A class of non-reversible hypercube long-range random walks and Bernoulli autoregression

The uniform measure for quantum walk on hypercube: a quantum Bernoulli noises approach

In this paper, we present a quantum Bernoulli noises approach to quantum walks on hypercubes. We first obtain an alternative description of a general hypercube and then, based on the alternative description, we find that the operators $\partial_k^* + \partial_k$ behave actually as the shift operators, where $\partial_k$ and $\partial_k^*$ are the annihilation and creation operators acting on Bernoulli functionals, respectively. With the above operators as the shift operators on the position space, we introduce a discrete-time quantum walk model on a general hypercube and obtain an explicit for…

基于量子伯努利噪声的超立方体上自旋耦合Grover行走的谐波约化

Harmonic Reduction of Spin-Coupled Grover Walks on Hypercubes via Quantum Bernoulli Noises

该研究在量子伯努利噪声框架下，通过对称群表示论对超立方体上自旋耦合Grover行走进行谐波约化，得到八维约化动力学与显式长时间概率行为，明确了其同型结构与约化谱。

超立方体上的量子辅助会合：一种量子伯努利噪声方法

Quantum-assisted rendezvous on hypercubes: a quantum Bernoulli noise approach

该研究在量子伯努利噪声框架下，针对超立方体上的量子辅助会合问题，通过量子行走与投影球面分解等方法，揭示了不同更新方式下的量子可达性差异，建立了相关刚性定理，连接了量子动力学与会合问题。

超立方体上量子行走无无序局域化的谱判据：QBN方法

Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach

本文在量子伯努利噪声框架下研究超立方体上自旋耦合量子行走，提出无无序局域化的谱判据，并在特定Grover行走中构造非均匀不动点，证明该现象发生。

伯努利渗流（及其他随机划分）中两个对称集合内受感染顶点数的比较

Comparing the number of infected vertices in two symmetric sets for Bernoulli percolation (and other random partitions)

该研究针对图上的伯努利渗流，在强对称条件下以随机支配形式证明离固定顶点更远的等大对称集合含簇顶点数更少，结果可推广至多种随机划分模型，并给出多类图的应用。

超立方体上磁性量子游走的谱性质

Spectral Property of Magnetic Quantum Walk on Hypercube

本文研究超立方体上磁性量子游走模型，利用量子伯努利噪声构造磁性移位算子，证明演化算子的点谱和近似谱独立于磁势，揭示量子游走对磁场的谱稳定性。