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.