Advertisement

Acta Mathematicae Applicatae Sinica, English Series

, Volume 31, Issue 4, pp 1013–1020 | Cite as

Construction of a class of quantum Boolean functions based on the Hadamard matrix

  • Jiao DuEmail author
  • Shan-qi Pang
  • Qiao-yan Wen
  • Jie Zhang
Article
  • 73 Downloads

Abstract

In this study, a new methodology based on the Hadamard matrix is proposed to construct quantum Boolean functions f such that \(f = {I_{{2^n}}} - 2{P_{{2^n}}}\), where \({I_{{2^n}}}\) is an identity matrix of order 2 n and \({P_{{2^n}}}\) is a projective matrix with the same order as \({I_{{2^n}}}\). The enumeration of this class of quantum Boolean functions is also presented.

Keywords

quantum information matrix image quantum boolean function projective matrix 

2000 MR Subject Classification

15A90 05B20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ashley, Montanaro, Tobias J.O. Quantum Boolean functions. Chicago Journal of Theoretical Computer Science, 2010: 1–45(2010), DOI: 10.4086/cjtcs.2010.001, http://cjtcs.cs.uchicago.eduGoogle Scholar
  2. [2]
    Cusick, T.W., Stanica, P. Cryptographic Boolean Functions and Applications, the First Edition. Academic Press, San Diego, 2009Google Scholar
  3. [3]
    MacWilliams, F.J., Sloane, N.J.A. The theory of Error-Correcting Codes. North-Holland, Amsterdam, New York, Oxford, 1978Google Scholar
  4. [4]
    Menezes, A.J., Oorschot, P.C., Vanstone, S.A. Handbook of applied cryptography, CRC Press, Boca Raton, Florida, 1996CrossRefGoogle Scholar
  5. [5]
    Michael A. N., Chuang, I.L. Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000. MR,1, 796–805zbMATHGoogle Scholar
  6. [6]
    Pang, S.Q., Zhang, Y.S., Liu, S.Y. Further results on the orthogonal arrays obtained by generalized Hadamard product. Statistics Probability Letters, 68: 17–25 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Reichardt, B.W. Span programs and quantum query complexity: The general adversary bound is nearly tight for every Boolean function. proceedings of 50th Annual IEEE Symposium on Foundations of Computer Science: 544–551, 2009Google Scholar
  8. [8]
    Wen Q.Y., Niu, X.X., Yang, Y.X. The Boolean Functions in Modern cryptology. Science Press, Beijing, 2000 (in Chinese)Google Scholar
  9. [9]
    Zhang J., Wen, Q.Y. Construction of quantum Boolean functions. The 2010 6th International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2010, Chengdu, China: 1–3Google Scholar
  10. [10]
    Zhang, X.D. Matrix analysis and applications, the First Edition. Tsinghua University Press, Beijing, 2004 (in Chinese)Google Scholar
  11. [11]
    Zhang, Y.S., Li, W.G., Mao, S.S., Zheng, Z.G. A simple method for constructing orthogonal arrays by the kronecker sum. Journal of System Science and Complexity, 19: 266–273 (2006)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jiao Du
    • 1
    • 2
    Email author
  • Shan-qi Pang
    • 1
    • 2
  • Qiao-yan Wen
    • 3
  • Jie Zhang
    • 4
  1. 1.College of Mathematics and Information ScienceHenan Normal UniversityXinxiangChina
  2. 2.Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal ControlHenan Normal UniversityXinxiangChina
  3. 3.State Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijingChina
  4. 4.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina

Personalised recommendations