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In quantum error correction using imperfect primitives, errors of high weightarising from a few faults are major concerns since they might not becorrectable by the quantum error correcting code. Fortunately, some errors ofdifferent weights are logically equivalent and the same correction procedure isapplicable to all equivalent errors, thus correcting high-weight errors issometimes possible. In this work, we introduce a technique called weight parityerror correction (WPEC) which can correct Pauli error of any weight in somestabilizer codes provided that the parity of the weight of the error is known.We show that the technique is applicable to concatenated codes constructed fromthe [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide afault-tolerant error correction protocol using WPEC for the [[49,1,9]]concatenated Steane code which can correct up to 3 faults and requires only 2ancillas.

Fault-tolerant quantum error correction using error weight parities