New Entanglement-Assisted Concatenated Quantum Codes Exceed Quantum Gilbert-Varshamov Bound

Quantum error-correction codes leverage encoding and redundancy to effectively detect and correct errors, thereby enhancing the reliability and accuracy of signal detection. Based on the scheme of entanglement-assisted concatenated quantum codes (EACQCs), we construct both new binary and non-binary EACQCs. Several of the new EACQCs achieve better parameters than the best-known standard entanglement-assisted quantum error-correction codes while maintaining the same code lengths and net transmissions. The quantum Gilbert-Varshamov (GV) bound serves as a crucial benchmark for evaluating quantum code parameters. As the code length increases, we construct binary and non-binary EACQCs that exceed the quantum GV bound. Index Terms-entanglement-assisted quantum error-correction code, entanglement-assisted concatenated quantum codes, quan-tum Gilbert-Varshamov bound