Abstract
In this paper, we give the geometric pictures for quantum search algorithms in decomposed form, namely in terms of a phase rotation of the marked state and a phase rotation about the average. We apply this formalism to various quantum search algorithms, and give explicit interpretations of the standard Grover algorithm, arbitrary phase rotations, phase matching and fixed-point search algorithm. The pictures straightforwardly show how state vectors evolve during the search process. These results are helpful in understanding how the quantum search algorithms work.
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Zhao, LJ., Li, YS., Hao, L. et al. Geometric pictures for quantum search algorithms. Quantum Inf Process 11, 325–340 (2012). https://doi.org/10.1007/s11128-011-0249-7
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DOI: https://doi.org/10.1007/s11128-011-0249-7