Affine-coset construction
A (3,8)-regular CSS base with CPM lifts. The paper's P=32 example has parameters [[16384, 4142, d]] with 18 ≤ d ≤ 32.
Construction methods
Other QLDPC constructions
Affine-coset, two-branch, random, and finite-degree approaches to quantum LDPC code design.
These pages give the construction idea, the particular code instances studied, and their data. Distance statements below refer to the linked paper versions; archived parameter files are identified separately where they define a different instance.
Construction families
Finite-field two-branch construction
A two-branch construction of regular CSS bases. The P=64 instance used in the paper's error-rate simulations has [[10240, 4108, d]] with 18 ≤ d ≤ 32. An earlier coefficient archive defines a different instance with d=16.
Rate-2/3 two-branch construction
A (3,18)-regular family with design rate 2/3 and girth 8. The paper's P=101 example is [[34542, 23032, 18]].
(3,6)-regular girth-8 construction
Sparse regular CSS checks with girth 8. The representative finite lift has [[28800, 62, d]] with 18 ≤ d ≤ 192, so it encodes 62 logical qubits.
Paper and distance bounds (v3) →Finite-degree GV construction
An asymptotic distance result reaching the quantum Gilbert–Varshamov bound through classical sparse-graph constructions. The supporting repository provides proof material and verification code.
Random QLDPC construction
A randomized approach to constructing commuting sparse quantum checks, complementing the explicit block constructions elsewhere on this site.
Paper →For pair-partition constructions and their development into low-weight canonical logical bases, see PP codes and logical bases. For affine-permutation-matrix constructions, see Kasai codes.