指数同余的经典和量子算法
Classical and Quantum Algorithms for Exponential Congruences
摘要：
本文讨论了有限域GF（q）上方程af^x + bg^y = c的可解性检验和整数解x，y的经典算法和量子算法。给出了一个时间复杂度为q^（3/8）（logq）^O（1）的量子算法.虽然仍然是log q的超多项式，但这个量子算法比时间复杂度为q^（9/8）（log q）^O（1）的经典算法要快得多。因此，它给出了一个自然问题的例子，其中量子算法提供了关于经典算法的立方加速。
英文摘要：
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is presented. While still superpolynomial in log q, this quantum algorithm is significantly faster than the best known classical algorithm, which has time complexity q^(9/8) (log q)^O(1). Thus it gives an example of a natural problem where quantum algorithms provide about a cubic speed-up over classical ones.
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