中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30310-030310.doi: 10.1088/1674-1056/22/3/030310

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Average position in quantum walks with a U(2) coin

李敏, 张永生, 郭光灿   

  1. Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Science, Hefei 230026, China
  • 收稿日期:2012-11-01 修回日期:2012-11-30 出版日期:2013-02-01 发布日期:2013-02-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10974192 and 61275122), the National Basic Research Program of China (Grant Nos. 2011CB921200 and 2011CBA00200), and K. C. Wong Education Foundation and the Chinese Academy of Sciences.

Average position in quantum walks with a U(2) coin

Li Min (李敏), Zhang Yong-Sheng (张永生), Guo Guang-Can (郭光灿)   

  1. Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Science, Hefei 230026, China
  • Received:2012-11-01 Revised:2012-11-30 Online:2013-02-01 Published:2013-02-01
  • Contact: Zhang Yong-Sheng E-mail:yszhang@ustc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10974192 and 61275122), the National Basic Research Program of China (Grant Nos. 2011CB921200 and 2011CBA00200), and K. C. Wong Education Foundation and the Chinese Academy of Sciences.

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摘要： We investigated discrete-time quantum walks with an arbitary unitary coin. Here we discover that the average position〈x〉=max(〈x〉)sin(α+γ), while the initial state is 1/√2(|0L〉+ i|0R〉). We verify the result, and obtain some symmetry properties of quantum walks with a U(2) coin with |0L〉 and |0R〉 as the initial state.

关键词: quantum random walk, U(2) coin, average position

Abstract: We investigated discrete-time quantum walks with an arbitary unitary coin. Here we discover that the average position〈x〉=max(〈x〉)sin(α+γ), while the initial state is 1/√2(|0L〉+ i|0R〉). We verify the result, and obtain some symmetry properties of quantum walks with a U(2) coin with |0L〉 and |0R〉 as the initial state.

Key words: quantum random walk, U(2) coin, average position

中图分类号:  (Decoherence; open systems; quantum statistical methods)

  • 03.65.Yz
03.67.-a (Quantum information) 03.67.Ac (Quantum algorithms, protocols, and simulations)