  Canonical discrete quantum error correction (DQEC) schemes use projective von
Neumann measurements on stabilizers to discretize the error syndromes into a
finite set, and fast unitary gates are applied to recover the corrupted
information. Quantum error correction (QEC) based on continuous measurement,
known as continuous quantum error correction (CQEC), in principle, can be
executed faster than DQEC and can also be resource efficient. However, CQEC
requires meticulous filtering of noisy continuous measurement data to reliably
extract error syndromes on the basis of which errors could be detected. In this
paper, we show that by constructing a measurement-based estimator (MBE) of the
logical qubit to be protected, which is driven by the noisy continuous
measurement currents of the stabilizers, it is possible to accurately track the
errors occurring on the physical qubits in real time. We use this MBE to
develop a continuous quantum error correction (MBE-CQEC) scheme that can
protect the logical qubit to a high degree, surpassing the performance of DQEC,
and also allows QEC to be conducted either immediately or in delayed time with
instantaneous feedbacks.
