论文标题
HyperCube上量子步行的强分散属性
Strong dispersion property for the quantum walk on the hypercube
论文作者
论文摘要
我们表明，在尺寸$ n $的布尔尺度上的离散时间量子步行具有强大的分散属性：如果步行是在一个顶点启动的，那么沃克在$ O（n）$ steps $ o（1.4818^{ - n}）$（1.4818^{ - n}）$ o（o（n）$ steps之后，沃克的概率是任何特定的顶点。这改善了此量子步行的已知混合结果，这表明$ O（n）$步骤后的概率分布接近统一，但并未表明每个顶点的概率很小。对此结果的严格证明涉及关于贝塞尔功能的分析特性的复杂论点。
We show that the discrete time quantum walk on the Boolean hypercube of dimension $n$ has a strong dispersion property: if the walk is started in one vertex, then the probability of the walker being at any particular vertex after $O(n)$ steps is of an order $O(1.4818^{-n})$. This improves over the known mixing results for this quantum walk which show that the probability distribution after $O(n)$ steps is close to uniform but do not show that the probability is small for every vertex. A rigorous proof of this result involves an intricate argument about analytic properties of Bessel functions.
