多态离散时间量子行走的概率表示
A Probabilistic Representation for Multi-State Discrete-time Quantum Walks
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中文总结 AI 辅助
研究构建整数格上三态离散时间量子行走的概率表示，通过实证验证，证明其收敛于多态狄拉克偏微分方程连续解，为模拟高维量子行走提供有力替代方法，开辟分析量子动力学新途径。
中文摘要 AI 辅助
基于Vu（2026）的开创性框架，我们构建了整数格上三态离散时间量子行走的概率表示，并通过实证示例进行验证。此外，我们证明这种表示收敛于多态狄拉克偏微分方程的连续解。总体而言，我们的发现表明这种概率范式是模拟高维量子行走的有力替代方法，为用经典随机过程分析量子动力学开辟了新的理论途径。
英文摘要
Building upon the pioneering framework of Vu (2026), we construct a probabilistic representation for three-state discrete-time quantum walks on integer lattices and validate it through empirical examples. Furthermore, we establish that this representation converges to the continuum solution of multi-state Dirac partial differential equations. Broadly, our findings demonstrate that this probabilistic paradigm serves as a robust alternative for simulating higher-dimensional quantum walks, opening new theoretical avenues to analyze quantum dynamics using classical stochastic processes.
