Stabilizer Formalism for Generalized Concatenated Quantum Codes
Yun-Jiang Wang, Bei Zeng, Markus Grassl, Barry C. S · 2016
The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum coset codes. This formalism offers a new perspective for GCQCs and enables us to derive a lower bound on the code distance of stabilizer GCQCs from component codes parameters, for both non-degenerate and degenerate component codes. Our formalism also shows how to exploit the error-correcting capacity of component codes to design good GCQCs efficiently.