Quantum search by local adiabatic evolution

Jérémie Roland and Nicolas J. Cerf
Phys. Rev. A 65, 042308 – Published 26 March 2002
PDFExport Citation

Abstract

The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which tends to the solution. We apply this time-dependent Hamiltonian approach to Grover’s problem, i.e., searching a marked item in an unstructured database. We find that by adjusting the evolution rate of the Hamiltonian so as to keep the evolution adiabatic on each infinitesimal time interval, the total running time is of order N, where N is the number of items in the database. We thus recover the advantage of Grover’s standard algorithm as compared to a classical search, scaling as N. This is in contrast with the constant-rate adiabatic approach of Farhi et al. (e-print quant-ph/0001106), where the requirement of adiabaticity is expressed only globally, resulting in a time of order N.

  • Received 24 July 2001

DOI:https://doi.org/10.1103/PhysRevA.65.042308

©2002 American Physical Society

Authors & Affiliations

Jérémie Roland1 and Nicolas J. Cerf1,2

  • 1Ecole Polytechnique, CP 165, Université Libre de Bruxelles, 1050 Brussels, Belgium
  • 2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109

References (Subscription Required)

Click to Expand
Issue

Vol. 65, Iss. 4 — April 2002

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×