  The standard quantum error correction protocols use projective measurements
to extract the error syndromes from the encoded states. We consider the more
general scenario of weak measurements, where only partial information about the
error syndrome can be extracted from the encoded state. We construct a feedback
protocol that probabilistically corrects the error based on the extracted
information. Using numerical simulations of one-qubit error correction codes,
we show that our error correction succeeds for a range of the weak measurement
strength, where (a) the error rate is below the threshold beyond which multiple
errors dominate, and (b) the error rate is less than the rate at which weak
measurement extracts information. It is also obvious that error correction with
too small a measurement strength should be avoided.
