Quantum algorithms for shifted subset problems

Details Quantum algorithms for shifted subset problems Quantum algorithms for shifted subset problems

2008-06-20

arxiv.org/abs/0806.3362v3

Quantum Information & Computation vol. 9 no. 5&6, pp. 500-512, 2009

Physics

Quantum Physics

15 pages; v3: simplified proof of main result

Scientific paper

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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