Quantum automata and quantum grammars
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
On the diameter of the rotation graph of binary coupling trees
Discrete Mathematics
Two-way finite automata with quantum and classical states
Theoretical Computer Science - Natural computing
Approximate Counting and Quantum Computation
Combinatorics, Probability and Computing
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Quantum Information & Computation
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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.