Logical operations

Hadamard up to logical swaps and control-Z on HGP logical sectors transversal claimed

Level: Clifford operations under the paper's logical-basis partition · Cost: apply the declared transversal layers and track their simultaneous action on the canonical HGP logical basis; targeted entangling actions require sequences interleaved with error correction, so this is not an arbitrary gate on an unanalysed factor pair

References: quintavalle2023partitioning

single-block Clifford gates through puncture and wormhole deformation measurement-based claimed

Level: fault-tolerant code-deformation protocol for selected HGP codes · Cost: introduce the required defects, modify and measure stabilizers along the deformation path, decode throughout the protocol, and use state injection for the non-Clifford resource; the bare HGP tensor rule supplies none of this hardware or scheduling structure

References: krishna2021gates