有理逼近与后选择量子算法
Rational approximations and quantum algorithms with postselection
摘要：
我们研究了近似给定布尔函数的有理函数和使用后选择计算相同函数的量子算法之间的密切联系。我们表明，前者的最小程度等于（最多2倍）后者的最小查询复杂性。我们给出了最佳的（常数因子）量子算法与后选择的多数函数，稍有改进的早期算法的Aaronson。最后，我们展示了如何纽曼的经典定理的低次有理逼近的绝对值函数遵循这些算法。
英文摘要：
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We give optimal (up to constant factors) quantum algorithms with postselection for the Majority function, slightly improving upon an earlier algorithm of Aaronson. Finally we show how Newman's classic theorem about low-degree rational approximation of the absolute-value function follows from these algorithms.
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