  We investigate the effect of quantum errors on a monitored Brownian
Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition
that can be understood as a symmetry-breaking transition of an effective $Z_4$
magnet in the replica space. The errors describe the loss of information about
the measurement outcomes and are applied during the non-unitary evolution or at
the end of the evolution. In the former case, we find that this error can be
mapped to an emergent magnetic field in the $Z_4$ magnet, and as a consequence,
the symmetry is explicitly broken independent of the measurement rate. R\'enyi
entropies computed by twisting boundary conditions now generate domain walls
even in the would-be symmetric phase at a high measurement rate. The entropy is
therefore volume-law irrespective of the measurement rate. In the latter case,
the error-induced magnetic field only exists near the boundary of the magnet.
Varying the magnetic field leads to a pinning transition of domain walls,
corresponding to error threshold of the quantum code prepared by the
non-unitary SYK dynamics.
