The trace formula with respect to the Grover matrix of a graph
The trace formula with respect to the Grover matrix of a graph
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DOI：
10.1080/03081087.2020.1779173
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发表时间：
2020-06
影响因子：
1.1
通讯作者：
N. Konno;H. Mitsuhashi;H. Morita;I. Sato
中科院分区：
文献类型：
--
作者：
N. Konno;H. Mitsuhashi;H. Morita;I. Sato
摘要是研究素数分布，图形循环的分布与量子行走概率的极限定理之间关系的第一步Grover的过渡矩阵在图上行走。我们针对图形的Grover矩阵定义了Zeta函数，并区分了常规图的Zeta函数的对数。此外，我们通过其对数差异的合适复合物积分获得了相对于Grover矩阵的痕量公式。
ABSTRACT As a first step of the study of the relation between the distribution of prime, reduced cycles of a graph and the limit theorem for the probability of a quantum walk on a graph, we present a trace formula with respect to the Grover matrix that is the transition matrix of the Grover walk on a graph. We define a zeta function with respect to the Grover matrix of a graph, and differentiate the logarithm of its zeta function of a regular graph. Furthermore, we obtain a trace formula with respect to the Grover matrix by a suitable complex integral of its logarithm differential.