vault backup: 2026-08-05 10:32:02

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+Another well known quantum algorithm for searching.
+Takes a function $f : \{0,1\}^n \rightarrow \{0,1\}$ where f(x) = 1 for exactly one x. 
+The goal is to find x.
+
+New gates: $V_f$ and FLIP$_*$ 
+
+$\ket{*}$ denotes the superposition over al classical possibilities.
+
+### Oracle $V_f$
+
+![[Pasted image 20260805102238.png]]
+
+We use the Unitary $U_f$ as previously defined to construct $V_f$
+
+![[Pasted image 20260805102605.png]]
+
+
+### FLIP$_*$
+
+We first need FLIP$_0$ defined as follows:
+![[Pasted image 20260805102659.png]]
+
+This is implemented via this circuit:
+
+![[Pasted image 20260805102717.png]]
+
+Z is a Pauli matrix and the empty circles denote negative control wires.
+So Z is only applied if all other wires are $\ket{0}$ 
+