Quantum Algorithms Related to \(\textit{HN}\)-Transforms of Boolean Functions

  • Sugata GangopadhyayEmail author
  • Subhamoy Maitra
  • Nishant Sinha
  • Pantelimon Stănică
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10194)


\(\textit{HN}\)-transforms, which have been proposed as generalizations of Hadamard transforms, are constructed by tensoring Hadamard and nega-Hadamard kernels in any order. We show that all the \(2^n\) possible \(\textit{HN}\)-spectra of a Boolean function in n variables, each containing \(2^n\) elements (i.e., in total \(2^{2n}\) values in transformed domain) can be computed in \(O(2^{2n})\) time (more specific with little less than \(2^{2n+1}\) arithmetic operations). We propose a generalization of Deutsch-Jozsa algorithm, by employing \(\textit{HN}\)-transforms, which can be used to distinguish different classes of Boolean functions over and above what is possible by the traditional Deutsch-Jozsa algorithm.


Boolean function \(\textit{HN}\)-transform, Deutsch-Jozsa algorithm 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sugata Gangopadhyay
    • 1
    Email author
  • Subhamoy Maitra
    • 2
  • Nishant Sinha
    • 1
  • Pantelimon Stănică
    • 3
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Applied Statistics UnitIndian Statistical InstituteKolkataIndia
  3. 3.Department of Applied MathematicsNaval Postgraduate SchoolMontereyUSA

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