A Quantum N-Queens Solver

Valentin Torggler; Philipp Aumann; Helmut Ritsch; Wolfgang Lechner

doi:10.22331/q-2019-06-03-149

A Quantum N-Queens Solver

Valentin Torggler¹, Philipp Aumann¹, Helmut Ritsch¹, and Wolfgang Lechner^1,2

¹Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
²Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria

Published:	2019-06-03, volume 3, page 149
Eprint:	arXiv:1803.00735v3
Doi:	https://doi.org/10.22331/q-2019-06-03-149
Citation:	Quantum 3, 149 (2019).

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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.

Popular summary

Solving puzzles can be a difficult task even for the fastest digital computers. A generic example already studied by the famous mathematician Gauss is the so-called N-queens problem. The task is to find all possibilities to place N queens on an NxN chess board, such that they cannot attack each other according to chess rules. Recently it was shown that variations of the problem with extra constraints are not solvable with classical algorithms within reasonable time.

In the last decades the idea emerged that special purpose quantum computers might find a solution faster. However, whether quantum effects can indeed speed up such calculations is still an open question and thus it is crucial to provide experimental possibilities to gauge an advantages of quantum computing.

In this work we propose a special purpose analog computer serving as a test bed to study speedup for the N-queens problem in the quantum regime. The idea is to build a miniaturized chess board from atoms and light at nearly zero temperature, where the rules of quantum mechanics apply. Ultra-cold atoms moving via quantum tunneling in a lattice created by laser light, take the role of the queens on the chess board. The chess rules are imposed by placing the atoms in an optical resonator and shining in specially structured light. Due to the one-to-one natural design of the experiment there is no overhead in atoms and fairly small system sizes are sufficient to enter the classically intractable regime.

► BibTeX data

@article{Torggler2019quantumnqueens,
  doi = {10.22331/q-2019-06-03-149},
  url = {https://doi.org/10.22331/q-2019-06-03-149},
  title = {A {Q}uantum {N}-{Q}ueens {S}olver},
  author = {Torggler, Valentin and Aumann, Philipp and Ritsch, Helmut and Lechner, Wolfgang},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {149},
  month = jun,
  year = {2019}
}

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[3] Valentin Torggler, Ivor Krešić, Ticijana Ban, and Helmut Ritsch, "Self-ordering and cavity cooling using a train of ultrashort pulses", New Journal of Physics 22 6, 063003 (2020).

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A Quantum N-Queens Solver

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