Hello all,
I have a question about the c-not operation in quantum physics.
Suppose the first qubit is represented by the amplitudes (a11, a12),
and the second qubit by (a21, a22). For a two-qubit system, the matrix
to perform a C-NOT looks like this:
[1 0 0 0] [a11] [a11]
|0 1 0 0| x |a12| = |a12|
|0 0 0 1| |a21| |a22|
[0 0 1 0] [a22] [a21]
My question is: C-NOT invloves an "if" as in: if the control bit (a11,
a12) is 1, then swap the two amplitude values of the second bit,
otherwise leave them as they are. Is this the correct understanding? It
seems that a21 and a22 are swapped anyway, no matter what is in a11 and
a12. So where is the "if" in the C-NOT matrix? How did they derive the
C-NOT matrix? All books I've read skip this part.
Thanks for any help, or mention of a book or webpage where this point
is explained.
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