Fixed-Point Quantum Search with an Optimal Number of Queries
Name
PhysRevLett.113.210501.pdf
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259.15 KB
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Adobe PDF
Checksum (MD5)
79a5e23652300c5118aabcecec0022a6
Author(s)
Low, Guang Hao
Yoder, Theodore James
Chuang, Isaac L.
Date Issued
November 2014
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Yoder, Theodore J., Guang Hao Low, Isaac L. Chuang. "Fixed-point quantum search with an optimal number of queries." Phys. Rev. Lett. 113, 210501 (November 2014). © 2014 American Physical Society
Version
Final published version
Abstract
Grover’s quantum search and its generalization, quantum amplitude amplification, provide a quadratic advantage over classical algorithms for a diverse set of tasks but are tricky to use without knowing beforehand what fraction λ of the initial state is comprised of the target states. In contrast, fixed-point search algorithms need only a reliable lower bound on this fraction but, as a consequence, lose the very quadratic advantage that makes Grover’s algorithm so appealing. Here we provide the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup. Our result incorporates an adjustable bound on the failure probability and, for a given number of oracle queries, guarantees that this bound is satisfied over the broadest possible range of λ.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.113.210501
