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 seven objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, connectivity enhancement, and maximization of the quantum Fisher information F_Q (which quantifies, via the Cram\'er--Rao bound, the metrological sensitivity of the encoded codespace) -- 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(n³) 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.