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


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.


quantum information matrix image quantum boolean function projective matrix 

2000 MR Subject Classification

15A90 05B20 


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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

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