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

• URL: http://arxiv.org/abs/2510.15223v2
• Date: Sat, 25 Oct 2025 00:44:27 GMT
• Title: Game-Theoretic Discovery of Quantum Error-Correcting Codes Through Nash Equilibria
• Authors: Rubén Darío Guerrero,
• Abstract summary: We recast code optimization as strategic interactions between competing objectives, where equilibria generates codes with desired properties.<n>We validate the framework by demonstrating it rediscovers the optimal $[![15,7,3]!]$Cal quantum Hamming code.<n>This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 analysis providing transparent mechanistic insights into why this topology emerges. Applied across six objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, and connectivity enhancement -- the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including $[\![100,50,4]\!]$ with distance-4 protection and 50\% encoding rate, with tractable $O(n^3)$ per-iteration complexity enabling discovery in under one hour. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.

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