估计高斯和的有效量子算法
Efficient Quantum Algorithms for Estimating Gauss Sums
摘要：
我们提出了一个有效的量子算法来估计有限域和有限环上的高斯和。这是一个自然的问题，因为高斯和的描述可以在不参考黑盒函数的情况下完成。通过将离散对数问题转化为高斯和估计问题，证明了该问题对于经典算法是困难的。量子算法的工作依赖于傅里叶变换的加性特征与高斯和的乘性特征之间的相互作用。
英文摘要：
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction from the discrete logarithm problem to Gauss sum estimation we also give evidence that this problem is hard for classical algorithms. The workings of the quantum algorithm rely on the interaction between the additive characters of the Fourier transform and the multiplicative characters of the Gauss sum.
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