Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fault-Tolerant Renormalization Group Decoder for Abelian Topological
  Codes   We present a three-dimensional generalization of a renormalization group
decoding algorithm for topological codes with Abelian anyonic excitations that
we previously introduced for two dimensions. This 3D implementation extends our
previous 2D algorithm by incorporating a failure probability of the syndrome
measurements, i.e., it enables fault-tolerant decoding. We report a
fault-tolerant storage threshold of 1.9(4)% for Kitaev's toric code subject to
a 3D bit-flip channel (i.e. including imperfect syndrome measurements). This
number is to be compared with the 2.9% value obtained via perfect matching. The
3D generalization inherits many properties of the 2D algorithm, including a
complexity linear in the space-time volume of the memory, which can be
parallelized to logarithmic time.

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The categories of this paper are: cs
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th