An integer $a$ is a quadratic nonresidue for a prime $p$ if $x^2 \equiv a \bmod p$ has no solution. Quadratic nonresidues may be found by probabilistic methods in polynomial time. However, without assuming the Generalized Riemann Hypothesis, no deterministic polynomial-time algorithm is known. We present a quantum algorithm which generates a random quadratic nonresidue in deterministic polynomial time.

中文翻译：

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量子计算机可以在确定性多项式时间内找到二次非残差

如果 $x^2 \equiv a \bmod p$ 没有解，则整数 $a$ 是素数 $p$ 的二次非残差。二次非残差可以通过多项式时间内的概率方法找到。但是，如果不假设广义黎曼假设，则不知道确定性多项式时间算法。我们提出了一种在确定性多项式时间内生成随机二次非残差的量子算法。