基于量子Bernoulli噪声方法的超立方体上的磁量子游荡
Magnetic Quantum Walk on the Hypercube in Terms of Quantum Bernoulli Noises Method
DOI: 10.12677/pm.2025.153081, PDF,   
作者: 杨 铮：西北师范大学数学与统计学院，甘肃 兰州
关键词: 量子Bernoulli噪声；超立方体；磁量子游荡；Quantum Bernoulli Noises； Hypercube； Magnetic Quantum Walk
摘要: 本文介绍并研究了Bernoulli泛函框架下的离散时间磁量子游荡。根据作用于Bernoulli泛函的湮灭和增生算子引入了磁位移算子 ( e −i θ k ∂ k * + e i θ k ∂ k ) ，其中 e −i θ k ∂ k * 和 e i θ k ∂ k 分别是作用于Bernoulli泛函的磁增生和湮灭算子，然后在此基础上使用它们来定义新的磁量子游荡模型。
Abstract: In this paper, we introduce and investigate a discrete-time magnetic quantum walk in the framework of Bernoulli functionals. We first introduce magnetic shift operators ( e −i θ k ∂ k * + e i θ k ∂ k ) in terms of the annihilation and creation operators acting on Bernoulli functionals, where e −i θ k ∂ k * and e i θ k ∂ k are the magnetic creation and annihilation operators acting on Bernoulli functionals. On this basis, we constructed a new model of magnetic quantum walk on the hypercube.
文章引用：杨铮. 基于量子Bernoulli噪声方法的超立方体上的磁量子游荡[J]. 理论数学, 2025, 15(3): 104-111. https://doi.org/10.12677/pm.2025.153081

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