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    Quantum circuits with uniformly controlled one-qubit gates

    Ville Bergholm*, Juha J. Vartiainen, Mikko Möttönen, and Martti M. Salomaa

    • Materials Physics Laboratory, POB 2200 (Technical Physics) FIN-02015 HUT, Helsinki University of Technology, Finland

    • *Electronic address: vberghol@focus.hut.fi

    Phys. Rev. A 71, 052330 – Published 27 May, 2005

    DOI: https://doi.org/10.1103/PhysRevA.71.052330

    Abstract

    Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2n−1−1 controlled-NOT gates, 2n−1 one-qubit gates, and a single diagonal n-qubit gate. To illustrate the versatility of these gates we then apply them to the decomposition of a general n-qubit gate and a state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.

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