Quantum Finite Automata and Weighted Automata

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dc.creatorRao, M. V. Panduranga
dc.creatorVinay, V.
dc.date2007-01-20
dc.date.accessioned2026-07-07T07:42:27Z
dc.date.available2026-07-07T07:42:27Z
dc.descriptionQuantum finite automata derive their strength by exploiting interference in complex valued probability amplitudes. Of particular interest is the 2-way model of Ambainis and Watrous that has both quantum and classical states (2QCFA) [A. Ambainis and J. Watrous, Two-way finite automata with quantum and classical state, Theoretical Computer Science, 287(1), pp. 299-311, 2002], since it combines the advantage of the power of interference in a constant-sized quantum system with a 2-way head. This paper is a step towards finding the least powerful model which is purely classical and can mimic the dynamics of quantum phase. We consider weighted automata with the Cortes-Mohri definition of language recognition [C. Cortes and M. Mohri, Context-Free Recognition with Weighted Automata, Grammars 3(2/3), pp. 133-150, 2000] as a candidate model for simulating 2QCFA. Given any 2QCFA that (i) uses the accept-reject-continue observable, (ii) recognizes a language with one-sided error and (iii) the entries of whose unitary matrices are algebraic complex numbers, we show a method of constructing a weighted automaton over $\mathbb{C}$ that simulates it efficiently.
dc.description10 pages, Preliminary version appears in the Proceedings of ACiD-2005, Texts in Algorithmics series of KCL publications, pp. 123-134, 2005
dc.identifierhttps://arxiv.org/abs/quant-ph/0701144
dc.identifierhttp://arxiv.org/abs/quant-ph/0701144
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122449
dc.subjectQuantum Physics
dc.titleQuantum Finite Automata and Weighted Automata
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