I’m trying to understand how decoding algorithms are implemented in quantum error correction (QEC). As I know, QEC requires syndrome measurements, which are typically done using gates like CNOTs. However, I have not seen much discussion on how the decoding part, which takes the syndrome measurements as input and produces error corrections, is implemented in terms of quantum circuits.

Are the decoding algorithms implemented using quantum gates like CNOT, or can they be implemented using classical VLSI architectures, as in classical error correction? If there are any resources or papers that explain how the decoding algorithm is deployed in quantum circuits, I would appreciate any recommendations..