TY - JOUR
T1 - Adiabatic optimization without local minima
JF - Quantum Information and Computation
Y1 - 2015
A1 - Michael Jarret
A1 - Stephen P. Jordan
AB - Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even more basic question of whether adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there are no local energy minima other than the global minimum. Surprisingly, we find a counterexample in which the potential is a single basin on a graph, but the eigenvalue gap is exponentially small as a function of the number of vertices. In this counterexample, the ground state wavefunction consists of two "lobes" separated by a region of exponentially small amplitude. Conversely, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap scales at worst as one over the square of the number of vertices.
VL - 15
U4 - 181-199
UR - http://arxiv.org/abs/1405.7552
CP - 3-4
J1 - Quantum Information and Computation
ER -