{"paper":{"title":"Geometric-Symmetry Logical Gate and Local-Probe Selectivity in the Three-Leg AKLT Ladder","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jingnuo Han, Youning Li","submitted_at":"2026-08-04T16:04:13Z","abstract_excerpt":"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 log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03861","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03861/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}