A Game Theoretic Approach for Optimizing Quantum Error Budget Distribution
For quantum computing researchers, this provides a principled method to reduce physical resource overhead in fault-tolerant quantum circuits, addressing a key bottleneck in scalable quantum computing.
A game-theoretic approach optimizes error budget distribution in fault-tolerant quantum computing, achieving an average 30.22% reduction in physical resource requirements across 433 benchmarks, with peak improvements of 97.81%.
Current fault-tolerant quantum compilers allocate error budgets uniformly during resource estimation, causing suboptimal physical resource overhead. We optimize this allocation using a potential game formulation, where Nash Equilibrium yields a Pareto-optimal distribution across logical operations, T-state distillation, and rotation synthesis. An iterated best response (IBR) algorithm converges to this equilibrium through monotonic descent of the shared cost function. Evaluation across 433 MQT benchmarks demonstrates an average reduction of 30.22\% in physical resource requirements relative to uniform baselines, with peak improvements of 97.81\% for specific circuit instances. This establishes a game-theoretic foundation for strategic error budget optimization in fault-tolerant quantum design automation.