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Polynomial Time Quantum Algorithm for Search Problem and Its Application

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Quantum Interaction (QI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8369))

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Abstract

The well known quantum algorithm for search problem is Grover’s one. However, its computational complexity is not a polynomial in the input. In this study, we propose a polynomial time quantum algorithm for it based on quantum binary search and an amplification process. This process can be written as a quantum Turing machine form, a so called generalized quantum Turing machine (GQTM). We introduce the definition of GQTM and its language classes.

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References

  1. Levin, L.A.: Universal sequential search problems. Probl. Inf. Transm. 9(3), 265–266 (1973)

    Google Scholar 

  2. Levin, L.A.: Randomness conservation inequalities: information and independence in mathematical theories. Inf. Control 61, 15–37 (1984)

    Article  MATH  Google Scholar 

  3. Solomonoff, R.J.: Optimum sequential search. Memorandum, Oxbridge Research, Cambridge (1984)

    Google Scholar 

  4. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science. IEEE Press, Los Alamitos (1994)

    Google Scholar 

  5. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing, p. 212 (1996)

    Google Scholar 

  6. Ohya, M., Volovich, I.V.: New quantum algorithm for studying NP-complete problems. Rep. Math. Phys. 52(1), 25–33 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ohya, M., Volovich, I.V.: Quantum computing and chaotic amplifier. J. Opt. B 5(6), 639–642 (2003)

    Article  MathSciNet  Google Scholar 

  8. Ohya, M., Volovich, I.V.: Mathematical Foundation of Quantum Information and Quantum Computation. Springer, New York (2011)

    Google Scholar 

  9. Iriyama, S., Ohya, M.: Language classes defined by generalized quantum turing machine. Open Syst. Inf. Dyn. 15(4), 383–396 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Iriyama, S., Ohya, M., Volovich, I.V.: Generalized quantum turing machine and its application to the SAT chaos algorithm. QP-PQ:Quantum Prob. White Noise Anal., Quantum Information and Computing, vol. 19, pp. 204–225. World Scientific Publishing, Singapore (2006)

    Google Scholar 

  11. Iriyama, S., Ohya, M., Volovich, I.V.: On quantum algorithm for binary search and its computational complexity. TUS preprint (2012)

    Google Scholar 

  12. Goto, K., Iriyama, S., Ohya, M., Volovich, I.V.: On quantum algorithm of prime factoring using quantum binary search. TUS preprint (2012)

    Google Scholar 

  13. Iriyama, S., Ohya, M., Volovich, I.V.: On computational complexity of shor’s quantum factoring algorithm. TUS preprint (2012)

    Google Scholar 

  14. Iriyama, S., Ohya, M.: On semigroup dynaical representation of non-linear chaos dynamics (in preparation)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Tokyo University of Science, 2641 Yamazaki, Noda City, Chiba, Japan

    Satoshi Iriyama & Masanori Ohya

Authors
  1. Satoshi Iriyama
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  2. Masanori Ohya
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Corresponding author

Correspondence to Satoshi Iriyama .

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Editors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Harald Atmanspacher

  2. School of Management, University of Leicester, Leicester, United Kingdom

    Emmanuel Haven

  3. Queensland University of Technology, Brisbane, Queensland, Australia

    Kirsty Kitto

  4. Department of Physics and Astronomy Centre for Interdisciplinary Science, University of Leicester, Leicester, United Kingdom

    Derek Raine

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Iriyama, S., Ohya, M. (2014). Polynomial Time Quantum Algorithm for Search Problem and Its Application. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-54943-4_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54942-7

  • Online ISBN: 978-3-642-54943-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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