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First, we have V• C• W• R• g• f• q• p• Giving R• = F9 2 F14 2 F4 2 ∂R• 2 ∂R• 1 with R2 = W2⊕C2, as V2 = 0

Error-corrected Z-merge with the Shor code 245 with ∂W• 2 =   1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1  , ∂W• 1 =   1 1 0 0 0 0 1 0 1 0 1 0 0 0

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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 7

    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.