Pith Number

pith:QQDJRXCA

pith:2025:QQDJRXCAAZXTK7NPTZO2AGD3TD

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Game-Theoretic Discovery of Quantum Error-Correcting Codes Through Nash Equilibria

Rub\'en Dar\'io Guerrero

A game-theoretic framework rediscovers the optimal [[15,7,3]] quantum Hamming code by finding Nash equilibria among competing objectives.

arxiv:2510.15223 v4 · 2025-10-17 · quant-ph

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\usepackage{pith}
\pithnumber{QQDJRXCAAZXTK7NPTZO2AGD3TD}

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Record completeness

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2 Internet Archive

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

We validate the framework by demonstrating it rediscovers the optimal [[15,7,3]] quantum Hamming code (Calderbank-Shor-Steane 1996) from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges.

C2weakest assumption

That Nash equilibria arising from strategic interactions among the seven competing objectives will systematically produce codes with the targeted properties even when no algebraic structure is supplied in advance.

C3one line summary

A game-theoretic approach using Nash equilibria rediscovers the [[15,7,3]] quantum Hamming code without algebraic priors and generates new code families up to 100 qubits across seven objectives.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-28T01:04:31.702103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

840698dc40066f357daf9e5da0187b98d6f99e2d4411e94c526ea05b00a6c758

Aliases

arxiv: 2510.15223 · arxiv_version: 2510.15223v4 · doi: 10.48550/arxiv.2510.15223 · pith_short_12: QQDJRXCAAZXT · pith_short_16: QQDJRXCAAZXTK7NP · pith_short_8: QQDJRXCA

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/QQDJRXCAAZXTK7NPTZO2AGD3TD \
  | 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: 840698dc40066f357daf9e5da0187b98d6f99e2d4411e94c526ea05b00a6c758

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58abdf51a08cdca15c4c16958904e4b9e8a4ebb742fd31f708a463157f80e308",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-10-17T01:11:32Z",
    "title_canon_sha256": "82a09e98a7df2b248a52b73329c3fe9da236a1ad6496142bf1797fa1636c198d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.15223",
    "kind": "arxiv",
    "version": 4
  }
}