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Implications of Quantum Automata for Contextuality

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

Abstract

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.

Keywords

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