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. 
Alexei Ashikhmin and Ching-Yi Lai and Todd Brun
cs.IT math.IT quant-ph