Improved Constructions of Quantum Automata

  • Andris Ambainis
  • Nikolajs Nahimovs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5106)


We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use \(\frac{4}{\epsilon} \log 2p + O(1)\) states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of logp than the previously known construction of [2].

Similarly to [2], our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some preliminary results in this direction.


Unitary Transformation Minimal Generator Good Constant Quantum Code Input Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Nikolajs Nahimovs
    • 1
  1. 1.Department of Computer ScienceUniversity of LatviaRigaLatvia

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