Adiabatic optimization without local minima

Published

March 1, 2015

Author(s)

Stephen P. Jordan, Michael Jarret

Abstract

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. On the other hand, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap can be at worst polynomially small.

Citation

Quantum Information & Computation

Volume

14

Issue

3/4

Pub Type

Journals

Keywords

quantum algorithm, adiabatic, computational complexity

Citation

Jordan, S. and Jarret, M. (2015), Adiabatic optimization without local minima, Quantum Information & Computation (Accessed July 1, 2025)