{"paper":{"title":"Extensive long-range magic in non-Abelian topological orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Non-Abelian topological orders exhibit extensive long-range magic in low-energy states, which cannot be removed by constant-depth circuits and distinguishes them via a no-go theorem from stabilizer states.","cross_cats":["cond-mat.str-el","cs.CC","hep-th"],"primary_cat":"quant-ph","authors_text":"Isaac H. Kim, Sagar Vijay, Yimu Bao, Yuzhen Zhang","submitted_at":"2026-05-14T17:50:20Z","abstract_excerpt":"We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit. This refines conventional notions of complexity beyond the linear circuit depth which is required to prepare any topological phase, and provides a new resource-theoretic characterization of topological orders. A central technical result is a no-go theorem establishing that stabilizer states--even up to constant-depth local unitarie--cannot approximate low-energy states of non-Abelian string-net models which satisf"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The states satisfy the entanglement bootstrap axioms for non-Abelian string-net models.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-Abelian topological orders exhibit extensive long-range magic in low-energy states, which cannot be removed by constant-depth circuits and distinguishes them via a no-go theorem from stabilizer states.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"7a678503c0c8f240a98adef51e3a2d639d7b85588c3497c3e93fac137481989f"},"source":{"id":"2605.15150","kind":"arxiv","version":1},"verdict":{"id":"a06d0150-0caa-48db-bf22-49e7ac96fd0d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:19:06.284496Z","strongest_claim":"We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit.","one_line_summary":"Non-Abelian topological orders exhibit extensive long-range magic in low-energy states, which cannot be removed by constant-depth circuits and distinguishes them via a no-go theorem from stabilizer states.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The states satisfy the entanglement bootstrap axioms for non-Abelian string-net models.","pith_extraction_headline":""},"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"}