随机算法和量子算法求解初值问题的几乎最优解
Almost Optimal Solution of Initial-Value Problems by Randomized and Quantum Algorithms
摘要：
我们建立了基本上最优的边界上的随机和量子设置的初值问题的复杂性。为了这个目的，我们定义了一系列的新算法，其错误/成本属性从一步到一步的改善。这些算法产生新的复杂性上限，这不同于已知的下限，只有一个任意小的正参数的指数，和一个对数因子。在随机和量子环境中，初值问题本质上和标量积分一样困难。
英文摘要：
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These algorithms yield new upper complexity bounds, which differ from known lower bounds by only an arbitrarily small positive parameter in the exponent, and a logarithmic factor. In both the randomized and quantum settings, initial-value problems turn out to be essentially as difficult as scalar integration.
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