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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Jin, W.L., Chen, X.D.: A desired state can not be found with certainty for Grover’s algorithm in a possible three-dimensional complex subspace. Quantum Inf. Process. doi:10.1007/s11128-010-0209-7, Online First (2010)
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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