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Quantum Identification of Boolean Oracles

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STACS 2004 (STACS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2996))

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Abstract

The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \(O(\sqrt{N})\) for anyS if |S| = N, which includes the upper bound for the Grover search as a special case. (iii) For a wide range of oracles (|S| = N) such as random oracles and balanced oracles, the query complexity is \(O(\sqrt{N/K})\), where K is a simple parameter determined by S.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia,  

    Andris Ambainis

  2. Quantum Computation and Information, ERATO, Japan Science and Technology Corporation (JST),  

    Kazuo Iwama, Akinori Kawachi, Hiroyuki Masuda & Raymond H. Putra

  3. Graduate School of Informatics, Kyoto University,  

    Kazuo Iwama, Akinori Kawachi, Hiroyuki Masuda & Raymond H. Putra

  4. Graduate School of Information Science, Nara Institute of Science and Technology,  

    Shigeru Yamashita

Authors
  1. Andris Ambainis
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  2. Kazuo Iwama
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  3. Akinori Kawachi
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  4. Hiroyuki Masuda
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  5. Raymond H. Putra
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  6. Shigeru Yamashita
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Editor information

Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIAFA and the University of Paris 7, Denis Diderot,  

    Michel Habib

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© 2004 Springer-Verlag Berlin Heidelberg

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Ambainis, A., Iwama, K., Kawachi, A., Masuda, H., Putra, R.H., Yamashita, S. (2004). Quantum Identification of Boolean Oracles. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_10

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  • DOI: https://doi.org/10.1007/978-3-540-24749-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21236-2

  • Online ISBN: 978-3-540-24749-4

  • eBook Packages: Springer Book Archive

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