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.

Atom-only descriptions of the driven-dissipative Dicke model

“…The ability to describe the dissipative dynamics with an atom-only theory is a crucial step to understand the quantum dynamics in more complicated situations. Specifically, for multimode cavities [4][5][6][7][8][9][10][11][12][13][14], it enables one to adiabatically eliminate the bosonic cavity modes (which massively increases the size of the Hilbert space), and provides a description of the key slow dynamics with only atomic variables. Such a description can then form a basis for numerical methods, such as matrix-product-density-operator [49][50][51], corner-spacerenormalization [52], or cluster expansions [53], to be applied, allowing a full quantum description of the problem.…”

“…For this reason, much theoretical work has been restricted to modelling single-mode cavities [1][2][3], and cases where all atoms behave identically, so that mean-field descriptions can be applied, or permutation symmetry can be exploited. However, to fully explore many body physics one must move beyond mean-field descriptions, and consider multimode optical cavities [4][5][6][7][8][9][10][11][12][13][14]. Modelling such systems beyond a semiclassical approximation is a major challenge.…”

“…These include realization of quantum liquid crystalline states [4,5], simulating dynamical gauge fields and the Meissner effect [15], realization of spin-glass phases [6], and creating of associative memories [7]. Related to this last concept there have also been a number of proposals of information processing using such systems, including proposing alternate routes to realize Hopfield associative memory [10], and to solve specific NP hard problems such as the N -queens problem [12]. Other quantum generalizations of the Hopfield associative memory [16] have also been studied.…”

Emergent Quasicrystalline Symmetry in Light-Induced Quantum Phase Transitions

“…Furthermore, the quantum phase transition to the quasicrystalline and localized states can be attributed to the interplay between two-body contact interaction and cavity-mediated long-range interactions. Therefore, our work demonstrates that cavity QED offers a novel nondemolishing platform [79][80][81][82] for exploring the spontaneous formation and stabilization mechanisms of a quasicrystal at very low temperatures. It opens a new avenue for realizing in state-of-the-art quantum-gas-cavity systems quantum phase transitions which are accompanied by an emergent (C 8 rotational) symmetry.…”

Self-ordering and cavity cooling using a train of ultrashort pulses

“…When several laser frequencies and field modes are simultaneously applied, the corresponding atom-field dynamics gets much more complex. Recently ultracold atomic gases in cavities have been used to simulate or emulate a wide class of other exotic solid state phenomena like edge states, topological insulators or quasi-crystal formation [13,14] or general Hamiltonians for quantum enhanced simulated annealing [15,16]. Using atoms with internal spin, cavity mediated interactions have the potential to implement a large class of lattice spin models [17,18,19,20].…”