Size Dependence of the Minimum Excitation Gap in the Quantum Adiabatic Algorithm
Abstract
We study the typical (median) value of the minimum gap in the quantum version of the exact cover problem using quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm for much larger sizes than before. For a range of sizes N≤128, where the classical DavisPutnam algorithm shows exponential median complexity, the quantum adiabatic algorithm shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoidedcrossing point of a LandauZener type (collision between the two lowest energy levels only).
 Publication:

Physical Review Letters
 Pub Date:
 October 2008
 DOI:
 10.1103/PhysRevLett.101.170503
 arXiv:
 arXiv:0803.3971
 Bibcode:
 2008PhRvL.101q0503Y
 Keywords:

 03.67.Ac;
 03.67.Lx;
 75.10.Nr;
 89.70.Eg;
 Quantum algorithms protocols and simulations;
 Quantum computation;
 Spinglass and other random models;
 Computational complexity;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 4 pages, 5 figures