We devise a protocol to build 1D time-dependent quantum walks in 1D maximizing the spatial spread throughout the procedure. We allow only one of the physical parameters of the coin-tossing operator to vary, i.e. the angle $\theta$, such that for $\theta =0$ we have the ${\hat{\sigma }}_z$, while for $\theta =\pi /4$ we obtain the Hadamard gate. The optimal $\theta$ sequences present non-trivial patterns, with mostly $\theta \approx 0$ alternated with $\theta \approx \pi /4$ values after increasingly long periods. We provide an analysis of the entanglement properties, quasi-energy spectrum and survival probability, providing a full physical picture.

中文翻译：

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优化量子行走的空间扩散

我们设计了一种协议，以在1D中建立1D时间相关的量子游走，从而在整个过程中最大化空间分布。我们仅允许抛硬币操作员的一个物理参数发生变化，即角度$\theta$，这样 $\theta =0$ 我们有 ${\hat{\sigma }}_{ž}$，而 $\theta =\pi /4$我们获得了哈达玛门。最优的$\theta$ 序列呈现出非平凡的模式，大部分 $\theta \approx 0$ 与...交替 $\theta \approx \pi /4$长期增长后的价值。我们提供了纠缠特性，准能量谱和生存概率的分析，提供了完整的物理图像。