Understanding X Quantum Gate: Act on |i> State?

[markoX]

Hi everybody ...
One of the one-qbit simple quantum gate is X which defined by:

X: |0> ----- |1>
|1> ----- |0>

but how does this gate ( unitary operator ) act on |i> state? (i=0 or 1)
I mean at first we have to measure what state is ( 0 or 1) and so flip them but after we know the state, it will calapse to |0> or |1>.
so X|i>=|-i> is not correct according what I said.

 

[Hurkyl]

I mean at first we have to measure what state is ( 0 or 1)

No! Quantum gates aren't measurements^* -- they are, as you said, linear operators. So the transformation of a linear combination of basis states is the linear combination of transformed basis states.

(I'm not sure what you mean by the |i> state, can you elaborate? I worry that you have a wrong idea in your head about qubits...)


*: at least not in the sense you're thinking. But that's quite another topic.

 

[markoX]

yes,I know what you are saying but how does this linear operator made in real quantum computer?

as I learned a qbit is linear combination of two basis like a|0> + b|1> ( |a|^2 + |b|^2 = 1 ).

I can not understand differen between linear operator and measurment as you said?