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

Abstract

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.

6 pages, 3 figures

References in corpus (4)

• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• Simple Glass Models and their Quantum Annealing
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• The Phase Diagram of the Quantum Curie-Weiss Model

Cited by in corpus (3)

• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Adiabatic Quantum Algorithms for the NP-Complete Maximum-Weight Independent Set, Exact Cover and 3SAT Problems
• Avoid First Order Quantum Phase Transition by Changing Problem Hamiltonians