论文标题
朝固定点和脉动量子搜索在图形上搜索由量子行动驱动的，并具有外流量：完整图的试验
Toward fixed point and pulsation quantum search on graphs driven by quantum walks with in- and out-flows: a trial to the complete graph
论文作者
论文摘要
我们在从外部步骤中以内流和流量来处理量子步行模型。我们表明，此量子步行可以找到完整图的标记顶点，其固定状态的可能性很高。为了交换稳定性，收敛时间由$ o（n \ log n）$估算，其中$ n $是顶点的数量。但是，直到时间步骤$ o（n）$，我们才表明，周期性$ o（\ sqrt {n}）$存在脉动。我们发现在此脉动阶段具有较高相对概率的标记顶点。这意味着我们有两种机会找到具有较高相对概率的标记顶点。短时间步骤$ O（\ sqrt {n}）$在脉动阶段的第一次机会访问，而在长时间步骤$ o（n \ log n）$之后，第二次机会访问稳定阶段。这些证据基于加藤的扰动理论。
We treat a quantum walk model with in- and out- flows at every time step from the outside. We show that this quantum walk can find the marked vertex of the complete graph with a high probability in the stationary state. In exchange of the stability, the convergence time is estimated by $O(N\log N)$, where $N$ is the number of vertices. However until the time step $O(N)$, we show that there is a pulsation with the periodicity $O(\sqrt{N})$. We find the marked vertex with a high relative probability in this pulsation phase. This means that we have two chances to find the marked vertex with a high relative probability; the first chance visits in the pulsation phase at short time step $O(\sqrt{N})$ while the second chance visits in the stable phase after long time step $O(N\log N)$. The proofs are based on Kato's perturbation theory.
