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.

Optimization by quantum annealing: Lessons from simple cases / Stella, Lorenzo; Santoro, Giuseppe E.; Tosatti, Erio. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - 72:(2005), pp. 014303.014303-1-014303.014303-15. [10.1103/PhysRevB.72.014303]

Optimization by quantum annealing: Lessons from simple cases

Santoro, Giuseppe E.;Tosatti, Erio
2005-01-01

Abstract

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.
2005
72
014303-1
014303-15
https://arxiv.org/pdf/cond-mat/0502129.pdf
Stella, Lorenzo; Santoro, Giuseppe E.; Tosatti, Erio
File in questo prodotto:
File Dimensione Formato  
Stella_PRB05.pdf

non disponibili

Licenza: Non specificato
Dimensione 916.33 kB
Formato Adobe PDF
916.33 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/16940
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 53
  • ???jsp.display-item.citation.isi??? 43
social impact