Beichl, I.
, Bullock, S.
and Song, D.
(2007),
A Quantum Algorithm Detecting Concentrated Maps, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150002
(Accessed October 15, 2025)
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A Quantum Algorithm Detecting Concentrated Maps
Published
Author(s)
, ,
Abstract
We consider an arbitrary mapping for , some number of quantum bits. Using calls to a classical oracle evaluating and an classical bit data store, it is possible to determine whether is one-to-one. For some radian angle , we say is -concentrated iff for some fixed and any . This manuscript presents a quantum algorithm that distinguishes a -concentrated from a one-to-one in calls to a quantum oracle function with high probability. For rad., the quantum algorithm outperforms a classical analog on average, with maximal outperformance at rad. Thus, the constructions generalize Deutsch¿s algorithm, in that quantum outperformance is robust for (slightly) nonconstant .Citation
Journal of Research (NIST JRES) - Research
Report Number
Research
Volume
112
Issue
6
NIST Pub Series
Pub Type
NIST Pubs
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Keywords
Deutsch's algorithm, quantum computation
Citation
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Created October 31, 2007, Updated October 12, 2021