More general quantum search algorithm Q = -I gamma VI tau U and the precise formula for the amplitude and the non-symmetric effects of different rotating angles

This Letter presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise for mula for the amplitude in the desired state. A mathematical proof of Grover algorithm being optimal among the algorithms with arbitrary phase rotation s was given in this Letter. This first reported the non-symmetric effects o f different rotating angles, and gave the first-order approximate phase con dition when rotating angles are different. (C) 2001 Elsevier Science B.V. A ll rights reserved.