论文标题
用一，二维和三维量子步行模拟拓扑现象
Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
论文作者
论文摘要
我们研究了随后三个维度的拓扑阶段的模拟。我们主要集中于完成量子步行协议的表格，该协议可以在一个维度上模拟拓扑阶段的不同家族，并采取第一个计划来为三维案例构建必要的协议。我们还强调了在不同维度上可以观察到的每个方案的可能边界状态，并提取其出现或缺勤的条件。为了进一步丰富拓扑现象的仿真，我们将依赖的硬币包括在量子步行的进化算子中。因此，这导致了模拟拓扑现象及其特性的逐步依赖性，进而将动力学作为模拟拓扑阶段和边界状态的特征。这种动力学提供了量子步行的阶级数，是控制和设计拓扑阶段和边界状态，其种群，类型甚至发生的人数的平均值。
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the topological phases in one, two dimensions and take the first initiatives to build necessary protocols for three-dimensional cases. We also highlight the possible boundary states that can be observed for each protocol in different dimensions and extract the conditions for their emergences or absences. To further enrich the simulation of the topological phenomenas, we include step-dependent coins in the evolution operators of the quantum walks. Consequently, this leads to step-dependency of the simulated topological phenomenas and their properties which in turn introduce dynamicality as a feature to simulated topological phases and boundary states. This dynamicality provides the step-number of the quantum walk as a mean to control and engineer the number of topological phases and boundary states, their populations, types and even occurrences.
