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

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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 Φ 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 Φ for any given \({\Phi\in\left[0,\pi/2\right)}\).

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Authors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Wenliang Jin & Xiangdong Chen

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  1. Wenliang Jin
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  2. Xiangdong Chen
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Correspondence to Wenliang Jin.

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Jin, W., Chen, X. A desired state can not be found with certainty for Grover’s algorithm in a possible three-dimensional complex subspace. Quantum Inf Process 10, 419–429 (2011). https://doi.org/10.1007/s11128-010-0209-7

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  • DOI: https://doi.org/10.1007/s11128-010-0209-7

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