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Quantum Walks with Memory Provided by Parity of Memory

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Abstract

Quantum walks are a kind of basic quantum computation model. Quantum walks with memory(QWM) are types of modified quantum walks that record the walker’s latest path. In this paper we present QWM-P, a kind of QWM whose evolution depends on the parity of memory. QWM-P has an identity coin shift function which helps in analyzing and designing algorithms. Then we discuss some properties of QWM-P. We find that the parity of memory length affects the appearance of QWM-P.

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Acknowledgements

This work is supported by NSFC (Grant Nos. 61701229, 61571226, 61572053, 61702367, 61901218), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170802, BK20190407), China Postdoctoral Science Foundation funded Project (Grant Nos. 2018M630557, 2018T110499), Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 1701139B), the Beijing Natural Science Foundation (Grant No. 4162005), The Research Project of Tianjin Municipal Commission of Education(Grant No. 2017KJ033), the Fundamental Research Funds for the Central Universities (Grant No. 2018RC55), the Beijing Talents Foundation (Grant No. 2017000020124G062).

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Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics(NUAA), Nanjing, China

    Dan Li & Juan Xu

  2. State Key Laboratory of Cryptology, P.O.Box 5159, Beijing, 100878, China

    Dan Li

  3. Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing, China

    Dan Li

  4. National University of Ireland, Galway, Ireland

    Michael Mc Gettrick

  5. Faculty of Information Technology, Beijing University of Technology, Beijing, China

    Yu-Guang Yang

  6. College of Computer Science and Information Engineering, Tianjin University of Science and Technology, Tianjin, China

    Yuan Wang

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  1. Dan Li
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  2. Michael Mc Gettrick
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  3. Yu-Guang Yang
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  4. Juan Xu
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  5. Yuan Wang
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Correspondence to Dan Li.

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Li, D., Mc Gettrick, M., Yang, YG. et al. Quantum Walks with Memory Provided by Parity of Memory. Int J Theor Phys 59, 1934–1943 (2020). https://doi.org/10.1007/s10773-020-04466-5

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