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Partial adiabatic quantum search algorithm and its extensions

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Abstract

In this paper, we again discuss quantum search by partial adiabatic evolution, which was first proposed by Zhang et al. In contrast to previous conclusions, we show that partial adiabatic search does not improve the time complexity of a local adiabatic algorithm. Firstly, we show a variant of this algorithm and find that it is equivalent to the original partial adiabatic algorithm, in the sense of the same time complexity. But we give two alternate viewpoints on this “new” adiabatic algorithm—“global” adiabatic evolution and local adiabatic evolution approaches, respectively. Then, we discuss how global and local adiabatic quantum search can be recast in the framework of partial adiabatic search algorithm. It is found here that the former two algorithms could be considered as special cases of the later one when appropriately tuning the evolution interval of it. Also this implies the flexibility of quantum search based on partial adiabatic evolution.

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Authors and Affiliations

  1. School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jie Sun, Songfeng Lu & Fang Liu

Authors
  1. Jie Sun
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  2. Songfeng Lu
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  3. Fang Liu
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Corresponding author

Correspondence to Songfeng Lu.

Additional information

The work is supported by the National Natural Science Foundation of China under Grant No. 61173050 and No. U1233119.

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Sun, J., Lu, S. & Liu, F. Partial adiabatic quantum search algorithm and its extensions. Quantum Inf Process 12, 2689–2699 (2013). https://doi.org/10.1007/s11128-013-0557-1

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  • DOI: https://doi.org/10.1007/s11128-013-0557-1

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