The First Iteration
A preliminary observation, in parallel with our definition
- ,
is that Uω can be expressed in an alternate way:
- .
To prove this it suffices to check how Uω acts on basis states:
- .
- for all .
The following computations show what happens in the first iteration:
- .
- .
- .
- .
After application of the two operators ( and ), the amplitude of the searched-for element has increased from to .
Read more about this topic: Grover's Algorithm
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