dorsal/arxiv
View SchemaComputing Spin Networks
| Authors | Annalisa Marzuoli, Mario Rasetti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410105 |
| URL | https://arxiv.org/abs/quant-ph/0410105 |
| DOI | 10.1016/j.aop.2005.01.005 |
| Journal | Annals of Physics 318 (2005) 345-407 |
Abstract
We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum information manipulation is based on the (re)coupling theory of SU(2) angular momenta. Such scheme automatically incorporates all the essential features that make quantum information encoding much more efficient than classical: it is fully discrete; it deals with inherently entangled states, naturally endowed with a tensor product structure; it allows for generic encoding patterns. The model proposed can be thought of as the non-Boolean generalization of the quantum circuit model, with unitary gates expressed in terms of 3nj coefficients connecting inequivalent binary coupling schemes of n+1 angular momentum variables, as well as Wigner rotations in the eigenspace of the total angular momentum. A crucial role is played by elementary j-gates (6j symbols) which satisfy algebraic identities that make the structure of the model similar to "state sum models", employed in discretizing Topological Quantum Field Theories and quantum gravity. The spin network simulator can thus be viewed also as a Combinatorial QFT model for computation. The semiclassical limit (large j's) is discussed.
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"abstract": "We expand a set of notions recently introduced providing the general setting\nfor a universal representation of the quantum structure on which quantum\ninformation stands. The dynamical evolution process associated with generic\nquantum information manipulation is based on the (re)coupling theory of SU(2)\nangular momenta. Such scheme automatically incorporates all the essential\nfeatures that make quantum information encoding much more efficient than\nclassical: it is fully discrete; it deals with inherently entangled states,\nnaturally endowed with a tensor product structure; it allows for generic\nencoding patterns. The model proposed can be thought of as the non-Boolean\ngeneralization of the quantum circuit model, with unitary gates expressed in\nterms of 3nj coefficients connecting inequivalent binary coupling schemes of\nn+1 angular momentum variables, as well as Wigner rotations in the eigenspace\nof the total angular momentum. A crucial role is played by elementary j-gates\n(6j symbols) which satisfy algebraic identities that make the structure of the\nmodel similar to \"state sum models\", employed in discretizing Topological\nQuantum Field Theories and quantum gravity. The spin network simulator can thus\nbe viewed also as a Combinatorial QFT model for computation. The semiclassical\nlimit (large j\u0027s) is discussed.",
"arxiv_id": "quant-ph/0410105",
"authors": [
"Annalisa Marzuoli",
"Mario Rasetti"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2005.01.005",
"journal_ref": "Annals of Physics 318 (2005) 345-407",
"title": "Computing Spin Networks",
"url": "https://arxiv.org/abs/quant-ph/0410105"
},
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