Geometric Analysis of Grover's Search Algorithm in the Presence of Perturbation
Wenliang Jin · viXra · 2013
"For an initial uniform superposition over all pos- sible computational basis states, we explore the perfor- mance of Grover’s search algorithm geometrically when imposing a perturbation on the Walsh-Hadamard trans- formation contained in the Grover iteration. We give the geometric picture to visualize the quantum search process in the three-dimensional space and show that Grover’s search algorithm can work well with an appropriately chosen per- turbation. Thereby we corroborate Grover’s conclusion that if the perturbation is small, then it will have little impact on the implementation of this algorithm. We also prove that Grover’s path cannot achieve a geodesic under a perturba- tion of the Fubini-Study metric."