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Quantum Counterfeit Coin Problems

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Algorithms and Computation (ISAAC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6506))

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Abstract

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only “balanced” or “tilted” information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the number of weighings). In this paper, we study the quantum query complexity for this problem. Let Q(k,N) be the quantum query complexity of finding all k false coins from the N given coins. We show that for any k and N such that k < N/2, Q(k,N) = O(k 1/4), contrasting with the classical query complexity, Ω(klog(N/k)), that depends on N. So our quantum algorithm achieves a quartic speed-up for this problem. We do not have a matching lower bound, but we show some evidence that the upper bound is tight: any algorithm, including our algorithm, that satisfies certain properties needs Ω(k 1/4) queries.

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Author information

Authors and Affiliations

  1. School of Informatics, Kyoto University, Japan

    Kazuo Iwama & Junichi Teruyama

  2. School of Science, Osaka Prefecture University, Japan

    Harumichi Nishimura

  3. IBM Research, Tokyo, Japan

    Rudy Raymond

Authors
  1. Kazuo Iwama
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  2. Harumichi Nishimura
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  3. Rudy Raymond
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  4. Junichi Teruyama
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Editor information

Editors and Affiliations

  1. Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea

    Otfried Cheong  & Kyung-Yong Chwa  & 

  2. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

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Iwama, K., Nishimura, H., Raymond, R., Teruyama, J. (2010). Quantum Counterfeit Coin Problems. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17517-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-17517-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17516-9

  • Online ISBN: 978-3-642-17517-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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