Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple or states, generalizing code concatenation. More specifically, we represent the constructions as tensor networks built tensors of states in modular fashion. Using set local moves known operator pushing, one can derive properties more codes, such transversal non-Clifford gates, by tracing flow operators network. The endows network geometry to any it builds is valid for constructing stabilizer well non-stabilizer over qubits qudits. For contractible network, sequence contractions also decoding/encoding circuit. To highlight framework's range capabilities provide tutorial, lay out some examples where glue together construct non-trivial codes. These include toric its variants, holographic with operators, 3d code, other interesting properties. Surprisingly, find surface equivalent 2d Bacon-Shor after "dualizing" encoding map.