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In this note we use ideas of Farhi, Goldstone, Gosset, Gutmann, Nagaj andShor who link a lower bound on the run time of their quantum adiabatic searchalgorithm to an upper bound on the energy gap above the ground-state of thegenerators of this algorithm. We apply these ideas to the quantum random energymodel (QREM). Our main result is a simple proof of the conjectured exponentialvanishing of the energy gap of the QREM.

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