Limitations of discrete-time quantum walk on a one-dimensional infinite chain

Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun

doi:10.1016/j.physleta.2018.01.035

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…However, it does not solve the problem after a long-time evolution. In our earlier work [15], we obtain that the probabilities are equal when a walker moves along coin evolution sequences with the same blocks that make it reach a certain position. We say that these coin evolution sequences are equivalent.…”

Section: Discussionmentioning

confidence: 88%

The sojourn times of one dimensional discrete-time quantum walks

Cai¹,

Huang²,

Ye³

et al. 2023

Laser Phys. Lett.

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In the existing literature, a sojourn time of a discrete-time quantum walk is not a random variable. To solve this problem, we redefine the sojourn time of a quantum walk where its coin evolution operator can be general. We first discuss a class of quantum walks governed by flip operators. We cumulatively calculate how much time a walker spends in the set of non-negative integers up to a fixed evolution time. Whether a walker makes a left or right evolution, we add up the staying times as long as it stays within the target set. We define a sojourn time as the total amount of the staying times. Compared with existing definitions, we show that this definition can satisfy the probability normalization. From this, we define a random variable about the sojourn time and discuss its probability distribution. We build a mathematical model to characterize a sojourn time that is embedded into a quantum walk. These results are also valid for a class of quantum walks governed by general coin operators. We also give a method for calculating the sojourn time and analyze the shape features of its probability distribution.

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Section: Discussionmentioning

confidence: 88%

The sojourn times of one dimensional discrete-time quantum walks

Cai¹,

Huang²,

Ye³

et al. 2023

Laser Phys. Lett.

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Quantum Network Communication With a Novel Discrete-Time Quantum Walk

Chen

Wang

et al. 2019

IEEE Access

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In this paper, we propose a scheme using a new kind of quantum walk to realize quantum communication well. In our scheme, obviously, there are three advantages. First, the initial states can be transferred from the source to the target by finite steps, which will make execution easier in practice. Second, due to fewer restrictions to the network models, our scheme can be adapted to more general network models, such as the butterfly network, the inverted crown network, the grail network, and the generalized butterfly network G k. Finally, arbitrary single-qubit and two-qubit initial states can be transferred to different kinds of network models. At the same time, the fidelity and probability equal 1. Our work promotes more applications of combining quantum computation with quantum communication in the future.

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Limitations of discrete-time quantum walk on a one-dimensional infinite chain

Cited by 2 publications

References 22 publications

The sojourn times of one dimensional discrete-time quantum walks

The sojourn times of one dimensional discrete-time quantum walks

Quantum Network Communication With a Novel Discrete-Time Quantum Walk

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