A rank-ℓ local operator on the three-leg AKLT ladder reads boundary-encoded qubits only through the L=ℓ transfer-matrix sector, with decay length ξ(L=ℓ), and leg exchange generates a multi-qubit SWAP gate.
16) ug :A s →A s g = X s′ [ug]ss′As′ =α g V(g)A sV(g) −1, α g =±1,(G1) 44 whereu(g) is the physical representation andV(g) =u 1/2(g)⊗3 acts on the virtual space V= (C 2)⊗3
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Geometric-Symmetry Logical Gate and Local-Probe Selectivity in the Three-Leg AKLT Ladder
A rank-ℓ local operator on the three-leg AKLT ladder reads boundary-encoded qubits only through the L=ℓ transfer-matrix sector, with decay length ξ(L=ℓ), and leg exchange generates a multi-qubit SWAP gate.