从蒙特卡罗到量子计算
From Monte Carlo to Quantum Computation
摘要：
量子计算到目前为止主要关注离散问题。最近，E. Novak和作者研究了高维积分的量子算法，并处理了这个问题，量子计算的优势可以带来经典的确定性或随机方法，这类问题。本文简要介绍了量子计算的基本思想，综述了近年来在高维积分方面的研究成果。我们讨论连接到蒙特卡罗方法学和比较量子算法的最佳错误率的经典确定性和随机算法。
英文摘要：
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring over classical deterministic or randomized methods for this type of problem. In this paper we give a short introduction to the basic ideas of quantum computing and survey recent results on high dimensional integration. We discuss connections to the Monte Carlo methology and compare the optimal error rates of quantum algorithms to those of classical deterministic and randomized algorithms.
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