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Probabilistic implementation of universal Hadamard and Unitary gates

Wei Song·Ming Yang·Zhuo-Liang Cao
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Abstract

We show that the Hadamard and Unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set $A = {{| {Ψ_i} > ,| {\bar Ψ_i} >}}({i = 1,2})$ if and only if $| {Ψ_1} > ,| {Ψ_2} > ,| {\bar Ψ_1} > ,| {\bar Ψ_2} >$ are linearly independent. We also derive the best transformation efficiencies.

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Wei Song, Ming Yang, Zhuo-Liang Cao. 2004-09-02. Probabilistic implementation of universal Hadamard and Unitary gates. https://doi.org/10.1016/j.physleta.2004.07.060

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