Decoding Algorithm to Composite Errors Consisting of Deletions and Insertions for Quantum Deletion-Correcting Codes Based on Quantum Reed-Solomon Codes
Although Hagiwara codes are capable of correcting combined deletion and insertion errors, the longstanding absence of an efficient decoding algorithm has hindered their practical deployment. This work presents the first efficient decoding scheme for Hagiwara codes constructed from quantum Reed–Solomon codes. By integrating classical synchronization error correction techniques with the structural properties of quantum codes, the proposed method establishes a decoding framework tailored to quantum deletion–insertion errors. The approach successfully corrects composite synchronization errors, substantially enhancing the practicality and feasibility of Hagiwara codes and addressing a critical gap in efficient decoding for this class of quantum error-correcting codes.