Lets say I have the following quantum state:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{1}{\sqrt{2}}[/itex][itex]\left| 000\right\rangle[/itex] + [itex]\frac{1}{\sqrt{2}}[/itex][itex]\left| 111\right\rangle[/itex]

And that I apply a Hadamard gate to each of these qubits (H[1,2,3]).

The math shows that the resulting state will be:

[itex]\frac{1}{2}[/itex][itex]\left| 000\right\rangle[/itex] + [itex]\frac{1}{2}[/itex][itex]\left| 010\right\rangle[/itex] + [itex]\frac{1}{2}[/itex][itex]\left| 101\right\rangle[/itex] + [itex]\frac{1}{2}[/itex][itex]\left| 111\right\rangle[/itex]

I know how to do the math to get to the result, but i don't understand the logical reason why a [itex]\left| 000\right\rangle[/itex] and [itex]\left| 111\right\rangle[/itex] combined state generate that result. If anyone could help me understand why this happens i would appreciate it.

Thanks in advance

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# Understanding Hadamard Gates on Quantum Circuits

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