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<p>Quantum walks are quantum counterparts of random walks, and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space, and it is observed at a location with a probability. The finding probabilities have been investigated, and some interesting things have been analytically discovered. They are, for instance, ballistic behavior, localization, or a gap. We study a 1-dimensional quantum walk in this paper. Although the walker launches off at a location under a localized initial state, some numerical experiments show that the quantum walker does not seem to distribute around the launching location, which suggests that the probability distribution holds a gap around the launching location. To prove the gap analytically, we derive a long-time limit distribution, from which one can tell more details about the finding probability.</p>

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A simple model of quantum walk with a gap in distribution

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Takuya Machida

摘要

Quantum walks are quantum counterparts of random walks, and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space, and it is observed at a location with a probability. The finding probabilities have been investigated, and some interesting things have been analytically discovered. They are, for instance, ballistic behavior, localization, or a gap. We study a 1-dimensional quantum walk in this paper. Although the walker launches off at a location under a localized initial state, some numerical experiments show that the quantum walker does not seem to distribute around the launching location, which suggests that the probability distribution holds a gap around the launching location. To prove the gap analytically, we derive a long-time limit distribution, from which one can tell more details about the finding probability.