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arXiv · 0808.0174

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

D. Bacon
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Abstract

The 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.

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D. Bacon. 2008-08-01. Simon's Algorithm, Clebsch-Gordan Sieves, and Hidden Symmetries of Multiple Squares. https://arxiv.org/abs/0808.0174

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