Efficient construction of stabilizer codes via ZX-calculus Zipeng Wu [1]ORCID iD , Song Cheng* [2]ORCID iD , Bei Zeng [3] + +...

https://www.academia.edu/3064-979X/3/2/10.20935/AcadQuant8237 Introduction: Quantum error-correcting codes (QECCs) are essential for fault-tolerant quantum computation, but standard algebraic and graph-state descriptions each expose only part of the encoder structure. Materials and methods: We introduce the ZX encoder diagram, a graph-like Clifford ZX representation that keeps the encoding map, the code geometry, and the extraction of stabilizers, logical operators, and encoder circuits within a single formalism. We apply this representation to two modular code-construction tasks: concatenation of graph and stabilizer codes, and tensor-network-style encoder contraction. The cost model counts local rewrites and binary matrix reductions. Results: For concatenation, the ZX language recovers generalized local complementation as a special case and remains effective when overlapping neighborhoods obstruct pure generalized local complementation. For holographic constructions, it yields a deterministic pipeline for building the 4-to-12 HaPPY instance and, more generally, bounded-degree tensor-network families. Under this cost model, the contraction stage uses a constant number of local rewrites per contracted leg, and the full extraction pipeline is polynomial in the final diagram size. Conclusions: ZX-calculus provides a code-construction-native framework for concatenated and tensor-network quantum codes, with complexity governed by the number of encoder blocks rather than by an exponential search over local Clifford equivalents. https://www.academia.edu/journals/academia-quantum/articles?source=journal-top-nav