Skip to main content
Springer Nature Link
Log in

An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation

  • Conference paper
Mathematical Foundations of Computer Science 2004 (MFCS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3153))

Abstract

This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem, which is a natural generalization of the ordered search problem. Apart from much studied polynomial and adversary methods for quantum query complexity lower bounds, our argument shows that the multiple-block ordered search needs a large number of nonadaptive oracle queries on a black-box model of quantum computation that is also supplemented with advice. Our argument is also applied to the notions of computational complexity theory: quantum truth-table reducibility and quantum truth-table autoreducibility.

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Adleman, L.M., DeMarrais, J., Huang, M.A.: Quantum computability. SIAM J. Comput. 26, 1524–1540 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ambainis, A.: A better lower bound for quantum algorithms searching an ordered list. In: Proc. 40th FOCS, pp. 352–357 (1999)

    Google Scholar 

  3. Ambainis, A.: Quantum lower bounds by quantum arguments. J. Comput. System Sci. 64, 750–767 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ambainis, A.: Polynomial degree vs. quantum query complexity. In: Proc. 44th FOCS, pp. 230–240 (2003)

    Google Scholar 

  5. Barnum, H., Saks, M., Szegedy, M.: Quantum query complexity and semidefinite programming. In: Proc. 18th CCC, pp. 179–193 (2003)

    Google Scholar 

  6. Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. J. ACM 48, 778–797 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Beigel, R., Feigenbaum, J.: On being incoherent without being very hard. Comput. Complex. 2, 1–17 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26, 1510–1523 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Blum, M., Kannan, S.: Designing programs that check their work. In: Proc. 21st STOC, pp. 86–97 (1989)

    Google Scholar 

  10. Buhrman, H., van Dam, W.: Bounded quantum query complexity. In: Proc. 14th CCC, pp. 149–157 (1999)

    Google Scholar 

  11. Buhrman, H., de Wolf, R.: A lower bound of quantum search for an ordered list. Inform. Process. Lett. 70, 205–209 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: A limit on the speed of quantum computation for insertion into an ordered list, See ArXiv quant-ph/9812057

    Google Scholar 

  13. Feigenbaum, J., Fortnow, L., Laplante, S., Naik, A.: On coherence, random-selfreducibility, and self-correction. Comput. Complex. 7, 174–191 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Høyer, P., Neerbek, J., Shi, Y.: Quantum lower bound of ordered searching, sorting, and element distinctness. Algorithmica 34, 429–448 (2002)

    Article  MathSciNet  Google Scholar 

  15. Laplante, S., Magniez, F.: Lower bounds for randomized and quantum query complexity using Kolmogorov arguments. To appear in Proc. 19th CCC (2004)

    Google Scholar 

  16. Nishimura, H., Yamakami, T.: Polynomial time quantum computation with advice. Inform. Process. Lett. 90, 195–204 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Trakhtenbrot, B.: On autoreducibility. Doklady Akad. Nauk. SSSR 192, 1224–1227 (1970), English translation in Soviet Math. Dokl. 11, 814–817 (1970)

    Google Scholar 

  18. Yamakami, T.: Analysis of quantum functions. International Journal of Foundations of Computer Science 14, 815–852 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Program, Trent University, Peterborough, Ontario, Canada, K9J 7B8

    Harumichi Nishimura & Tomoyuki Yamakami

Authors
  1. Harumichi Nishimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomoyuki Yamakami
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science and Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Jiří Fiala  & Jan Kratochvíl  & 

  2. Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranske nam. 25, 118 00, Praha1, Czech Republic

    Václav Koubek

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nishimura, H., Yamakami, T. (2004). An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_65

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-28629-5_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22823-3

  • Online ISBN: 978-3-540-28629-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics