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• W2164423904 abstract "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 $ s $ satisfying $ s(n)=o(log log n) $. For one-way Turing machines, where the input tape head is not allowed to move left, the above result holds for $s(n)=o(log n) $. 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." @default.
• W2164423904 created "2016-06-24" @default.
• W2164423904 creator A5002142749 @default.
• W2164423904 creator A5060493020 @default.
• W2164423904 date "2010-07-21" @default.
• W2164423904 modified "2023-10-16" @default.
• W2164423904 title "Unbounded-error quantum computation with small space bounds" @default.
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• W2164423904 doi "https://doi.org/10.1016/j.ic.2011.01.008" @default.
• W2164423904 hasPublicationYear "2010" @default.
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