移位子集问题的量子算法
Quantum algorithms for shifted subset problems
摘要：
我们考虑最近提出的广义阿贝尔隐子群问题：移动子集问题。问题是确定某个阿贝尔群的子集S，给定访问以下形式的量子态：|S+x>，对于某个未知的移位x。我们给出了量子算法来寻找汉明球和布尔立方体{0，1}^n的其他子集。该算法的时间复杂度为n的多项式，并从经典计算中产生指数分离。
英文摘要：
We consider a recently proposed generalisation of the abelian hidden subgroup problem: the shifted subset problem. The problem is to determine a subset S of some abelian group, given access to quantum states of the form |S+x>, for some unknown shift x. We give quantum algorithms to find Hamming spheres and other subsets of the boolean cube {0,1}^n. The algorithms have time complexity polynomial in n and give rise to exponential separations from classical computation.
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