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arXiv · 1807.03600

On quantum computation of Kloosterman sums

Peter Bruin
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Abstract

We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field $\mathbf{F}$ of $q$ elements. The first algorithm computes a quantum state containing, as its coefficients with respect to the standard basis, all Kloosterman sums for $\mathbf{F}$ twisted by a given multiplicative character, and runs in time polynomial in $\log q$. The second algorithm computes a single Kloosterman sum to a prescribed precision, and runs in time quasi-linear in $\sqrt{q}$.

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Peter Bruin. 2018-07-10. On quantum computation of Kloosterman sums. https://arxiv.org/abs/1807.03600

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