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EPL Association, European Physical Society Letters, 4(89), p. 40004

DOI: 10.1209/0295-5075/89/40004

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Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve

Journal article published in 2009 by T. Jorg, F. Krzakala ORCID, J. Kurchan, A. C. Maggs, J. Pujos
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This paper is available in a repository.

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Abstract

We study first-order quantum phase transitions in models where the mean-field treatment is exact, and in particular the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing. Copyright (C) EPLA, 2010