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Exact quantum algorithms for the leader election problem
 In Proceedings of the TwentySecond Symposium on Theoretical Aspects of Computer Science (STACS 2005), volume 3404 of Lecture Notes in Computer Science
, 2005
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Quantum automata, braid group and link polynomials
"... The spin–network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah–Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite–states and ..."
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Cited by 11 (4 self)
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The spin–network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah–Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite–states and discrete–time quantum automata capable of accepting the language generated by the braid group, and whose transition amplitudes are colored Jones polynomials. The automaton calculation of the polynomial of (the plat closure of) a link L on 2N strands at any fixed root of unity is shown to be bounded from above by a linear function of the number of crossings of the link, on the one hand, and polynomially bounded in terms of the braid index 2N, on the other. The growth rate of the time complexity function in terms of the integer k appearing in the root of unity q can be estimated to be (polynomially) bounded by resorting to the field theoretical background given by the Chern–Simons theory. Key words: link invariants; braid group representations; Chern–Simons theory; quantum automata; Racah–Wigner algebra; spin–network simulator; topological quantum computation; Uq(su(2)) representation theory. 1 1
An application of quantum finite automata to interactive proof systems
 in Proc. 9th International Conference on Implementation and Application of Automata, LNCS, Vol.3317
, 2004
"... Abstract: Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finitedimensional quantum memory space. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover commun ..."
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Cited by 9 (2 self)
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Abstract: Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finitedimensional quantum memory space. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover communicates with a quantumautomaton verifier through a common communication cell. Our quantum interactive proof systems are juxtaposed to DworkStockmeyer’s classical interactive proof systems whose verifiers are twoway probabilistic automata. We demonstrate strengths and weaknesses of our systems and further study how various restrictions on the behaviors of quantumautomaton verifiers affect the power of quantum interactive proof systems.
Succinctness of twoway probabilistic and quantum finite automata
, 2009
"... We prove that two–way probabilistic and quantum finite automata (2PFA’s and 2QFA’s) can be considerably more concise than both their one–way versions (1PFA’s and 1QFA’s), and two–way nondeterministic automata (2NFA’s). For this purpose, we demonstrate several infinite families of regular languages ..."
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We prove that two–way probabilistic and quantum finite automata (2PFA’s and 2QFA’s) can be considerably more concise than both their one–way versions (1PFA’s and 1QFA’s), and two–way nondeterministic automata (2NFA’s). For this purpose, we demonstrate several infinite families of regular languages which can be recognized with some fixed probability greater than 1 2 by just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with a constant number of states, whereas the sizes of the corresponding 1PFA’s, 1QFA’s and 2NFA’s grow without bound. We also show that 2QFA’s with mixed states can support highly efficient probability amplification. The effects of enhancing several finite automaton models with the capability of restarting the computation from the beginning of the tape are examined.