Logical operations

CNOT between aligned blocks transversal claimed

Level: Clifford · Cost: one layer of fifteen pairwise physical CNOTs; the pairing of the seven logical control-target pairs depends on the declared logical basis, and routing plus syndrome extraction are additional

References: gottesman1997stabilizer

logical Clifford transformations induced by GL(4,2) transversal claimed

Level: Clifford · Cost: one physical permutation of the fifteen nonzero-vector coordinates; hardware routing is additional and the induced seven-qubit symplectic action must be tracked in a chosen logical basis

References: grassl2013automorphisms

gauge-out to the [[15,1,3]] quantum Reed–Muller block gauge-fixing verified

Level: code conversion with logical-dimension reduction · Cost: measure six independent Z-type normalizer constraints and condition the Pauli frame on their outcomes; only the selected remaining logical qubit is preserved