Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hidden Subgroup Problem for Universal Algebras   The Hidden Subgroup Problem (HSP) is a computational problem which includes
as special cases integer factorization, the discrete logarithm problem, graph
isomorphism, and the shortest vector problem. The celebrated polynomial-time
quantum algorithms for factorization and the discrete logarithm are restricted
versions of a generic polynomial-time quantum solution to the HSP for abelian
groups, but despite focused research no full solution has yet been found. We
propose a generalization of the HSP to include arbitrary algebraic structures
and analyze this new problem on powers of 2-element algebras. We prove a
complete classification of every such power as quantum tractable (i.e.
polynomial-time), classically tractable, quantum intractable, and classically
intractable. In particular, we identify a class of algebras for which the
generalized HSP exhibits super-polynomial speedup on a quantum computer
compared to a classical one.

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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: q-fin