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.
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