Abstract:

Bivariate-bicycle (BB) quantum LDPC codes combine sparse stabilizers with nonzero finite-length rate, but the discrete search over polynomial supports and graph covers grows rapidly. We study a two-stage construction procedure for weight-six BB codes. Tabular Q-learning searches the supports of two threeterm bivariate polynomials. For each selected base, directional covers and monomial shifts are then evaluated. After gauge fixing, a cover of size h has h ^ 4 shift assignments; hence every reported case h E {2, 3, 4, 6} has at most 1296 < Nex = 6500 assignments and was exhaustively enumerated. The shifts are voltage labels, but the reported reward used no additive voltage term (Bv = 0); voltage order is therefore used only as a structural interpretation of lifted collisions. We recall the standard BB commutation/parity and voltage-lifting facts, specify the screening and exact-distance criteria, and report representative descendants including [[126, 10, 10]] and [[126, 6, 12]]. Code-capacity simulations with QBP and BP-OSD are presented as descriptive illustrations rather than matched-parameter or equal-budget superiority claims.