  Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the
robustness of quantum computing and communication systems against errors.
Within the realm of QECCs, stabilizer codes, and specifically graph codes,
stand out for their distinct attributes and promising utility in quantum
technologies. This study underscores the significance of devising expansive
QECCs and adopts the ZX-calculus a graphical language adept at quantum
computational reasoning-to depict the encoders of graph codes effectively.
Through the integration of ZX-calculus with established encoder frameworks, we
present a nuanced approach that leverages this graphical representation to
facilitate the construction of large-scale QECCs. Our methodology is rigorously
applied to examine the intricacies of concatenated graph codes and the
development of holographic codes, thus demonstrating the practicality of our
graphical approach in addressing complex quantum error correction challenges.
This research contributes to the theoretical understanding of quantum error
correction and offers practical tools for its application, providing objective
advancements in the field of quantum computing.
