816 research outputs found
Quantum Pushdown Automata
Quantum finite automata, as well as quantum pushdown automata (QPA) were
first introduced by C. Moore and J. P. Crutchfield. In this paper we introduce
the notion of QPA in a non-equivalent way, including unitarity criteria, by
using the definition of quantum finite automata of Kondacs and Watrous. It is
established that the unitarity criteria of QPA are not equivalent to the
corresponding unitarity criteria of quantum Turing machines. We show that QPA
can recognize every regular language. Finally we present some simple languages
recognized by QPA, not recognizable by deterministic pushdown automata.Comment: Conference SOFSEM 2000, extended version of the pape
Unbounded-error quantum computation with small space bounds
We prove the following facts about the language recognition power of quantum
Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more
powerful than probabilistic Turing machines for any common space bound
satisfying . For "one-way" Turing machines, where the
input tape head is not allowed to move left, the above result holds for
. We also give a characterization for the class of languages
recognized with unbounded error by real-time quantum finite automata (QFAs)
with restricted measurements. It turns out that these automata are equal in
power to their probabilistic counterparts, and this fact does not change when
the QFA model is augmented to allow general measurements and mixed states.
Unlike the case with classical finite automata, when the QFA tape head is
allowed to remain stationary in some steps, more languages become recognizable.
We define and use a QTM model that generalizes the other variants introduced
earlier in the study of quantum space complexity.Comment: A preliminary version of this paper appeared in the Proceedings of
the Fourth International Computer Science Symposium in Russia, pages
356--367, 200
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