  It is recognized that Grover arrived at his original quantum search algorithm
inspired by his comprehension of the interference of classical waves
originating from an array of antennas. It is also known that quantum-mechanical
characterization of electromagnetic radiation is isomorphic to the treatment of
the orientation of a spin-1/2 particle. In this paper, motivated by Grover's
original intuition and starting from this mathematical equivalence, we present
a quantitative link between the geometry of time-independent optimal-speed
Hamiltonian evolutions on the Bloch sphere and the geometry of
intensity-preserving propagation of light with maximal degree of coherence on
the Poincar\'e sphere. Finally, identifying interference as the fundamental
physical ingredient underlying both physical phenomena, we propose that our
work can provide in retrospect a quantitative geometric background underlying
Grover's powerful intuition.
