  We study the eigenlevel spectrum of quantum adiabatic algorithm for
3-satisfiability problem, focusing on single-solution instances. The properties
of the ground state and the associated gap, crucial for determining the running
time of the algorithm, are found to be far from the predictions of random
matrix theory. The distribution of gaps between the ground and the first
excited state shows an abundance of small gaps. Eigenstates from the central
part of the spectrum are, on the other hand, well described by random matrix
theory.

Quantum Physics