  There are well known necessary and sufficient conditions for a quantum code
to correct a set of errors. We study weaker conditions under which a quantum
code may correct errors with probabilities that may be less than one. We work
with stabilizer codes and as an application study how the nine qubit code, the
seven qubit code, and the five qubit code perform when there are errors on more
than one qubit. As a second application, we discuss the concept of syndrome
quality and use it to suggest a way that quantum error correction can be
practically improved.
