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
Famous quotes containing the words the first:
“Behind every individual closes organization; before him opens liberty,—the Better, the Best. The first and worse races are dead. The second and imperfect races are dying out, or remain for the maturing of the higher. In the latest race, in man, every generosity, every new perception, the love and praise he extorts from his fellows, are certificates of advance out of fate into freedom.”
—Ralph Waldo Emerson (1803–1882)