dorsal/arxiv
View SchemaEfficient quantum processing of 3-manifold topological invariants
| Authors | Silvano Garnerone, Annalisa Marzuoli, Mario Rasetti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703037 |
| URL | https://arxiv.org/abs/quant-ph/0703037 |
| Journal | Adv.Theor.Math.Phys.13:6,2009 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
A quantum algorithm for approximating efficiently 3--manifold topological invariants in the framework of SU(2) Chern-Simons-Witten (CSW) topological quantum field theory at finite values of the coupling constant k is provided. The model of computation adopted is the q-deformed spin network model viewed as a quantum recognizer in the sense of Wiesner and Crutchfield, where each basic unitary transition function can be efficiently processed by a standard quantum circuit. This achievement is an extension of the algorithm for approximating polynomial invariants of colored oriented links found in Refs 2,3. Thus all the significant quantities - partition functions and observables - of quantum CSW theory can be processed efficiently on a quantum computer, reflecting the intrinsic, field-theoretic solvability of such theory at finite k. The paper is supplemented by a critical overview of the basic conceptual tools underlying the construction of quantum invariants of links and 3-manifolds and connections with algorithmic questions that arise in geometry and quantum gravity models are discussed.
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"abstract": "A quantum algorithm for approximating efficiently 3--manifold topological\ninvariants in the framework of SU(2) Chern-Simons-Witten (CSW) topological\nquantum field theory at finite values of the coupling constant k is provided.\nThe model of computation adopted is the q-deformed spin network model viewed as\na quantum recognizer in the sense of Wiesner and Crutchfield, where each basic\nunitary transition function can be efficiently processed by a standard quantum\ncircuit.\n This achievement is an extension of the algorithm for approximating\npolynomial invariants of colored oriented links found in Refs 2,3. Thus all the\nsignificant quantities - partition functions and observables - of quantum CSW\ntheory can be processed efficiently on a quantum computer, reflecting the\nintrinsic, field-theoretic solvability of such theory at finite k.\n The paper is supplemented by a critical overview of the basic conceptual\ntools underlying the construction of quantum invariants of links and\n3-manifolds and connections with algorithmic questions that arise in geometry\nand quantum gravity models are discussed.",
"arxiv_id": "quant-ph/0703037",
"authors": [
"Silvano Garnerone",
"Annalisa Marzuoli",
"Mario Rasetti"
],
"categories": [
"quant-ph",
"gr-qc"
],
"journal_ref": "Adv.Theor.Math.Phys.13:6,2009",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Efficient quantum processing of 3-manifold topological invariants",
"url": "https://arxiv.org/abs/quant-ph/0703037"
},
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