发表机构
Graduate School of Environment and Information Sciences, Yokohama National University（横滨国立大学环境与信息科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究磁矢势对有限图上周期性格罗弗游走的影响，通过量子图框架引入磁矢势，将其视为微扰研究周期性稳健性，依据图谱结构分析，在图有非单特征值时推导厄米矩阵，揭示微扰动力学与连续时间量子游走的关系。
AI 中文摘要
我们研究了磁矢势对有限图上周期性格罗弗游走的影响。通过量子图框架引入磁矢势，它在特殊情况下诱导出格罗弗游走。我们将矢势视为周期性格罗弗游走的微扰并研究其周期性的稳健性。分析表明对这种微扰的响应取决于底层图的谱结构。特别是当图至少有一个非单特征值时，我们推导了一个表征其周期性稳健性的厄米矩阵。结果表明，微扰动力学渐近地由该厄米矩阵生成的连续时间量子游走描述。
英文摘要
We study the effect of magnetic vector potentials on periodic Grover walks on finite graphs. The magnetic vector potential is introduced through the framework of quantum graphs, which induces the Grover walk as a special case. We regard the magnetic vector potential as a perturbation of a periodic Grover walk and investigate the robustness of its periodicity. Our analysis reveals that the response to such perturbations depends on the spectral structure of the underlying graph. In particular, when the graph possesses at least one non-simple eigenvalue, we derive a Hermitian matrix that characterizes the robustness of its periodicity. As a consequence, for initial states orthogonal to the eigenspaces of the unperturbed Grover walk corresponding to the eigenvalues $\pm1$, we show that the perturbed dynamics is asymptotically described by a continuous-time quantum walk generated by this Hermitian matrix.
Comments41 pages, 3 figures
