Quantum computation of zeta functions of curves
Abstract
Description
We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field F_q, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of a curve, plus a recipe for recovering a Weil polynomial from enough of its cyclic resultants. The latter effectivizes a result of Fried in a restricted setting.
17 pages; v3 (refereed version): minor corrections
17 pages; v3 (refereed version): minor corrections