Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simon's Algorithm, Clebsch-Gordan Sieves, and Hidden Symmetries of
  Multiple Squares   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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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg