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arXiv:math/0411623 · Computational Complexity

Quantum computation of zeta functions of curves

Kiran Sridhara Kedlaya

Published Apr 25, 2006• 29 citations
arXivHTMLPDF
DOI
10.1007/s00037-006-0204-7

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The Grover algorithm is one of the most famous quantum algorithms. On the other hand, the absolute zeta function can be regarded as a zeta function over [Formula: see text] defined by a function satisfying the absolute automorphy. In this study, we show the property of the Grover algorithm and present a relation between the Grover algorithm and the absolute zeta function. We focus on the period of the Grover algorithm because if the period is finite, then we are able to get an absolute zeta function explicitly by Kurokawa’s theorem. In addition, whenever the period is finite or not, an expansion of the absolute zeta function can be obtained by a direct computation.