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Quantum search in a possible three-dimensional complex subspace

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Abstract

Suppose we are given an unsorted database with N items and N is sufficiently large. By using a simpler approximate method, we re-derive the approximate formula cos2 Φ, which represents the maximum success probability of Grover’s algorithm corresponding to the case of identical rotation angles \({\phi=\theta}\) for any fixed deflection angle \({\Phi \in\left[0,\pi/2\right)}\). We further show that for any fixed \({\Phi \in\left[0,\pi/2\right)}\), the case of identical rotation angles \({\phi=\theta}\) is energetically favorable compared to the case \({\left|{\theta - \phi}\right|\gg 0}\) for enhancing the probability of measuring a unique desired state.

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

    Wenliang Jin

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  1. Wenliang Jin
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Jin, W. Quantum search in a possible three-dimensional complex subspace. Quantum Inf Process 11, 41–54 (2012). https://doi.org/10.1007/s11128-011-0230-5

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  • DOI: https://doi.org/10.1007/s11128-011-0230-5

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