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Performing active quantum error correction to protect fragile quantum stateshighly depends on the correctness of error information--error syndromes. Toobtain reliable error syndromes using imperfect physical circuits, we proposethe idea of quantum data-syndrome (DS) codes that are capable of correctingboth data qubits and syndrome bits errors. We study fundamental properties ofquantum DS codes and provide several CSS-type code constructions of quantum DScodes.

Correction of Data and Syndrome Errors by Stabilizer Codes