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

J. Adame, S. Warzel

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Abstract

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.

Original languageEnglish
Article number113301
JournalJournal of Mathematical Physics
Volume56
Issue number11
DOIs
StatePublished - 1 Nov 2015

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