基于Bernoulli泛函的离散时间量子游荡模型
A Model of Discrete-Time Quantum Walk in Terms of Bernoulli Functionals
DOI: 10.12677/pm.2026.162060, PDF,   
作者: 杨 扬：西北师范大学数学与统计学院，甘肃 兰州
关键词: 离散时间量子游荡；Bernoulli泛函；概率分布；Discrete-Time Quantum Walk； Bernoulli Functional； Probability Distribution
摘要: 本文基于Bernoulli泛函的数学框架，构建了一类新的离散时间量子游荡(DTQW)模型。该研究将量子概率中的Bernoulli泛函方法应用于离散时间量子游荡的构建中，提供了一种从代数角度生成图和游荡算子的途径。
Abstract: Based on the mathematical framework of Bernoulli functionals, this paper constructs a new class of discrete-time quantum walk (DTQW) models. The study applies the Bernoulli functional method from quantum probability to the construction of discrete-time quantum walks, providing an algebraic approach to generating graphs and walk operators.
文章引用：杨扬. 基于Bernoulli泛函的离散时间量子游荡模型[J]. 理论数学, 2026, 16(2): 314-325. https://doi.org/10.12677/pm.2026.162060

参考文献

[1] Aharonov, Y., Davidovich, L. and Zagury, N. (1993) Quantum Random Walks. Physical Review A, 48, 1687-1690. [Google Scholar] [CrossRef] [PubMed]
[2] Kempe, J. (2003) Quantum Random Walks: An Introductory Overview. Contemporary Physics, 44, 307-327. [Google Scholar] [CrossRef] 
[3] Konno, N. (2008) Quantum Walks. Lecture Notes in Mathematics.
[4] Venegas-Andraca, S.E. (2012) Quantum Walks: A Comprehensive Review. Quantum Information Processing, 11, 1015-1106. [Google Scholar] [CrossRef] 
[5] Cao, X. (2021) Perfect Edge State Transfer on Cubelike Graphs. Quantum Information Processing, 20, Article No. 285. [Google Scholar] [CrossRef] 
[6] Wang, C. and Ye, X. (2016) Quantum Walk in Terms of Quantum Bernoulli Noises. Quantum Information Processing, 15, 1897-1908. [Google Scholar] [CrossRef] 
[7] Wang, C., Tang, Y. and Ren, S. (2019) Weighted Number Operators on Bernoulli Functionals and Quantum Exclusion Semigroups. Journal of Mathematical Physics, 60, Article ID: 113506. [Google Scholar] [CrossRef] 
[8] Ren, S., Wang, C. and Tang, Y. (2020) Quantum Bernoulli Noises Approach to Stochastic Schrödinger Equation of Exclusion Type. Journal of Mathematical Physics, 61, Article ID: 063509. [Google Scholar] [CrossRef] 
[9] Wang, C. (2022) The Uniform Measure for Quantum Walk on Hypercube: A Quantum Bernoulli Noises Approach. Journal of Mathematical Physics, Article ID: 63, Article ID: 113501. [Google Scholar] [CrossRef] 
[10] Privault, N. (2008) Stochastic Analysis of Bernoulli Professes. Probability Surveys, 5, 435-483.
[11] Wang, C., Chai, H. and Lu, Y. (2010) Discrete-Time Quantum Bernoulli Noises. Journal of Mathematical Physics, 51, Article ID: 053528. [Google Scholar] [CrossRef] 
[12] Wang, C. (2023) Abstract Model of Continuous-Time Quantum Walk Based on Bernoulli Functionals and Perfect State Transfer. International Journal of Quantum Information, 21, 3. [Google Scholar] [CrossRef] 

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