(adsbygoogle = window.adsbygoogle || []).push({}); 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* (AâŠ—1)*CNOT*(BâŠ—1)*CNOT*(CâŠ—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.

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# Homework Help: How do I construct a controlled Hadamard gate?

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