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 13, 2025)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
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
Download Paper
Keywords
Deutsch's algorithm, quantum computation
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact [email protected].
Created October 31, 2007, Updated October 12, 2021