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.
The results are summarized in Table IV
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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.