  The competition between non-commuting projective measurements in discrete
quantum circuits can give rise to entanglement transitions. It separates a
regime where initially stored quantum information survives the time evolution
from a regime where the measurements destroy the quantum information. Here we
study one such system - the projective transverse field Ising model - with a
focus on its capabilities as a quantum error correction code. The idea is to
interpret one type of measurement as an error and the other type as a syndrome
measurement. We demonstrate that there is a finite threshold below which
quantum information encoded in an initially entangled state can be retrieved
reliably. In particular, we implement the maximum likelihood decoder to
demonstrate that the error correction threshold is distinct from the
entanglement transition. This implies that there is a finite regime where
quantum information is protected by the projective dynamics, but cannot be
retrieved by using syndrome measurements.
