Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical and Quantum Algorithms for Testing Equivalence of Group
  Extensions   While efficient algorithms are known for solving many important problems
related to groups, no efficient algorithm is known for determining whether two
arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a
special type of central extension, is widely believed to contain the essential
hard cases. However, looking specifically at central extensions, the natural
formulation of being "the same" is not isomorphism but rather "equivalence,"
which requires an isomorphism to preserves the structure of the extension. In
this paper, we show that equivalence of central extensions can be computed
efficiently on a classical computer when the groups are small enough to be
given by their multiplication tables. However, in the model of black box
groups, which allows the groups to be much larger, we show that equivalence can
be computed efficiently on a quantum computer but not a classical one (under
common complexity assumptions). Our quantum algorithm demonstrates a new
application of the hidden subgroup problem for general abelian groups.

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The categories of this paper are: math
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
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The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys