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Analytic methods in quantum computing

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Abstract

Here we consider a model of quantum computation, based on the monodromy representation of a Fuchsian system. The rôle of local and entangling operators in monodromic quantum computing is played by monodromy matrices of connections with logarithmic singularities acting on the fiber of a holomorphic vector bundle as on the space of qubits. The leading theme is the problem of constructing a set of universal gates as monodromy operators induced from a connection with logarithmic singularity. In the formal scheme developed by us, already known models — topological and holonomic — can be incorporated.

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  1. Institute of Cybernetics, Georgian Academy of Sciences, Tbilisi, Georgia

    G. Giorgadze

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 44, Quantum Computing, 2007.

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Giorgadze, G. Analytic methods in quantum computing. J Math Sci 153, 70–119 (2008). https://doi.org/10.1007/s10958-008-9121-4

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