  Grover's Search algorithm was a breakthrough at the time it was introduced,
and its underlying procedure of amplitude amplification has been a building
block of many other algorithms and patterns for extracting information encoded
in quantum states. In this paper, we introduce an optimization of the
inversion-by-the-mean step of the algorithm. This optimization serves two
purposes: from a practical perspective, it can lead to a performance
improvement; from a theoretical one, it leads to a novel interpretation of the
actual nature of this step. This step is a reflection, which is realized by (a)
cancelling the superposition of a general state to revert to the original
all-zeros state, (b) flipping the sign of the amplitude of the all-zeros state,
and finally (c) reverting back to the superposition state. Rather than
canceling the superposition, our approach allows for going forward to another
state that makes the reflection easier. We validate our approach on set and
array search, and confirm our results experimentally on real quantum hardware.
