aiqbench analysis
This research investigates how geometric symmetries in the three-leg AKLT ladder model protect boundary-encoded quantum information against local noise. By deriving selection rules based on Wigner-Eckart theorem, the study quantifies decay lengths and identifies finite-size channels independent of probe position, offering theoretical insights for topological qubit design.
Geometric-Symmetry Logical Gate and Local-Probe Selectivity in the Three-Leg AKLT Ladder
arXiv:2608.03861v1 Announce Type: new Abstract: Symmetry-protected topological (SPT) phases provide a platform for encoding quantum information in protected boundary degrees of freedom. Here we study the three-leg Affleck-Kennedy-Lieb-Tasaki (AKLT) ladder as an exactly solvable SPT system with on-site symmetry $SO(3)\times \mathbb{Z}_2$. Using an exact matrix product state construction, we characterize the symmetry action on the edge encoding space and the accessibility of this space by local operators. We find that the continuous $SO(3)$ symmetry induces boundary rotations, while the leg-exchange symmetry generates a geometry-dependent logical permutation of edge qubits. Furthermore, by introducing a distinguishability measure motivated by the Knill--Laflamme condition, we derive a symmetry-resolved decay law for local accessibility. The decay is controlled by a selection rule raised from the Wigner--Eckart theorem, whereby a rank-$\ell$ local operator couples only to the $\mathcal L=\ell$ transfer-matrix sector, with a decay length determined by the corresponding correlation length. We further identify a finite-size channel that is independent of the probe operator position. These results establish a quantitative connection between SPT symmetry, lattice geometry, and the protection of boundary-encoded quantum information.
Abstract:Symmetry-protected topological (SPT) phases provide a platform for encoding quantum information in protected boundary degrees of freedom. Here we study the three-leg Affleck-Kennedy-Lieb-Tasaki (AKLT) ladder as an exactly solvable SPT system with on-site symmetry $SO(3)\times \mathbb{Z}_2$. Using an exact matrix product state construction, we characterize the symmetry action on the edge encoding space and the accessibility of this space by local operators. We find that the continuous $SO(3)$ symmetry induces boundary rotations, while the leg-exchange symmetry generates a geometry-dependent logical permutation of edge qubits. Furthermore, by introducing a distinguishability measure motivated by the Knill--Laflamme condition, we derive a symmetry-resolved decay law for local accessibility. The decay is controlled by a selection rule raised from the Wigner--Eckart theorem, whereby a rank-$\ell$ local operator couples only to the $\mathcal L=\ell$ transfer-matrix sector, with a decay length determined by the corresponding correlation length. We further identify a finite-size channel that is independent of the probe operator position. These results establish a quantitative connection between SPT symmetry, lattice geometry, and the protection of boundary-encoded quantum information.
57 pages, 3 figures. Comments welcome
arXiv:2608.03861 [quant-ph]
(or arXiv:2608.03861v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.03861 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 269 words
