ISSN 1000-1239 CN 11-1777/TP

Journal of Computer Research and Development ›› 2021, Vol. 58 ›› Issue (9): 1897-1905.doi: 10.7544/issn1000-1239.2021.20210266

Special Issue: 2021量子计算专题

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Dynamics of Coherence in Quantum Walk with Two Coins

Li Meng1,2 Shang Yun1,3,4   

  1. 1(Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190);2(School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049);3(NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190);4(MDIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190)
  • Online:2021-09-01
  • Supported by: 
    This work was supported by the National Key Research and Development Program of China (2016YFB1000902), the National Natural Science Foundation of China (61872352, 61472412), and the Program for Creative Research Group of the National Natural Science Foundation of China (61621003).

Abstract: Quantum walk is an important model of quantum computing, and quantum walk with multiple coins has attracted more and more attention due to its outstanding performance in quantum communication protocols. Quantum coherence can not only describe the characteristics of quantum states, but also reflect the properties of quantum evolution process. In this paper, we analyze quantum coherence for the model of quantum walk with two coins on the one dimensional circle. On the one hand, we discuss the influence of the choice of initial quantum state and coin operators on quantum coherence. When the coin operator is Hadamard operator, as long as the initial state in subspace is equal superposition, the whole evolutionary process of quantum walk is periodic, and quantum coherence only depends on the number of vertexes of the circle and steps; When the initial state is equal superposition and there are no limits on the coin operators, the evolution of the quantum state is also extremely regular. On the other hand, we find that in the process of perfect state transfer by quantum walk, the coin operator will determine the quantum coherence directly. In addition, we also discuss the equivalence between the two quantum walk models, and based on this, we point out the possibility of application and improvement in quantum teleportation.

Key words: quantum walk, two coins, quantum coherence, state transfer, quantum teleportation

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