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arXiv · 2510.15223

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

Rubén Darío Guerrero
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Abstract

Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking equilibrium-topology analysis. 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 in 20\% of independent runs (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 $\mathcal{F}_Q$ (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 $O(n^3)$ 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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BibTeXRIS

Rubén Darío Guerrero. 2025-10-17. Game-Theoretic Discovery of Quantum Error-Correcting Codes Through Nash Equilibria. https://arxiv.org/abs/2510.15223

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