Quantum Annealing: From Viewpoints of Statistical Physics, Condensed Matter Physics, and Computational Physics

Tanaka, Shu

doi:10.1142/9789814425193_0001

Cited by 3 publications

(2 citation statements)

References 104 publications

(125 reference statements)

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“…Recent experimental studies have suggested that some models with q-fold symmetry breaking in two dimensions do not display the same transition order as the corresponding ferromagnetic q-state Potts model [2][3][4]. Motivated by such discrepancies, Tamura et al investigated an extended Potts model with a number of 'colourless' or 'invisible' states [5][6][7][8]. These redundant states do not contribute to the internal energy of the system, nor do they alter its symmetry or the number of ground states available.…”

Section: Introductionmentioning

confidence: 99%

Potts models with invisible states on general Bethe lattices

Ananikian¹,

Izmailyan²,

Johnston³

et al. 2013

J. Phys. A: Math. Theor.

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Abstract.The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q = 2 case, a Bragg-Williams, mean-field approach necessitates four such invisible states while a 3-regular, random-graph formalism requires seventeen. In both of these cases, the changeover from second-to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent BlumeEmery-Griffiths model.Here we investigate the generalised Potts model on a Bethe lattice with z neighbours. We show that, in the q = 2 case, r c (z) = 4z 3(z − 1)states are required to manifest the equivalent Blume-Emery-Griffiths tricriticality. When z = 3, the 3-regular, random-graph result is recovered, while z → ∞ delivers the Bragg-Williams, mean-field result.arXiv:1307.2803v1 [cond-mat.stat-mech]

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Section: Introductionmentioning

confidence: 99%

Potts models with invisible states on general Bethe lattices

Ananikian¹,

Izmailyan²,

Johnston³

et al. 2013

J. Phys. A: Math. Theor.

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“…Despite its length this review has no pretension of exhaustivity; complementary point of views on the quantum adiabatic algorithm can be found in the reviews [21,22,23,24,50,51,52] and references therein.…”

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confidence: 99%

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

et al. 2013

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Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.

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