Stopping time of a one-dimensional bounded quantum walk

doi:10.1088/1674-1056/25/11/110304

中国物理B ›› 2016, Vol. 25 ›› Issue (11): 110304-110304.doi: 10.1088/1674-1056/25/11/110304

Stopping time of a one-dimensional bounded quantum walk

Hao Luo(骆浩), Xiang Zhan(詹翔), Peng Zhang(张芃), Peng Xue(薛鹏)

1 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China;
2 Department of Physics and Information Engineering, Jining University, Qufu 273155, China

收稿日期:2016-06-22 修回日期:2016-07-29 出版日期:2016-11-05 发布日期:2016-11-05
通讯作者: Peng Xue E-mail:gnep.eux@gmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11222430, 11434011, and 11474049), the National Basic Research Program of China (Grant No. 2012CB922104), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 16XNLQ03).

Stopping time of a one-dimensional bounded quantum walk

Hao Luo(骆浩)¹, Xiang Zhan(詹翔)², Peng Zhang(张芃)¹, Peng Xue(薛鹏)²

1 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China;
2 Department of Physics and Information Engineering, Jining University, Qufu 273155, China

Received:2016-06-22 Revised:2016-07-29 Online:2016-11-05 Published:2016-11-05
Contact: Peng Xue E-mail:gnep.eux@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11222430, 11434011, and 11474049), the National Basic Research Program of China (Grant No. 2012CB922104), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 16XNLQ03).

摘要/Abstract

摘要：

The stopping time of a one-dimensional bounded classical random walk (RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time. A quantum walk (QW) is a non-trivial generalization of RW, and has attracted a great deal of interest from researchers working in quantum physics and quantum information. In this paper, we develop a method to calculate the stopping time for a one-dimensional QW. Using our method, we further compare the properties of stopping time for QW and RW. We find that the mean value of the stopping time is the same for both of these problems. However, for short times, the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW. This means that, although the mean stopping time of a quantum and classical walker are the same, the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker.

关键词: quantum walk, stopping time, cumulative probability

Abstract:

Key words: quantum walk, stopping time, cumulative probability

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

05.40.Fb (Random walks and Levy flights)

骆浩, 詹翔, 张芃, 薛鹏. Stopping time of a one-dimensional bounded quantum walk[J]. 中国物理B, 2016, 25(11): 110304-110304.

Hao Luo(骆浩), Xiang Zhan(詹翔), Peng Zhang(张芃), Peng Xue(薛鹏). Stopping time of a one-dimensional bounded quantum walk[J]. Chin. Phys. B, 2016, 25(11): 110304-110304.

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Stopping time of a one-dimensional bounded quantum walk

Stopping time of a one-dimensional bounded quantum walk

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