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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“Show me a man who has acted, and who has not been the victim and slave of his action. What they have done commits and enforces them to do the same again. The first act, which was to be an experiment, becomes a sacrament.”
—Ralph Waldo Emerson (1803–1882)