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SS2026/Quantum Computing/12. Grover's Algorithm/Grover's Algorithm.md

@@ -38,4 +38,20 @@ Now we define the unitary FLIP$_*$:
 
 The algorithm works as follows:
 1. $\ket{0}$ on every qubit.
-2. 
+2. Superposition over all entries via H which results in the quantum state $\ket{*}$
+3. Apply unitary $V_f$
+4. Apply unitary FLIP$_*$
+5. Repeat 3 and 4 t times
+6. Measure.
+
+How does this work?:
+We want the algorithm to terminate in $\ket{x_0}$
+First, we bring the system into uniform superposition $\ket{*}$
+We know that $\ket{x_0}$ is part of the superposition so we can rewrite as follows:
+
+![[Pasted image 20260805110521.png]]
+
+![[Pasted image 20260805110633.png]]
+![[Pasted image 20260805110641.png]]
+![[Pasted image 20260805110648.png]]
+