Logical operations

constant-overhead fault-tolerant encoded computation measurement-based claimed

Level: protocol-level fault tolerance · Cost: combine quantum-expander blocks with encoded ancillas, repeated recovery, classical decoding, and the paper's scheduling assumptions; constant overhead is an asymptotic property of the complete scheme, not a native transversal gate of one HGP check matrix

References: fawzi2018constant

addressable gates through single-shot code switching switching claimed

Level: addressable logical operation in a multi-code protocol · Cost: switch into the auxiliary code required by the protocol, perform the addressed operation, recover through the single-shot boundary, and track the logical frame; the base quantum-expander block alone is not thereby an addressably universal transversal code

References: golowich2025addressable