Approximate quantum error correction can lead to better codes
Debbie Leung, Michael A. Nielsen, Isaac L. Chuang, Y. Yamamoto · Physical Review A · 1997
We present relaxed criteria for quantum error correction that are useful when the specific dominant quantum noise process is known. As an example, we provide a four-bit code that corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process and has no simple explanation in terms of the usual Pauli basis GF(4) codes.