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

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

2009-12-24

arxiv.org/abs/0912.4865v2

EPL, 89 (2010) 40004

Physics

Quantum Physics

6 pages, 3 figures

Scientific paper

10.1209/0295-5075/89/40004

We study first-order quantum phase transitions in models where the mean-field traitment is exact, and 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.

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