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)


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.


Boolean Function Regular Language Pure Quantum State Symmetric Boolean Function Quantum Part 
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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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