Correction of data and syndrome errors by stabilizer codes

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information-error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea of quantum data-syndrome (DS) codes that are capable of correcting both data qubits and syndrome bits errors. We study fundamental properties of quantum DS codes and provide several CSS-type code constructions of quantum DS codes.