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We now relate the above cell complexes to chain complexes by way of functors

Graphs, cell complexes 237 One can define quantum codes using abstract cell complexes more generally, but abstract cubical complexes are the specific type which we make use of i

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Homology, Hopf Algebras and Quantum Code Surgery

quant-ph · 2025-08-02 · conditional · novelty 4.0

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.

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  • Homology, Hopf Algebras and Quantum Code Surgery quant-ph · 2025-08-02 · conditional · none · ref 2

    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.