Quantum span program algorithms for function evaluation sometimes have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these improvements persist even without a promise ahead of time, and we extend this approach to the more general problem of state conversion. As an application, we prove exponential and superpolynomial quantum advantages in average query complexity for several search problems, generalizing Montanaro's Search with Advice [Montanaro, TQC 2010].

中文翻译：

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通过更简单的输入提高了量子查询复杂性

当承诺输入具有一定的结构时，用于函数评估的量子跨度程序算法有时会降低查询复杂性。我们设计了一种修改后的跨度程序算法，以表明即使没有提前承诺，这些改进仍然存在，并且我们将这种方法扩展到更普遍的状态转换问题。作为一个应用，我们证明了几个搜索问题的平均查询复杂度上的指数和超多项式量子优势，概括了 Montanaro 的搜索建议 [Montanaro, TQC 2010]。