Quantum automata and quantum grammars
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Quantum computation and quantum information
Quantum computation and quantum information
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
Two-way finite automata with quantum and classical states
Theoretical Computer Science - Natural computing
Exact results for accepting probabilities of quantum automata
Theoretical Computer Science - Mathematical foundations of computer science
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
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Quantum 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 (2002) 1, 299-311], 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 (2000) 2/3, 133-150] 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 C that simulates it efficiently.