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Title: Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.
Authors:
;  [1]
  1. Zentrum Mathematik, TU M√ľnchen, Boltzmannstr. 3, 85747 Garching (Germany)
Publication Date:
OSTI Identifier:
22479556
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ENERGY GAP; GROUND STATES; QUANTUM COMPUTERS; RANDOMNESS