First-order transitions and the performance of quantum algorithms in random optimization problems
Disordered Systems and Neural Networks
2010-05-24 v2 Statistical Mechanics
Computational Complexity
Quantum Physics
Abstract
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase transition. We provide evidence that the gap vanishes exponentially with the system size at the transition. This indicates that the Quantum Adiabatic Algorithm requires a time growing exponentially with system size to find the ground state of this problem.
Cite
@article{arxiv.0911.3438,
title = {First-order transitions and the performance of quantum algorithms in random optimization problems},
author = {T. Jorg and F. Krzakala and G. Semerjian and F. Zamponi},
journal= {arXiv preprint arXiv:0911.3438},
year = {2010}
}
Comments
4 pages, 4 figures; final version accepted on Phys.Rev.Lett