# Quantum search in a possible three-dimensional complex subspace

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantum search in a possible three-dimensional complex subspace

, Volume 11 (1) – Feb 11, 2011
14 pages

/lp/springer_journal/quantum-search-in-a-possible-three-dimensional-complex-subspace-sqMVW0RQpo
Publisher
Springer Journals
Subject
Physics; Computer Science, general; Theoretical, Mathematical and Computational Physics; Quantum Physics; Mathematics, general; Physics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0230-5
Publisher site
See Article on Publisher Site

### 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 11, 2011

### References

• Experimental NMR realization of a generalized quantum search algorithm
Long, G.L.; Yan, H.Y.; Li, Y.S.; Tu, C.C.; Tao, J.X.; Chen, H.M.; Liu, M.L.; Zhang, X.; Luo, J.; Xiao, L.; Zeng, X.Z.

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