Pith Number

pith:KABQ2TV7

pith:2026:KABQ2TV7K5DTZQWCOZXAFCXIKI

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Stabilizer R\'enyi entropy of 3-uniform hypergraph states

Daichi Kagamihara, Shunji Tsuchiya

The stabilizer Rényi entropy of 3-uniform hypergraph states equals the rank of a matrix built from their hypergraph structure.

arxiv:2602.23687 v2 · 2026-02-27 · quant-ph

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Claims

C1strongest 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)

C2weakest 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

C3one 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.

References

38 extracted · 38 resolved · 2 Pith anchors

[1] S. Bravyi and A. Kitaev, Universal quantum computa- tion with ideal Clifford gates and noisy ancillas, Phys. Rev. A71, 022316 (2005) 2005

[2] V. Veitch, S. A. Hamed Mousavian, D. Gottesman, and J. Emerson, The resource theory of stabilizer quantum computation, New Journal of Physics16, 013009 (2014) 2014

[3] 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) 2017

[4] The Heisenberg Representation of Quantum Computers 1998 · arXiv:quant-ph/9807006

[5] S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A70, 052328 (2004) 2004

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:59.885525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50030d4ebf57473cc2c2766e028ae8523347d3638e0338763feb3b0780726e6f

Aliases

arxiv: 2602.23687 · arxiv_version: 2602.23687v2 · doi: 10.48550/arxiv.2602.23687 · pith_short_12: KABQ2TV7K5DT · pith_short_16: KABQ2TV7K5DTZQWC · pith_short_8: KABQ2TV7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KABQ2TV7K5DTZQWCOZXAFCXIKI \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 50030d4ebf57473cc2c2766e028ae8523347d3638e0338763feb3b0780726e6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5353b54bc2f7c2d42643f6512a77ce145b6df01d40cabbe3b064744e17b6c4e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-02-27T05:37:52Z",
    "title_canon_sha256": "77067c8e4cb2bc623f48cfa0f02e18b23ba9e84c0815cda0f47fb38482d550b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.23687",
    "kind": "arxiv",
    "version": 2
  }
}