用数学方法量化量子计算中的噪声与随机性，提升结果可靠性。
Uncertainty Quantification for Quantum Computing
- 以统计推断为基础，用概率建模和贝叶斯分析处理量子误差。
- 揭示了噪声传播与相关误差特征对计算结果的影响机制。
- 适合数学、计算科学与量子信息交叉研究者阅读。
本文从不确定性量化（UQ）视角出发，为数学家与计算科学家提供量子计算的严谨且易懂的叙述，阐述噪声与内在随机性如何在数学语言下影响量子计算结果。通过将量子计算建立在统计推断基础上，强调概率建模、随机分析、贝叶斯推断与敏感性分析等工具可直接应对当前量子设备中的误差传播与可靠性挑战。文中还关联这些方法与领域关键目标，如可扩展的不确定性感知算法及相关误差表征。旨在弥合应用数学、科学计算与量子信息科学之间的概念鸿沟，展示以数学为基础的UQ方法如何指导验证、误差缓解与严谨算法设计，应对现代高性能与容错量子计算所面临的挑战与机遇。
原文摘要 · Abstract (English)
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for understanding how noise and intrinsic randomness shape quantum computational outcomes in the language of mathematics. By grounding quantum computation in statistical inference, we highlight how mathematical tools such as probabilistic modeling, stochastic analysis, Bayesian inference, and sensitivity analysis, can directly address error propagation and reliability challenges in today's quantum devices. We also connect these methods to key scientific priorities in the field, including scalable uncertainty-aware algorithms and characterization of correlated errors. The purpose is to narrow the conceptual divide between applied mathematics, scientific computing and quantum information sciences, demonstrating how mathematically rooted UQ methodologies can guide validation, error mitigation, and principled algorithm design for emerging quantum technologies, in order to address challenges and opportunities present in modern-day quantum high performance and fault-tolerant quantum computing paradigms.
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