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Combinatorial Framework for Topological Quantum Computing

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Quantum Triangulations

Part of the book series: Lecture Notes in Physics ((LNP,volume 845))

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Abstract

Unlike perturbatively renormalizable quantum field theory—representing the basic tool in the standard model in particle physics, where the physically measurable quantities are obtained as finite limits of infinite series in the physical coupling constant.

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Notes

  1. 1.

    Recall that this scheme is the quantum version of the classical Boolean circuit in which strings written in the basic binary alphabet (0,1) are replaced by collections of ‘qubits’, namely quantum states in \(({\mathbb{C}}^{2})^{\otimes N},\) and the gates are unitary transformations that can be expressed, similarly to what happens in the classical case, as suitable sequences of elementary gates associated with the Boolean logic operations and, or, not.

  2. 2.

    It has been recently proposed to describe topological phases of matter and anyonic-type vertex operators within a Turaev–Viro background [31, 32]. Such a proposal seems quite promising but at present only a few features of this approach have been worked out, so that we have not included it in this monography.

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  1. Annalisa Marzuoli

    Present address: Dipto. di Matematica “F. Casorati”, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy

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  1. Dipto. Fisica Nucleare e Teorica, Istituto Nazionale di Fisica Nucleare e Teorica, Sez. di Pavia, Università degli Studi di Pavia, Via Bassi 6, 27100, Pavia, Italy

    Mauro Carfora & Annalisa Marzuoli

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Carfora, M., Marzuoli, A. (2012). Combinatorial Framework for Topological Quantum Computing. In: Quantum Triangulations. Lecture Notes in Physics, vol 845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24440-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-24440-7_6

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