12:59 PM
Greetings y'all. I'm currently cramming for an exam around the basics of quantum computing and I am running into an issue with my intution around function descriptions.
Currently I am revising the grover algorithm (or to be specific the prerequisite of it) where an indicator function is applied to an equally likely superposition of register states.
So given an indicator function $f(x) = 1 \leftrightarrow x = x*$ the associated oracle is defined as $U_f: |x, y\rangle \mapsto |x, y \oplus f(x) \rangle$
The lecture notes continue stating that $U_f((\frac{1}{\sqrt{N}}\sum\limits_{x=0}^{N-1} |x\rangle) \otimes \frac{1}{\sqrt{2}}(|0\rangle - |1\rangle))$ will equal $\frac{1}{\sqrt{N}}(-|x*\rangle + \sum\limits_{x=0, x \neq x*}^{N - 1} |x\rangle) \otimes \frac{1}{\sqrt{2}}(|0\rangle - |1\rangle)$, i.e. leaves the register y unaltered.
I mechanically validated that, but it feels incredibly wrong to me that the computaton description alters register y (and not register x), but the opposite of that actually happens.
Is there maybe a more intuitive way to think about applying operations to quantum registers like that?
