A Game Theoretic Approach for Optimizing Quantum Error Budget Distribution

2026-04-16

AI Summary

This work addresses the suboptimal physical resource overhead in existing fault-tolerant quantum compilers, which typically employ uniform error budget allocation strategies. To overcome this limitation, the paper introduces, for the first time, a game-theoretic framework that formulates error budget allocation as a potential game among logical operations, T-state distillation, and rotation synthesis. By leveraging Nash equilibrium, the approach achieves a Pareto-optimal distribution of the error budget across these components. An Iterative Best Response (IBR) algorithm is developed to efficiently compute this equilibrium. Experimental evaluation on 433 MQT benchmark circuits demonstrates that the proposed method reduces physical resource requirements by 30.22% on average, with improvements reaching up to 97.81% in certain instances, thereby substantially enhancing system-level resource efficiency.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• quantum error budget
• fault-tolerant quantum computing
• resource overhead
• error allocation
• quantum compilation

Innovation

• quantum error budget
• potential game
• Nash Equilibrium
• fault-tolerant quantum compilation
• iterated best response