Fiber-bundle qLDPC codes

A fiber-bundle code is a twisted homological-product CSS code. Base edges connect neighboring fibers while transporting fiber coordinates through automorphisms. Nontrivial monodromy changes global homology, so the construction is not an ordinary Cartesian product.

A reproducible record specifies the base complex, fiber complex, fiber permutation or automorphism on every oriented base edge, the twisted boundary, and distance balancing. Reversing an edge uses the inverse transport so that the assembled boundary still satisfies $\partial^2=0$. Base graph and fiber length alone do not reconstruct $H_X,H_Z$.

Twisting prevents logical chains from separating into independent base and fiber directions, avoiding the shortest-direction limitation of ordinary products. The original construction combines a random LDPC base with a cyclic repetition fiber, followed by weight reduction and distance balancing.

Fiber transport and base automorphisms may induce physical permutations or actions on homology, but the distance theorem does not supply a universal transversal gate set. A logical-gate record must compute the induced action on a logical homology basis and verify effective circuit distance.

The original work gives an efficient greedy method for one Pauli error direction, without a matching general efficient guarantee for the other. This must not be translated into a complete CSS decoder or circuit-level threshold. BP+OSD on a finite expansion would be a separate benchmark protocol.

Static qLDPC sparsity bounds stabilizer support only. Twisted edges may require nonlocal couplings; syndrome circuits still need a connectivity map, ancillas, schedule, hook orientation, and measurement-noise treatment. The code-parameter theorem is not a complete fault-tolerant memory theorem.

The minimum implementation object contains base/fiber checks, the connection permutation table, expanded sparse $H_X,H_Z$, a logical basis, and distance-balancing/weight-reduction parameters. QECDB and QECirc currently provide no verified fiber-bundle-specific family or circuit page.

Fiber bundles are twisted homological products. Specific constructions admit direct BP formulations and can also be written as LPs of a length-one and a longer complex. Moving between these languages still requires an explicit isomorphism; matching names or parameters do not identify finite matrices.

Distinguish the original unbalanced code, weight-reduced code, and final distance-balanced code, and identify which stage defines $n$. An asymptotic formula without connection data remains a family theorem and cannot become a finite landscape point.