What is ZX applied to H|0?

Question

What is ZX applied to H|0>?

turingtest · Answer

$$|0\rangle=\binom 10$$$$X=\left(\begin{matrix}0&1\1&0\end{matrix}\right)$$do the multiplication first, and tell me what you get

anonymous · Answer

the result is a 2*1 matrix the upper portion is 0, the lower portion is 1

turingtest · Answer

and what do we call that in bra-ket notation ?

anonymous · Answer

0|0> +1|1> ???

turingtest · Answer

yes, or just |1>
now apply$$Z=\begin{pmatrix}
1 &0 \0 
 &-1 
\end{pmatrix}$$to$$|1\rangle=\binom01$$

anonymous · Answer

-|1>

turingtest · Answer

yes

turingtest · Answer

congrads :)

anonymous · Answer

I should write something like that ; x|0>+y|1> as an answer. I am writing 0 for x , -1 for y and system says that it is wrong... ??

anonymous · Answer

And remember problem has H before |0>... Is it change anything?

turingtest · Answer

oh crap, I forgot the Hadamard, my mistake :P

turingtest · Answer

so then, what is$$H=\frac1{\sqrt2}\begin{pmatrix}
1 &1 \1 
 &-1 
\end{pmatrix}$$mapped to |0> ?

turingtest · Answer

Happy to help, I hope we can work together sometimes on this stuff, it's new to me too :)