论文标题
Grover在梯子图上行走的生存概率
Survival probability of the Grover walk on the ladder graph
论文作者
论文摘要
我们提供了带有吸收水槽的梯形图上Grover Walk的生存概率的详细分析。在Mare \ V S等人的物理学中讨论了该模型。 Rev. A 101，032113（2020），作为量子运输中违反直觉行为的一个例子，发现尽管暗状态的数量增加了，但随着梯子$ L $的长度，生存率随梯子$ L $的长度而降低。构建了黑暗子空间中的正顺序基础，这使我们能够为生存概率得出一个封闭的公式。结果表明，生存概率作为$ l $的函数的过程可以从迅速增加和融合到减少和收敛，例如$ l^{ - 1} $，只需通过将环连接到梯子的一个角落即可。研究了初始状态和图形配置之间的相互作用。
We provide a detailed analysis of the survival probability of the Grover walk on the ladder graph with an absorbing sink. This model was discussed in Mare\v s et al., Phys. Rev. A 101, 032113 (2020), as an example of counter-intuitive behaviour in quantum transport where it was found that the survival probability decreases with the length of the ladder $L$, despite the fact that the number of dark states increases. An orthonormal basis in the dark subspace is constructed, which allows us to derive a closed formula for the survival probability. It is shown that the course of the survival probability as a function of $L$ can change from increasing and converging exponentially quickly to decreasing and converging like $L^{-1}$ simply by attaching a loop to one of the corners of the ladder. The interplay between the initial state and the graph configuration is investigated.
