{"paper":{"title":"Game-Theoretic Discovery of Quantum Error-Correcting Codes Through Nash Equilibria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A game-theoretic framework rediscovers the optimal [[15,7,3]] quantum Hamming code by finding Nash equilibria among competing objectives.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Rub\\'en Dar\\'io Guerrero","submitted_at":"2025-10-17T01:11:32Z","abstract_excerpt":"Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking mechanistic interpretability. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. 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 analys"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A game-theoretic framework rediscovers the optimal [[15,7,3]] quantum Hamming code by finding Nash equilibria among competing objectives.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1d73a1610e63331be3075e4d0bf339fa17edb607c1f792aa8a5f82e256473653"},"source":{"id":"2510.15223","kind":"arxiv","version":4},"verdict":{"id":"bcc55852-a17d-4ae9-974f-556bd7dfb9aa","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T06:58:38.204987Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"A game-theoretic framework rediscovers the optimal [[15,7,3]] quantum Hamming code by finding Nash equilibria among competing objectives."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.15223/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"cf7cdf60849aa660d3f41d14ad5f49693fbd0272cace56a1b56db61bb6608a21"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}