Implement quantum search and quantum counting algorithms by geometric quantum computation

We derive the matching condition in the SO(3) picture of the generalized Grover's quantum search algorithm. We also give a more concise formula for evaluating the number of the iterations needed in the searching. This will help us a lot in the operation and get the target with certainty easily. We propose a new adiabatic Abelian geometric quantum computation strategy to implement quantum search and quantum counting algorithms based on the non-degenerate energy eigenstates in superconducting phase-qubit systems.