,4,5,6,7,8,9,10,11]
Following Ref. [1], we identify a combination of several unique features of the proposed model that makes it a viable candidate to test quantum advantage in near term devices. (a) The completion and excluded diagonals problem is proven to be NP-complete and hard instances for the excluded diagonals variant are known from computer science literature [30], (b) the problem maps naturally to the available toolbox of atoms in cavities and can be implemented without intermediate embedding and no qubit overhead, (c) the verification is computationally simple and (d) the number of qubits required to solve problems which are hard for classical computers (N > 21 for the solvers used in Ref. [30]) is available in the lab
In our model implementation the non-local qubit interactions are mediated via the field modes of an optical resonator, which will attain non-classical atom-field superposition states during the parameter sweep. This appears to be an essential asset of the system as we find that the ground-state is reached only with a very low probability, when the full quantum dynamics of the fields is replaced by a classical mean-field approximation
Summary
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
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