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Quantum search by local adiabatic evolution
Open accessAbstract
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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“It is also worth mentioning that we achieved a transfer time faster than that obtained (for Ising coupling) in Ref. [19].”
From Optimal Control at the Quantum Speed Limit (2009) · cites this paper as [19]
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“Interestingly enough, however, our method only uses single-site local pulses while in Ref. [19] this was achieved using global pulses that operate jointly on the whole chain.”
From Optimal Control at the Quantum Speed Limit (2009) · cites this paper as [19]
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Quantum Mechanics Helps in Searching for a Needle in a Haystack
Grover, L. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.325 · Cited by 4,306 · cited 2×
“We therefore recover the advantage of Grover’s usual algorithm compared to a classical search [3].”
BackgroundResultA Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., & Preda, D. (2001) · Science · doi:10.1126/science.1057726 · Cited by 2,056
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Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (2000) · arXiv · doi:10.48550/arxiv.quant-ph/0001106 · Cited by 536
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Cerf, N. J., Grover, L. K., & Williams, C. P. (2000) · Physical Review A · doi:10.1103/physreva.61.032303 · Cited by 115
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- S. L. Braunstein, 2000, Fortschr. Phys., 48, 767
- 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)
- 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
- 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
- green
- arxiv.org
- 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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