The Quantum Query Complexity of Algebraic Properties

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dc.creatorDoern, Sebastian
dc.creatorThierauf, Thomas
dc.date2007-05-10
dc.date.accessioned2026-07-07T08:00:38Z
dc.date.available2026-07-07T08:00:38Z
dc.descriptionWe present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether $S$ is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms for these problems that improve the best known classical complexity bounds. In particular, we give the first application of the new quantum random walk technique by Magniez, Nayak, Roland, and Santha that improves the previous bounds by Ambainis and Szegedy. We also present several lower bounds for testing algebraic properties.
dc.description13 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/0705.1446
dc.identifierhttp://arxiv.org/abs/0705.1446
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128713
dc.subjectQuantum Physics
dc.titleThe Quantum Query Complexity of Algebraic Properties
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