论文标题
带电位的量子空间搜索：长期动态和噪声的鲁棒性
Quantum spatial search with electric potential : long-time dynamics and robustness to noise
论文作者
论文摘要
我们在引入的方案上介绍了各种结果，这是二维（2D）正方形空间网格上的量子空间搜索算法，并以2D DIRAC离散时间量子步行（DQW）耦合到与标记节点上的COULOMB电场相连。在这样的步行中，电术语充当算法的甲骨文，而自由步行（即没有电术语）充当“扩散”部分，正如Grover的算法中所谓的那样。结果如下。首先，我们在较长的时间内对此电动狄拉克DQW进行模拟，而不是参考\ \ cite {zd21}中的探索，并观察到在oracle标记的节点周围有第二个定位峰，在时间$ o o（\ sqrt {n}）$中达到的节点达到了$ n $ n $ n of n of of of o o（\ sqrt {n}）$ of of of o o o（n of n of of of o o o（ n）$。这与振幅扩增之前的最新2D DQW搜索算法相匹配。然后，我们研究添加噪声对库仑电势的影响，并观察到步行，尤其是第二个定位峰，对空间噪声非常强大，对时空噪声更适度稳定，并且第一个定位峰甚至对时空噪声也很强。
We present various results on the scheme introduced , which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field centered on the marked node. In such a walk, the electric term acts as the oracle of the algorithm, and the free walk (i.e., without electric term) acts as the "diffusion" part, as it is called in Grover's algorithm. The results are the following. First, we run simulations of this electric Dirac DQW during longer times than explored in Ref.\ \cite{ZD21}, and observe that there is a second localization peak around the node marked by the oracle, reached in a time $O(\sqrt{N})$, where $N$ is the number of nodes of the 2D grid, with a localization probability scaling as $O(1/\ln N)$. This matches the state-of-the-art 2D DQW search algorithms before amplitude amplification. We then study the effect of adding noise on the Coulomb potential, and observe that the walk, especially the second localization peak, is highly robust to spatial noise, more modestly robust to spatiotemporal noise, and that the first localization peak is even highly robust to spatiotemporal noise.
