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Cited by 633Quantum Computing Algorithms and ArchitectureQuantum Mechanics and ApplicationsQuantum Information and Cryptography

The DOI matches its Crossref record; 8 of the 9 references it cites were found in a registry or an index.

Quantum search by local adiabatic evolution

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Roland, Jérémie, Cerf, Nicolas J.·2002·Physical Review A
DOI 10.1103/physreva.65.042308
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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 $\sqrt{N},$ 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.

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Research works printed but not linked: 2

  1. S. L. Braunstein, 2000, Fortschr. Phys., 48, 767
  2. N. J. Cerf, 2000, Phys. Rev. A, 61, 032

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Metadata

Authors
Roland, J., & Cerf, N. J.
Affiliations
  • Université Libre de Bruxelles (BE)
  • California Institute of Technology (US)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2002-03-26
Volume
65
Issue
4
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.65.042308
OpenAlex
W2155521441
Cited by
629
References
9
Citations by year
2026: 29 · 2025: 50 · 2024: 35 · 2023: 26 · 2022: 43 · 2021: 35 · 2020: 34 · 2019: 44 · 2018: 28 · 2017: 16 · 2016: 28 · 2015: 24 · 2014: 30 · 2013: 17 · 2012: 26
FWCI
13.10
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
Keywords
quantum search, adiabatic quantum computation, Grover's algorithm, unstructured database search, time-dependent Hamiltonian, adiabaticity, evolutionary rates, ground state, quantum algorithms

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