Simon's Algorithm, Clebsch-Gordan Sieves, and Hidden Symmetries of Multiple Squares

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dc.creatorBacon, D.
dc.date2008-08-01
dc.date.accessioned2026-07-07T09:54:18Z
dc.date.available2026-07-07T09:54:18Z
dc.descriptionThe first quantum algorithm to offer an exponential speedup (in the query complexity setting) over classical algorithms was Simon's algorithm for identifying a hidden exclusive-or mask. Here we observe how part of Simon's algorithm can be interpreted as a Clebsch-Gordan transform. Inspired by this we show how Clebsch-Gordan transforms can be used to efficiently find a hidden involution on the group G^n where G is the dihedral group of order eight (the group of symmetries of a square.) This problem previously admitted an efficient quantum algorithm but a connection to Clebsch-Gordan transforms had not been made. Our results provide further evidence for the usefulness of Clebsch-Gordan transform in quantum algorithm design.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0808.0174
dc.identifierhttp://arxiv.org/abs/0808.0174
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166264
dc.subjectQuantum Physics
dc.titleSimon's Algorithm, Clebsch-Gordan Sieves, and Hidden Symmetries of Multiple Squares
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