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Optimality of partial adiabatic search and its circuit model

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Abstract

In this paper, we first uncover a fact that a partial adiabatic quantum search with \(O(\sqrt{N/M})\) time complexity is in fact optimal, in which \(N\) is the total number of elements in an unstructured database, and \(M\)(\(M\ge 1\)) of them are the marked ones(one) \((N\gg M)\). We then discuss how to implement a partial adiabatic search algorithm on the quantum circuit model. From the implementing procedure on the circuit model, we can find out that the approximating steps needed are always in the same order of the time complexity of the adiabatic algorithm.

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Acknowledgments

We gratefully acknowledge the support of the National Natural Science Foundation of China under Grant No. 61173050. The second author also gratefully acknowledge the support of the China Postdoctoral Science Foundation under Grant No 2014M552041.

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Authors and Affiliations

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

    Ying Mei, Jie Sun & Songfeng Lu

  2. Department of Information Technology, Vaasa University of Applied Sciences, Wolffintie 30, 65200 , Vaasa, Finland

    Chao Gao

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  1. Ying Mei
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  2. Jie Sun
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  3. Songfeng Lu
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  4. Chao Gao
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Correspondence to Songfeng Lu.

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Mei, Y., Sun, J., Lu, S. et al. Optimality of partial adiabatic search and its circuit model. Quantum Inf Process 13, 1751–1763 (2014). https://doi.org/10.1007/s11128-014-0770-6

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  • DOI: https://doi.org/10.1007/s11128-014-0770-6

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