Anderson localization makes adiabatic quantum optimization fail
Abstract
Understanding NPcomplete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NPcomplete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps between the ground and excited states of the quantum computer's Hamiltonian. We show that the statistics of the gaps can be analyzed in a novel way, borrowed from the study of quantum disordered systems in statistical mechanics. It turns out that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NPcomplete problems. This implies that unfortunately, adiabatic quantum optimization fails: The system gets trapped in one of the numerous local minima.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 July 2010
 DOI:
 10.1073/pnas.1002116107
 arXiv:
 arXiv:0912.0746
 Bibcode:
 2010PNAS..10712446A
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Computer Science  Computational Complexity
 EPrint:
 14 pages, 4 figures