Lattice surgery is reformulated as colimits in chain complexes and Hopf algebra (co)multiplication, enabling automated low-overhead logical measurements on quantum LDPC codes and an algebraic theory of boundaries in quantum double models.
As a consequence the family of pushout graphs as m scales is not bounded above by a constant, and so the corresponding family of codes is not LDPC
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Homology, Hopf Algebras and Quantum Code Surgery
Lattice surgery is reformulated as colimits in chain complexes and Hopf algebra (co)multiplication, enabling automated low-overhead logical measurements on quantum LDPC codes and an algebraic theory of boundaries in quantum double models.