ISSN 1000-1239 CN 11-1777/TP

计算机研究与发展 ›› 2021, Vol. 58 ›› Issue (9): 1897-1905.doi: 10.7544/issn1000-1239.2021.20210266

所属专题: 2021量子计算专题

• 基础理论 • 上一篇    下一篇

两硬币量子游走模型中的相干动力学

李萌1,2,尚云1,3,4   

  1. 1(中国科学院数学与系统科学研究院 北京 100190);2(中国科学院大学数学科学学院 北京 100049);3(中国科学院数学与系统科学研究院国家数学与交叉科学中心 北京 100190);4(中国科学院数学与系统科学研究院管理决策与信息系统重点实验室 北京 100190) (limeng162@mails.ucas.ac.cn)
  • 出版日期: 2021-09-01
  • 基金资助: 
    国家重点研发计划项目(2016YFB1000902);国家自然科学基金项目(61872352,61472412);国家自然科学基金创新群体项目(61621003)

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).

摘要: 量子游走是量子计算的重要模型,而多硬币量子游走模型由于在量子通讯协议中表现突出也越来越受到人们的关注.量子相干不仅可以刻画量子态的特点,也可以反映量子演化过程的性质.主要对一维圆上两硬币量子游走模型的量子相干性进行了分析.一方面,讨论了初始量子态和硬币算子的选取对量子相干的影响.当硬币算子为Hadamard算子且初态只要在位置子空间上是均衡叠加态,整个量子游走演化过程是具有周期性的,且量子相干仅依赖于步数和圆上顶点的个数;当初始态是均衡叠加态而对硬币算子没有任何限制时,量子相干的演化也极具规律性.另一方面,发现在利用量子游走实现完美状态转移(perfect state transfer)的过程中,硬币算子的选取直接影响量子相干的值.最后,探讨了2种量子游走模型之间的等价性,并基于此指出了其在量子隐形传输(quantum teleportation)中的应用和改进的可能性.

关键词: 量子游走, 两硬币, 量子相干, 状态转移, 量子隐形传输

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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