A simple model of quantum walk with a gap in distribution

• URL: http://arxiv.org/abs/2503.08151v1
• Date: Tue, 11 Mar 2025 08:07:48 GMT
• Title: A simple model of quantum walk with a gap in distribution
• Authors: Takuya Machida,
• Abstract summary: We study a 1-dimensional quantum walk in this paper.<n>Although the walker launches off a location under a localized initial state, some numerical experiments show that the quantum walker does not seem to distribute around the launching location.<n>To prove the gap analytically, we derive a long-time limit distribution, from which one can tell more details about the finding probability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 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.

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