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].

翻译：针对函数评估的量子跨度程序算法，当输入具有特定结构时，其查询复杂度有时会降低。我们设计了一种改进的跨度程序算法，证明即使在没有事先承诺的情况下，这些改进依然存在，并将该方法推广至更广泛的状态转换问题。作为应用，我们证明了若干搜索问题在平均查询复杂度方面具有指数级和超多项式级的量子优势，推广了Montanaro的带建议搜索算法（Montanaro, TQC 2010）。