标题： 磁量子漫步在超立方体上的谱性质 显示英文标题

标题： Spectral Property of Magnetic Quantum Walk on Hypercube

摘要： 在本文中，我们引入并研究了一种在一般超立方体上的磁量子行走模型。 我们首先通过使用量子伯努利噪声，构造与磁势$\nu$相关的一组幺正对合算子。 然后，以这些幺正对合算子作为磁移位算子，我们定义了该模型的演化算子$\mathsf{W}^{(\nu)}$，其中$\nu$是磁势。 我们检查了演化算子$\mathsf{W}^{(\nu)}$的点谱和近似谱，并获得了它们相对于模型的硬币算子系统的表示。 我们证明了$\mathsf{W}^{(\nu)}$的点谱和近似谱与磁势$\nu$完全无关，尽管$\mathsf{W}^{(\nu)}$本身依赖于磁势$\nu$。 我们的工作可能表明，受磁场扰动的量子行走相对于磁势可能具有谱稳定性。 显示英文摘要

摘要： In this paper, we introduce and investigate a model of magnetic quantum walk on a general hypercube. We first construct a set of unitary involutions associated with a magnetic potential $\nu$ by using quantum Bernoulli noises. And then, with these unitary involutions as the magnetic shift operators, we define the evolution operator $\mathsf{W}^{(\nu)}$ for the model, where $\nu$ is the magnetic potential. We examine the point-spectrum and approximate-spectrum of the evolution operator $\mathsf{W}^{(\nu)}$ and obtain their representations in terms of the coin operator system of the model. We show that the point-spectrum and approximate-spectrum of $\mathsf{W}^{(\nu)}$ are completely independent of the magnetic potential $\nu$ although $\mathsf{W}^{(\nu)}$ itself is dependent of the magnetic potential $\nu$. Our work might suggest that a quantum walk perturbed by a magnetic field can have spectral stability with respect to the magnetic potential.