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Quantum circuits synthesis using Householder transformations

Abstract : The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We provide a two-step algorithm: during the rst step we exploit the speci c structure of a quantum operator to compute its QR factorization, then the factorized matrix is used to produce a quantum circuit. We analyze several costs (circuit size and computational time) and compare them to existing techniques from the literature. For a nal quantum circuit twice as large as the one obtained by the best existing method, we accelerate the computation by orders of magnitude.
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Submitted on : Thursday, April 16, 2020 - 5:53:37 PM
Last modification on : Sunday, June 26, 2022 - 2:48:51 AM

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Timothée Goubault de Brugière, Marc Baboulin, Benoît Valiron, Cyril Allouche. Quantum circuits synthesis using Householder transformations. Computer Physics Communications, Elsevier, 2020, 248, pp.107001. ⟨10.1016/j.cpc.2019.107001⟩. ⟨hal-02545123⟩

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