Logical operations

CNOT between identical BB blocks transversal claimed

Level: Clifford · Cost: one aligned pairwise physical-CNOT layer; module transport, alignment, and correlated decoding are additional architecture costs

References: yoder2025tour

selected logical Clifford generators fold-transversal claimed

Level: Clifford · Cost: a fold/permutation plus constant-depth physical Clifford layers; only symmetric BB instances with a resolved logical action qualify

References: eberhardt2024fold

logical Clifford operations through automorphisms fold-transversal claimed

Level: Clifford · Cost: a certified Tanner-graph permutation and its physical routing; the induced symplectic action must be computed for the chosen block

References: sayginel2025automorphisms

inter-block Pauli measurements and Clifford surgery surgery claimed

Level: Clifford · Cost: long-range ancilla patches, repeated measurements, and a joint decoder; the resource count belongs to the selected modular protocol

References: yoder2025tour

H / S / CNOT in the self-dual BB subfamily transversal claimed

Level: Clifford · Cost: constant-depth physical layers on blocks satisfying the extra self-duality and twisted-torus conditions; not a gross-code claim

References: liang2025selfdual