Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:gr-qc/0511161 · Journal of Physics Conference Series

Spin networks, quantum automata and link invariants

Silvano Garnerone, Annalisa Marzuoli, Mario Rasetti

Published Mar 1, 2006• 5 citations
arXivHTMLPDF

Abstract

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU (2) Racah-Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states-quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern-Simons field theory.

DOI
10.1088/1742-6596/33/1/009

Related papers

Spin networks, quantum automata and link invariants

Garnerone, S., Marzuoli, A., Mario Rasetti +1 more

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU(2) Racah–Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states– quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern–Simons field theory. 1 1

•Jan 1, 2005•8 citations

Quantum automata, braid group and link polynomials

Silvano Garnerone, Annalisa Marzuoli, Mario Rasetti

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.

arXiv:quant-ph/0601169•Quantum Information and Computation•Jul 1, 2007•35 citations

SPIN NETWORK SETTING OF TOPOLOGICAL QUANTUM COMPUTATION

Annalisa Marzuoli, Mario Rasetti

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU (2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.

International Journal of Quantum Information•Dec 16, 2004•16 citations

Quantum automata, braid group and link polynomials

GarneroneSilvano, MarzuoliAnnalisa, RasettiMario

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...

Quantum Information and Computation•Jul 1, 2007•0 citations

Quantum Computation of Universal Link Invariants

Silvano Garnerone, Annalisa Marzuoli, Mario Rasetti

In the framework of the spin-network simulator based on the SU q(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.

Open Systems & Information Dynamics•Nov 13, 2006•10 citations

Spin network setting of topological quantum computation

Annalisa Marzuoli, Mario Rasetti

The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU(2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.

arXiv:quant-ph/0407119•Jul 15, 2004•0 citations
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU (2) Racah-Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states-quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern-Simons field theory.
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU(2) Racah–Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states– quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern–Simons field theory. 1 1
The spin--network quantum simulator model, which essentially encodes the (quantum deformed) SU(2)SU(2)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 LLL on 2N2N2N 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 2N2N2N, on the other. The growth rate of the time complexity function in terms of the integer kkk appearing in the root of unity qqq can be estimated to be (polynomially) bounded by resorting to the field theoretical background given by the Chern--Simons theory.
In the framework of the spin-network simulator based on the SU q(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.