Complexity of Quantum Uniform and Nonuniform Automata

  • Farid Ablayev
  • Aida Gainutdinova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)


We present two different types of complexity lower bounds for quantum uniform automata (finite automata) and nonuniform automata (OBDDs). We call them “metric” and “entropic” lower bounds in according to proof technique used. We present explicit Boolean functions that show that these lower bounds are tight enough.

We show that when considering “almost all Boolean functions” on n variables our entropic lower bounds gives exponential (2 c(δ)(n − − log n)) lower bound for the width of quantum OBDDs depending on the error δ allowed.

Next we consider “generalized measure-many” quantum automata. It is appeared that for uniform and nonuniform automata (for space restricted models) their measure-once and measure-many models have different computational power.


Boolean Function Unitary Transformation Sink Node Regular Language Quantum Circuit 
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 2005

Authors and Affiliations

  • Farid Ablayev
    • 1
  • Aida Gainutdinova
    • 1
  1. 1.Dept. of Theoretical CyberneticsKazan State UniversityKazanRussia

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