  The theory of stabilizer quantum error correction allows us to actively
stabilize quantum states and simulate ideal quantum operations in a noisy
environment. It is critical is to correctly diagnose noise from its syndrome
and nullify it accordingly. However, hardware that performs quantum error
correction itself is inevitably imperfect in practice. Here, we show that
stabilizer codes possess a built-in capability of correcting errors not only on
quantum information but also on faulty syndromes extracted by themselves.
Shor's syndrome extraction for fault-tolerant quantum computation is naturally
improved. This opens a path to realizing the potential of stabilizer quantum
error correction hidden within an innocent looking choice of generators and
stabilizer operators that have been deemed redundant.
