QW-Search/Zeta Correspondence
arxiv(2024)
摘要
We consider the connection between this zeta function and quantum search via
quantum walk. First, we give an explicit expression of the zeta function on the
one-dimensional torus in the general case of the number and position of marked
vertices. Moreover, we deal with the two special cases of the position of the
marked vertices on the d-dimensional torus (d ≥ 2). Additionally, we
treat the property of the zeta function by using the Mahler measure. Our
results show the relationship between the zeta function and quantum search
algorithms for the first time.
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