Implications of Quantum Automata for Contextuality

  • Jibran Rashid
  • Abuzer Yakaryılmaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8587)


We construct zero-error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded-error probabilistic finite automata (PFAs). Here is a summary of our results:

  1. 1

    There is a promise problem solvable by an exact two-way QFA in exponential expected time, but not by any bounded-error sublogarithmic space probabilistic Turing machines.

  2. 2

    There is a promise problem solvable by a Las Vegas realtime QFA, but not by any bounded-error realtime PFA. The same problem can be solvable by an exact two-way QFA in linear expected time but not by any exact two-way PFA.

  3. 3

    There is a family of promise problems such that each promise problem can be solvable by a two-state exact realtime QFAs, but, there is no such bound on the number of states of realtime bounded-error PFAs solving the members of this family.


Our results imply that there exist zero-error quantum computational devices with a single qubit of memory that cannot be simulated by any finite memory classical computational model. This provides a computational perspective on results regarding ontological theories of quantum mechanics [20,28]. As a consequence we find that classical automata based simulation models [24,6] are not sufficiently powerful to simulate quantum contextuality. We conclude by highlighting the interplay between results from automata models and their application to developing a general framework for quantum contextuality.


Physical Review Letter Input String Single Qubit Hide Variable Model Promise Problem 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jibran Rashid
    • 1
  • Abuzer Yakaryılmaz
    • 2
    • 3
  1. 1.Facoltà di InformaticaUniversità della Svizzera ItalianaLuganoSwitzerland
  2. 2.Faculty of ComputingUniversity of LatviaRīgaLatvia
  3. 3.National Laboratory for Scientific ComputingPetrópolisBrazil

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