A desired state can not be found with certainty for Grover's algorithm in a possible three-dimensional complex subspace

Authors:
Wenliang Jin;Xiangdong Chen
Affiliations:
School of Information Science and Technology, Southwest Jiaotong University, Chengdu, People's Republic of China 610031;School of Information Science and Technology, Southwest Jiaotong University, Chengdu, People's Republic of China 610031
Venue:
Quantum Information Processing
Year:
2011

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Abstract

Using an accurate method, we prove that no matter what the initial superposition may be, neither a superposition of desired states nor a unique desired state can be found with certainty in a possible three-dimensional complex subspace, provided that the deflection angle 驴 is not exactly equal to zero. By this method, we derive such a result that, if N is sufficiently large (where N denotes the total number of the desired and undesired states in an unsorted database), then corresponding to the case of identical rotation angles, the maximum success probability of finding a unique desired state is approximately equal to cos2 驴 for any given $${\Phi\in\left[0,\pi/2\right)}$$ .