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arXiv · 1412.8342

Exponential vanishing of the ground-state gap of the QREM via adiabatic quantum computing

Juan Adame·Simone Warzel
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Abstract

In this note we use ideas of Farhi, Goldstone, Gosset, Gutmann, Nagaj and Shor 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.

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Juan Adame, Simone Warzel. 2014-12-29. Exponential vanishing of the ground-state gap of the QREM via adiabatic quantum computing. https://arxiv.org/abs/1412.8342

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