3 ms·
Its not two paths to state |0>. Its one path to 1/sqrt(2)|0> and one to -1/sqrt(2)|0> and those cancel out. If you start at |0> and do a 45 degree rotation you
by ufo 12y ago
Its not two paths to state |0>. Its one path to 1/sqrt(2)|0> and one to -1/sqrt(2)|0> and those cancel out.
If you start at |0> and do a 45 degree rotation you end up at (|0> + |1>)/sqrt(2). If you start at |1> and do a 45 degree rotation you end up on (-|0> + |1>)/sqrt(2) (note that the coefficient on the |0> is negative now).
Now the trick is that rotations are a linear transformation so rotate(a(x+y)) = a(rotate(x) + rotate(y)). In our case, when we rotate |0> twice, we first end up at (|0> + |1>)/sqrt(2), then we can use linearity to split that into a |0> and a |1> component, rotate them individually and then add up the the results. When we rotate the |0> component we get a +|0> and when we rotate the |1> we get a -|0> and those cancel out (destructive interference).