Abstract
We introduce a family of high-rate amplitude-damping (AD) Shor Codes, designed to effectively correct AD errors while maintaining immunity to collective coherent (CC) errors. The proposed AD codes can approximately correct up to AD errors, with flexible parameters , and we provide a rigorous proof that these codes satisfy the approximate quantum error correction conditions. These codes leverage structured stabilizer measurements, enabling efficient detection of AD errors using only local operations and ancillary qubits. We further construct a family of CC-AD Shor codes by concatenating these AD codes with the dual-rail code.