Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing arbitrary Steane code single logical qubit fault-tolerant
  gates   We present a simple method for constructing optimal fault-tolerant
approximations of arbitrary unitary gates using an arbitrary discrete universal
gate set. The method presented is numerical and scales exponentially with the
number of gates used in the approximation. However, for the specific case of
arbitrary single-qubit gates and the fault-tolerant gates permitted by the
concatenated 7-qubit Steane code, we find gate sequences sufficiently long and
accurate to permit the fault-tolerant factoring of numbers thousands of bits
long. A general scaling law of how rapidly these fault-tolerant approximations
converge to arbitrary single-qubit gates is also determined.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys