Pith Number

pith:VUNTQP5M

pith:2025:VUNTQP5MZZPQO6RNGR3R26S3VL

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Code Swendsen-Wang Dynamics

Dominik Hangleiter, Nathan Ju, Umesh Vazirani

Code Swendsen-Wang dynamics mixes rapidly for the 4D toric code and other code Hamiltonians with efficient Gibbs samplers.

arxiv:2510.08446 v3 · 2025-10-09 · quant-ph · math-ph · math.MP · math.PR

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4 Citations open

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Claims

C1strongest claim

We establish Code Swendsen-Wang dynamics as the right generalization of Swendsen-Wang dynamics for the Ising model to quantum and classical code Hamiltonians: it mixes rapidly for all previously known code Hamiltonians with efficient Gibbs samplers, resolves the central open case of the 4D toric code, and meets fundamental barriers exactly at first-order phase transitions.

C2weakest assumption

The newly defined global updates in Code Swendsen-Wang dynamics are correctly formulated so that the resulting Markov chain is ergodic and its mixing-time analysis applies to arbitrary code Hamiltonians, including the 4D toric code.

C3one line summary

Code Swendsen-Wang dynamics generalizes classical Swendsen-Wang to quantum and classical code Hamiltonians, achieving rapid mixing for known cases including the open 4D toric code case while hitting barriers at first-order transitions.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T01:05:38.569295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad1b383facce5f077a2d34771d7a5baadb700aea4907d67ddbe310015638894e

Aliases

arxiv: 2510.08446 · arxiv_version: 2510.08446v3 · doi: 10.48550/arxiv.2510.08446 · pith_short_12: VUNTQP5MZZPQ · pith_short_16: VUNTQP5MZZPQO6RN · pith_short_8: VUNTQP5M

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VUNTQP5MZZPQO6RNGR3R26S3VL \
  | 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: ad1b383facce5f077a2d34771d7a5baadb700aea4907d67ddbe310015638894e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7bd684d7c9f518e060cad178751d5bf7d0343cb73cb91bf27b4d463073c5428",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-10-09T16:54:39Z",
    "title_canon_sha256": "d71e1cc70f67b480dd3c1c0f98de9585ebc482898a0e36849e60ac65d7914a9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.08446",
    "kind": "arxiv",
    "version": 3
  }
}