用于近似随机存在量化预言机期望值的量子算法
Quantum algorithm for approximating the expected value of a random-exist quantified oracle
AI总结：
该研究提出将量子振幅放大与估计相干组合的算法，在计算随机存在量化预言机期望值（玩家对自然决策有有效反应的概率）时实现二次加速，优于最优经典算法。
摘要：
量子振幅放大与估计已在非结构化搜索和估计任务中展现出二次加速。我们证明，这些量子算法的相干组合在计算随机存在量化预言机的期望值时也能提供二次加速。在此问题中，自然随机做出决策，即根据某概率分布选择比特串，玩家有机会通过找到互补比特串（使黑盒预言机输出1或True）做出反应。我们的任务是近似玩家对自然初始决策有有效反应的概率。我们将该量子算法与蒙特卡洛积分在暴力搜索上的平均性能（合理假设下的最优经典算法）进行比较，发现性能差距取决于部分问题参数，并展示了存在典型二次加速的场景。
英文摘要：
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the expectation value of a random-exist quantified oracle. In this problem, Nature makes a decision randomly, i.e. chooses a bitstring according to some probability distribution, and a player has a chance to react by finding a complementary bitstring such that an black-box oracle evaluates to $1$ (or True). Our task is to approximate the probability that the player has a valid reaction to Nature's initial decision. We compare the quantum algorithm to the average-case performance of Monte-Carlo integration over brute-force search, which is, under reasonable assumptions, the best performing classical algorithm. We find the performance separation depends on some problem parameters, and show a regime where the canonical quadratic speedup exists.
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