Pith Number

pith:QBJZRFNI

pith:2026:QBJZRFNI6SK44QOAF5CNA6EEC7

not attested not anchored not stored refs pending

Probes of chaos over the Clifford group and approach to Haar values

Alioscia Hamma, Gianluca Esposito, Stefano Cusumano

Expectation values of chaos probes match Haar distribution moments for GUE and T-doped circuits but deviate for GDE.

arxiv:2603.29695 v3 · 2026-03-31 · quant-ph

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\usepackage{pith}
\pithnumber{QBJZRFNI6SK44QOAF5CNA6EEC7}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The expectation values of the probes adhere to moments of the Haar distribution for chaotic behavior modeled by the Gaussian Unitary Ensemble and T-doped circuits, while deviating for the non-chaotic Gaussian Diagonal Ensemble and showing specific behavior on the Toric Code Hamiltonian.

C2weakest assumption

That isospectral twirling with randomly chosen eigenvectors from fixed spectra accurately models the approach to chaotic dynamics in real quantum systems, and that the Gaussian Diagonal Ensemble and Gaussian Unitary Ensemble correctly represent non-chaotic and chaotic regimes respectively.

C3one line summary

Probes of chaos in quantum systems approach Haar distribution moments under T-doped circuits and chaotic GUE ensembles but deviate under non-chaotic GDE ensembles.

Receipt and verification

First computed	2026-06-19T16:10:37.066176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80539895a8f495ce41c02f44d0788417f975feb09971a56da0303163ef02aac9

Aliases

arxiv: 2603.29695 · arxiv_version: 2603.29695v3 · doi: 10.48550/arxiv.2603.29695 · pith_short_12: QBJZRFNI6SK4 · pith_short_16: QBJZRFNI6SK44QOA · pith_short_8: QBJZRFNI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QBJZRFNI6SK44QOAF5CNA6EEC7 \
  | 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: 80539895a8f495ce41c02f44d0788417f975feb09971a56da0303163ef02aac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b22f0657e771104e07ed20335b28317715471f1b4b695a7e049055ea79b9861b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-03-31T12:49:34Z",
    "title_canon_sha256": "7fc43fb8c7afa3445989998ae1f63365904073d74cb409fe42a1e23e6c8285b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.29695",
    "kind": "arxiv",
    "version": 3
  }
}