{"paper":{"title":"Stabilizer R\\'enyi entropy of 3-uniform hypergraph states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The stabilizer Rényi entropy of 3-uniform hypergraph states equals the rank of a matrix built from their hypergraph structure.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Daichi Kagamihara, Shunji Tsuchiya","submitted_at":"2026-02-27T05:37:52Z","abstract_excerpt":"Nonstabilizerness, also known as magic, plays a central role in universal quantum computation. Hypergraph states are nonstabilizer generalizations of graph states and constitute a key class of quantum states in various areas of quantum physics, such as the demonstration of quantum advantage, measurement-based quantum computation, and the study of topological phases. In this work, we investigate nonstabilizerness of 3-uniform hypergraph states, which are solely generated by controlled-controlled-Z gates, in terms of the stabilizer R\\'{e}nyi entropy (SRE). We find that the SRE of 3-uniform hyper"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the SRE of 3-uniform hypergraph states can be expressed using the matrix rank, which reduces computational cost from O(2^{3N}) to O(N^3 2^N)","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"that the states are generated solely by controlled-controlled-Z gates on triples and that the stabilizer Rényi entropy definition applies without additional phase or normalization factors that would alter the rank mapping","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Stabilizer Rényi entropy of 3-uniform hypergraph states equals a matrix-rank expression, cutting computation from exponential in 3N to polynomial in N times exponential in N.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The stabilizer Rényi entropy of 3-uniform hypergraph states equals the rank of a matrix built from their hypergraph structure.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"613760bb7a8b24da3b8c1a0931e7011771988c705121c2db0ff81afc32cb6764"},"source":{"id":"2602.23687","kind":"arxiv","version":2},"verdict":{"id":"ce33f4df-b748-4ecc-b671-c94fea68ef39","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T19:09:51.891714Z","strongest_claim":"the SRE of 3-uniform hypergraph states can be expressed using the matrix rank, which reduces computational cost from O(2^{3N}) to O(N^3 2^N)","one_line_summary":"Stabilizer Rényi entropy of 3-uniform hypergraph states equals a matrix-rank expression, cutting computation from exponential in 3N to polynomial in N times exponential in N.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"that the states are generated solely by controlled-controlled-Z gates on triples and that the stabilizer Rényi entropy definition applies without additional phase or normalization factors that would alter the rank mapping","pith_extraction_headline":"The stabilizer Rényi entropy of 3-uniform hypergraph states equals the rank of a matrix built from their hypergraph structure."},"references":{"count":38,"sample":[{"doi":"","year":2005,"title":"S. Bravyi and A. Kitaev, Universal quantum computa- tion with ideal Clifford gates and noisy ancillas, Phys. Rev. A71, 022316 (2005)","work_id":"40406162-7b81-4b34-ace7-2d7907fe835c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"V. Veitch, S. A. Hamed Mousavian, D. Gottesman, and J. Emerson, The resource theory of stabilizer quantum computation, New Journal of Physics16, 013009 (2014)","work_id":"0aa1d1bb-3f70-4312-bdf4-5290533e2e72","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"M. Howard and E. Campbell, Application of a resource theory for magic states to fault-tolerant quantum com- puting, Phys. Rev. Lett.118, 090501 (2017)","work_id":"572ee163-20df-41fc-a53e-9f3233e7279a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"The Heisenberg Representation of Quantum Computers","work_id":"64ad356b-b16b-40e9-8055-ea3eb48cb88f","ref_index":4,"cited_arxiv_id":"quant-ph/9807006","is_internal_anchor":true},{"doi":"","year":2004,"title":"S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A70, 052328 (2004)","work_id":"f3f3f051-fc77-4a15-99c3-6c98bb44c5c5","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":38,"snapshot_sha256":"11ddc6b36d78418918b6973cba5ab9d60508bfc6d584999bae4b7070b42d5510","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5c79ccfbfffc74b17bf2c6a5456fa3a1719a54457471681f4a3551dc1c36665a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}