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Quantum Computation and Information pp 19–42Cite as

Query Complexity of Quantum Biased Oracles

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Part of the book series: Topics in Applied Physics ((TAP,volume 102))

Abstract

In this Chapter, our focus is the efficiency of computation with quantum oracles whose answers are correct only with probability 1/2 + ε. In real-world applications, quantum oracles might be realized from quantumization of probabilistic algorithms which are object to error in the success probability. Thus, designing efficient quantum algorithms for biased oracles is important. The first result to discuss such biased oracles was by Adcock and Cleve, who relate the efficiency of computation with biased oracles with the difficulty of inverting one-way functions. They showed a quantum algorithm for solving the so-called Goldreich-Levin problem, a result which has a special implication in the cryptographic setting. In this Chapter, we prove the optimality of their algorithm and show a general method for designing robust algorithms querying biased oracles for solving various problems. The method is optimal in the sense that the additional number of queries to biased oracles matches the lower bounds, which are also part of our results.

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Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Kazuo Iwama & Rudy Raymond

  2. Graduate School of Information Science, Nara Institute of Science and Technology, Nara, 630-0192, Japan

    Shigeru Yamashita

Authors
  1. Kazuo Iwama
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  2. Rudy Raymond
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  3. Shigeru Yamashita
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Editor information

Editors and Affiliations

  1. Graduate School of Information, Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Hiroshi Imai

  2. ERATO Quantum Computation and Information Project, Japan Science and Technology Agency, 201 Daini Hongo White Bldg 5-28-3, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hiroshi Imai  & Masahito Hayashi  & 

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Iwama, K., Raymond, R., Yamashita, S. (2006). Query Complexity of Quantum Biased Oracles. In: Imai, H., Hayashi, M. (eds) Quantum Computation and Information. Topics in Applied Physics, vol 102. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33133-6_2

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