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How do I construct a controlled Hadamard gate?

  1. Nov 8, 2017 #1
    1. The problem statement, all variables and given/known data
    I am supposed to construct a controlled Hadamard gate
    using only single qubit and CNOT gates.



    2. Relevant equations

    We know that any arbitrary unitary Operator U can be written as the Martrix product U=AXBXC, where X is the NOT-Matrix and ABC=1 (identity matrix)
    I've already shown that any arbitrary controlled operator can be written as CU=Cphase* (A⊗1)*CNOT*(B⊗1)*CNOT*(C⊗1), with ABC=1

    The other relevant equations are the standard equations from quantum mechanics

    3. The attempt at a solution


    I've tried everything, LU-Decomposition, QR, Diagonalization etc. I've read something about Sine-Cosine-Decomposition, I think this might be the right direction.

    I've also read something about Lie-Groups, though unfortunately, the Hadamard gate is not part of SO(2), only of O(2), there's way more explanation on the generators of SO (2), especially SU (2), and unfortunately I don't know that much about group theory.

     
    Last edited by a moderator: Nov 9, 2017
  2. jcsd
  3. Nov 14, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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