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arXiv · 0806.3362

Quantum algorithms for shifted subset problems

Ashley Montanaro
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Abstract

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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Ashley Montanaro. 2009-02-06. Quantum algorithms for shifted subset problems. https://arxiv.org/abs/0806.3362

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