  Quantum search/amplitude amplification algorithms are designed to be able to
amplify the amplitude in the target state linearly with the number of
operations. Since the probability is the square of the amplitude, this results
in the success probability rising quadratically with the number of operations.
This paper presents a new kind of quantum search algorithm in which the
amplitude of the target state, itself increases quadratically with the number
of operations. However, the domain of applications of this is much more limited
than standard amplitude amplification.

Quantum Physics