2010/07/31 by Abuzer Yakaryılmaz, Abuzer Yakaryilmaz, A. C. Cem Say +1 · 3 citations
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #cs.CC #quant-ph
paper · pdf · doi:10.1016/j.ic.2011.01.008
published as Information and Computation, Volume 209, Issue 6, June 2011, Pages 873-892 · A preliminary version of this paper appeared in the Proceedings of the Fourth International Computer Science Symposium in Russia, pages 356--367, 2009
arxiv created 2011/02/10 · openalex publication_date 2011/02/19 · crossref created 2011/02/19 · crossref issued 2011/06/01 · crossref published 2011/06/01 · crossref published-print 2011/06/01 · arxiv updated 2014/01/29 · openalex created_date 2016/06/24 · crossref deposited 2021/11/19 · crossref indexed 2026/03/01 · openalex updated_date 2026/08/02
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.