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Computing Boolean Functions via Quantum Hashing

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Book cover Computing with New Resources

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8808))

Abstract

In this paper we show a computational aspect of the quantum hashing technique. In particular we apply it for computing Boolean functions in the model of read-once quantum branching programs based on the properties of specific polynomial presentation of those functions.

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References

  1. Ablayev, F.M., Vasiliev, A.V.: Cryptographic quantum hashing. Laser Physics Letters 11(2), 025202 (2014). http://stacks.iop.org/1612-202X/11/i=2/a=025202

  2. Ablayev, F., Andrianov, S., Moiseev, S., Vasiliev, A.: Encoded universality of quantum computations on the multi-atomic ensembles in the qed cavity. Tech. Rep. arXiv:1109.0291 [quant-ph]. Cornell University Library (September 2011). http://arxiv.org/abs/1109.0291

  3. Ablayev, F., Gainutdinova, A., Karpinski, M.: On Computational Power of Quantum Branching Programs. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 59–70. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Ablayev, F., Gainutdinova, A., Karpinski, M., Moore, C., Pollett, C.: On the computational power of probabilistic and quantum branching programs of constant width. Information and Computation 203, 145–162 (2005). http://dx.doi.org/10.1016/j.ic.2005.04.003

  5. Ablayev, F., Vasiliev, A.: Algorithms for quantum branching programs based on fingerprinting. Electronic Proceedings in Theoretical Computer Science 9, 1–11 (2009). http://arxiv.org/abs/0911.2317

  6. Ablayev, F., Andrianov, S., Moiseev, S., Vasiliev, A.: Quantum computer with atomic logical qubits encoded on macroscopic three-level systems in common quantum electrodynamic cavity. Lobachevskii Journal of Mathematics 34(4), 291–303 (2013). http://dx.doi.org/10.1134/S1995080213040094

  7. Agrawal, V., Lee, D., Wozniakowski, H.: Numerical computation of characteristic polynomials of boolean functions and its applications. Numerical Algorithms 17, 261–278 (1998). http://dx.doi.org/10.1023/A:1016632423579

  8. Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87(16), 167902 (2001). www.arXiv.org/quant-ph/0102001v1

  9. Deutsch, D.: Quantum computational networks. Royal Society of London Proceedings Series A 425, 73–90 (1989). http://dx.doi.org/10.1098/rspa.1989.0099

  10. Gottesman, D., Chuang, I.: Quantum digital signatures. Tech. Rep. arXiv:quant-ph/0105032. Cornell University Library (November 2001). http://arxiv.org/abs/quant-ph/0105032

  11. Jain, J., Abraham, J.A., Bitner, J., Fussell, D.S.: Probabilistic verification of boolean functions. Formal Methods in System Design 1, 61–115 (1992)

    Article  MATH  Google Scholar 

  12. Nakanishi, M., Hamaguchi, K., Kashiwabara, T.: Ordered Quantum Branching Programs Are More Powerful than Ordered Probabilistic Branching Programs under a Bounded-Width Restriction. In: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, pp. 467–476. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Razborov, A.A., Szemeredi, E., Wigderson, A.: Constructing small sets that are uniform in arithmetic progressions. Combinatorics, Probability & Computing 2, 513–518 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sauerhoff, M., Sieling, D.: Quantum branching programs and space-bounded nonuniform quantum complexity. Theoretical Computer Science 334(1–3), 177–225 (2005). http://arxiv.org/abs/quant-ph/0403164

  15. Wegener, I.: Branching Programs and Binary Decision Diagrams. SIAM Monographs on Discrete Mathematics and Applications. SIAM Press (2000)

    Google Scholar 

  16. de Wolf, R.: Quantum Computing and Communication Complexity. Ph.D. thesis, University of Amsterdam (2001)

    Google Scholar 

  17. Yao, A.C.C.: Quantum circuit complexity. In: Proceedings of Thirty-fourth IEEE Symposium on Foundations of Computer Science, pp. 352–361. IEEE Computer Society, Palo Alto (1993)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Kazan Federal University, Kazan, Russian Federation

    Farid Ablayev & Alexander Vasiliev

Authors
  1. Farid Ablayev
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  2. Alexander Vasiliev
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Corresponding author

Correspondence to Farid Ablayev .

Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Latvia, Riga, Latvia

    Rūsiņš Freivalds

  3. School of Informatics, Kyoto University, Kyoto, Japan

    Iwama Kazuo

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Ablayev, F., Vasiliev, A. (2014). Computing Boolean Functions via Quantum Hashing. In: Calude, C., Freivalds, R., Kazuo, I. (eds) Computing with New Resources. Lecture Notes in Computer Science(), vol 8808. Springer, Cham. https://doi.org/10.1007/978-3-319-13350-8_11

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  • DOI: https://doi.org/10.1007/978-3-319-13350-8_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13349-2

  • Online ISBN: 978-3-319-13350-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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