We investigate the basic behavior and performance of simulated quantum annealing (QA) in comparison with classical annealing (CA). Three simple one-dimensional case study systems are considered: namely, a parabolic well, a double well, and a curved washboard. The time-dependent Schrodinger evolution in either real or imaginary time describing QA is contrasted with the Fokker-Planck evolution of CA. The asymptotic decrease of excess energy with annealing time is studied in each case, and the reasons for differences are examined and discussed. The Huse-Fisher classical power law of double-well CA is replaced with a different power law in QA. The multiwell washboard problem studied in CA by Shinomoto and Kabashima and leading classically to a logarithmic annealing even in the absence of disorder turns to a power-law behavior when annealed with QA. The crucial role of disorder and localization is briefly discussed.
|Titolo:||Optimization by quantum annealing: Lessons from simple cases|
|Autori:||LORENZO STELLA; GIUSEPPE E. SANTORO; ERIO TOSATTI|
|Rivista:||PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS|
|Data di pubblicazione:||2005|
|Digital Object Identifier (DOI):||10.1103/PhysRevB.72.014303|
|Appare nelle tipologie:||1.1 Journal article|