Quantum Information Processing

, Volume 11, Issue 1, pp 41–54 | Cite as

Quantum search in a possible three-dimensional complex subspace



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.


Grover’s search algorithm Identical rotation angles Deflection angle Three-dimensional complex subspace 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.School of Information Science and TechnologySouthwest Jiaotong UniversityChengduPeople’s Republic of China

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