Yep, it’s paper dance time. This one is less of a dance and more of a shuffle:
Title: Simon’s Algorithm, Clebsch-Gordan Sieves, and Hidden Symmetries of Multiple Squares
Author: D. Bacon
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.
Bonus points for identifying the song, of course.