论文标题
DTQW在2D+1中的连续时间限制和可塑性
Continuous Time Limit of the DTQW in 2D+1 and Plasticity
论文作者
论文摘要
塑料量子步行既可以接收连续的时间和连续的时空。该模型最近是由\ cite {molfetta2019quantum}的一位作者提出的，导致了一种通用的量子模拟方案，用于模拟相对论和非相对论方案中的费米子。仍然缺少两个物理维度的扩展，作为一个新的结果，我们证明了有关哪些离散时间量子步行的必要条件可以允许可塑性，从而显示了由此产生的汉密尔顿人。我们将硬币运算符视为一般$ 4 $参数统一矩阵，其参数是晶格步骤尺寸$ \ varepsilon $的功能。对$ \ varepsilon $的这种依赖性封装了$ \ varepsilon $的所有功能，$ \ varepsilon $中的泰勒系列扩展的定义很好，使我们的结果非常笼统。
A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in \cite{molfetta2019quantum}, leading to a general quantum simulation scheme for simulating fermions in the relativistic and non relativistic regimes. The extension to two physical dimensions is still missing and here, as a novel result, we demonstrate necessary and sufficient conditions concerning which discrete time quantum walks can admit plasticity, showing the resulting Hamiltonians. We consider coin operators as general $4$ parameter unitary matrices, with parameters which are function of the lattice step size $\varepsilon$. This dependence on $\varepsilon$ encapsulates all functions of $\varepsilon$ for which a Taylor series expansion in $\varepsilon$ is well defined, making our results very general.
