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AN EFFICIENT QUANTUM ALGORITHM FOR COLORED JONES POLYNOMIALS

Dipartimento di Fisica, and Scuola di Dottorato, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

ISI Foundation, Viale Settimio Severo 65, 10133 Torino, Italy

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SILVANO GARNERONE

Université Pierre et Marie Curie — Paris VI, LPTHE CNRS 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France

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ANNALISA MARZUOLI

Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, and INFN, Sezione di Pavia, Via A. Bassi 6, 27100 Pavia, Italy

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https://doi.org/10.1142/S0219749908004092Cited by:1 (Source: Crossref)

Abstract

We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. The construction exploits the q-deformed spin network as computational background. The complexity of such algorithm is bounded above linearly by the number of crossings of the link, and polynomially by the number of link strands.

Keywords:

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