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On Computational Power of Quantum Branching Programs

  • Farid Ablayev
  • Aida Gainutdinova
  • Marek Karpinski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2138)

Abstract

In this paper we introduce a model of a Quantum Branching Program (QBP) and study its computational power. We define several natural restrictions of a general QBP model, such as a read-once and a read-k-times QBP, noting that obliviousness is inherent in a quantum nature of such programs.

In particular we show that any Boolean function can be computed deterministically (exactly) by a read-once QBP in width O(2n), contrary to the analogous situation for quantum finite automata. Further we display certain symmetric Boolean function which is computable by a read-once QBP with O(logn) width, which requires a width Ω(n) on any deterministic read-once BP and (classical) randomized read-once BP with permanent transitions in each levels.

We present a general lower bound for the width of read-once QBPs, showing that the upper bound for the considered symmetric function is almost tight.

Keywords

Boolean Function Regular Language Pure Quantum State Symmetric Boolean Function Quantum Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Farid Ablayev
    • 1
    • 2
  • Aida Gainutdinova
    • 1
    • 2
  • Marek Karpinski
    • 1
    • 2
  1. 1.Dept. of Theoretical Cybernetics of Kazan State UniversityKazanRussia
  2. 2.Dept. of Computer ScienceUniversity of BonnBonn

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