Geometric pictures for quantum search algorithms

Authors:
Lian-Jie Zhao;Yan-Song Li;Liang Hao;Tao Zhou;Gui Lu Long
Affiliations:
Key Laboratory for Atomic and Molecular Nanosciences and Department of Physics, Tsinghua University, Beijing, China 100084;Key Laboratory for Atomic and Molecular Nanosciences and Department of Physics, Tsinghua University, Beijing, China 100084;Key Laboratory for Atomic and Molecular Nanosciences and Department of Physics, Tsinghua University, Beijing, China 100084;Key Laboratory for Atomic and Molecular Nanosciences and Department of Physics, Tsinghua University, Beijing, China 100084;Key Laboratory for Atomic and Molecular Nanosciences and Department of Physics, Tsinghua University, Beijing, China 100084 and Tsinghua National Laboratory for Information Science and Technology, ...
Venue:
Quantum Information Processing
Year:
2012

Citing 1
Cited 1

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Physics Letters A

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Quantum Information Processing

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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.