منابع مشابه
Hidden Symmetry Subgroup Problems
We advocate a new approach for addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the hidden symmetry subgroup problem (HSSP), which is a generalization of the well-studied hidden subgroup problem (HSP). Given a group acting on a set and an oracle whose level sets define a partition of the set, the task is to recover the subgroup of symme...
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We present an explicit measurement in the Fourier basis that solves an important case of the Hidden Subgroup Problem, including the case to which Graph Isomorphism reduces. This entangled measurement uses k = log 2 |G| registers, and each of the 2 subsets of the registers contributes some information. While this does not, in general, yield an efficient algorithm, it generalizes the relationship...
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We study the hidden subgroup problem (HSP) over groups of the form Gn where G is a group of constant size. While these groups are structurally simpler than the symmetric groups Sn, for which solving the HSP would yield a quantum algorithm for Graph Isomorphism, they share an important property with Sn: almost all of their irreducible representations are exponentially large. As a consequence, re...
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An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it easier to absorb the background necessary to begin research on the Hidden Subgroup Problem. Proofs are provided which give very concrete algorithms and bounds fo...
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One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versions of the hidden subgroup problem. As a consequence of the bounds, we show that the sample compl...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2013
ISSN: 0097-5397,1095-7111
DOI: 10.1137/120864416