collection

Quantum expander code

A quantum expander code is a hypergraph-product CSS code whose sparse classical Tanner factor expands every sufficiently small vertex set on both sides. Expansion belongs to the classical factor, not to the quantum check graph, and it is the hypothesis that makes the local small-set-flip decoder provable. The constructor exports two deterministic finite factors and exhaustively checks their declared cutoffs. Those witnesses teach the predicate and verify finite HGP blocks; they are not an explicit asymptotic family with fixed degrees and fixed expansion constants, which the founding source reports only through probabilistic existence.