Quantum Computation of Universal Link Invariants
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In the framework of the spin-network simulator based on the SUq(2) tensor algebra, we implement families of finite state quantum automata capable of accepting the language generated by the braid group, and whose transition amplitudes are coloured Jones polynomials. The automaton calculation of the polynomial of a link L on n strands at any fixed root of unity q is 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 n, on the other.
KeywordsQuantum Computation Transition Rule Braid Group Quantum Algorithm Topological Quantum
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- D. Aharonov, V. Jones and Z. Landau, quant-ph/0511096 (2005).Google Scholar
- J. Yard, P. Wocjan, quant-ph/0603069 (2006).Google Scholar
- S. Garnerone, A. Marzuoli and M. Rasetti, quant-ph/0601169 (2006).Google Scholar
- L.C. Biedenharn and J.D. Louck, The Racah-Wigner Algebra in Quantum Theory (Topic 12. Coupling of N Angular Momenta: Recoupling Theory), Encyclopedia of Mathematics and its Applications, Vol 9, G-C. Rota, ed., Addison-Wesley Publ. Co.,Reading MA, 1981.Google Scholar
- A. N. Kirillov and N. Y. Reshetikhin, Representations of the algebra Uq(sl2), q-orthogonal polynomials and invariants of links, in: Infinite dimensional Lie algebras and groups, V.G. Kac, ed., Adv. Ser. in Math. Phys. 7, World Scientific, Singapore, 1988.Google Scholar