Boolean functions with a low polynomial degree and quantum query algorithms

  • Authors:

  • Raitis Ozols;Rūsiņš Freivalds;Jevgeņijs Ivanovs;Elīna Kalniņa;Lelde Lāce;Masahiro Miyakawa;Hisayuki Tatsumi;Daina Taimiņa

  • Affiliations:

  • Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia;Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia;Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia;Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia;Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia;Tsukuba College of Technology, Tsukuba, Ibaraki, Japan;Tsukuba College of Technology, Tsukuba, Ibaraki, Japan;Department of Mathematics, Cornell University, Ithaca, NY

  • Venue:
  • SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

The complexity of quantum query algorithms computing Boolean functions is strongly related to the degree of the algebraic polynomial representing this Boolean function. There are two related difficult open problems. First, Boolean functions are sought for which the complexity of exact quantum query algorithms is essentially less than the complexity of deterministic query algorithms for the same function. Second, Boolean functions are sought for which the degree of the representing polynomial is essentially less than the complexity of deterministic query algorithms. We present in this paper new techniques to solve the second problem.