We study the +/- J random-plaquette Z_2 gauge model (RPGM) in three spatial
dimensions, a three-dimensional analog of the two-dimensional +/- J random-bond
Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly
chosen plaquettes (occuring with concentration p) have couplings with the
``wrong sign'' so that magnetic flux is energetically favored on these
plaquettes. Excitations of the model are one-dimensional ``flux tubes'' that
terminate at ``magnetic monopoles.'' Electric confinement can be driven by
thermal fluctuations of the flux tubes, by the quenched background of magnetic
monopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced
symmetry along a ``Nishimori line'' in the p-T plane (where T is the
temperature). The critical concentration p_c of wrong-sign plaquettes at the
confinement-Higgs phase transition along the Nishimori line can be identified
with the accuracy threshold for robust storage of quantum information using
topological error-correcting codes: if qubit phase errors, qubit bit-flip
errors, and errors in the measurement of local check operators all occur at
rates below p_c, then encoded quantum information can be protected perfectly
from damage in the limit of a large code block. Numerically, we measure p_{c0},
the critical concentration along the T=0 axis (a lower bound on p_c), finding
p_{c0}=.0293 +/- .0002. We also measure the critical concentration of
antiferromagnetic bonds in the two-dimensional RBIM on the T=0 axis, finding
p_{c0}=.1031 +/-.0001. Our value of p_{c0} is incompatible with the value of
p_c=.1093 +/-.0002 found in earlier numerical studies of the RBIM, in
disagreement with the conjecture that the phase boundary of the RBIM is
vertical (parallel to the T axis) below the Nishimori line.Comment: 16 pages, 11 figures, REVTeX, improved numerics and an additional
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