Automata and Quantum Computing

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Ambainis, Andris ; Yakaryılmaz, Abuzer (2015)
  • Subject: Computer Science - Computational Complexity | Computer Science - Formal Languages and Automata Theory | 68Q10, 68Q12, 68Q15, 68Q19, 68Q45 | Quantum Physics
    acm: TheoryofComputation_GENERAL | TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES | TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES | ComputerSystemsOrganization_MISCELLANEOUS
    arxiv: Computer Science::Formal Languages and Automata Theory

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity
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