U2L3f.txt

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So suppose this were a classical program.
What did we do?
Well, we started, we computed something
in the first register.
We did something, and we computed something
in the second register.
We did something and got a different value
in the first register.
Then, we measured the first register,
and we throw the second register away.

So if we throw the second register away,
because the only information we care about is y.
We don't actually care what f of x is, and in fact,
f of x is equally likely to be all possible f of x's.
Because the probability of seeing y f of x only
depends on y, which means f of x tells us
no information about anything, because all values of f of x
are equally likely.
So classically, if you ran this through an optimizing compiler,
we'll say, well, we compute f of x.
We never use it.
Why bother?

Let's see, am I--

y, yeah, we computed f of x, and we computed this y only
from this x.
So why bother computing f of x?
So this is what an optimizing compiler would
do for a classical program, but now, if you erase f of x,
there is no information about f anywhere.
So this program can't possibly work.
So the reason this works is back action
from f of x to x, when you computed f of x.
Which is, I don't know, I think it's very non-intuitive
when you first look at this kind of stuff,
because everything in quantum mechanics.
If system A affects system B, then system B
affects system A. and if system A system B,
in some basis, system B effect system
A and the conjugate basis.

So if you have optimizing compilers for quantum
computers, they're going to have to behave differently than ones
for classical computers.
So you can't do this.
OK so this is what we get.
We get a y such that y is perpendicular to c,
and we get a random y that is perpendicular to c,
since all possible y's have equal probability.