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 language | English |
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Article number | 113301 |
Journal | Journal of Mathematical Physics |
Volume | 56 |
Issue number | 11 |
DOIs | |
State | Published - 1 Nov 2015 |