Uncertainty Quantification for Quantum Computing

2026-03-26

AI Summary

This work addresses the challenge of error propagation and unreliable outcomes in noisy quantum computing, arising from both hardware noise and intrinsic stochasticity. It introduces, for the first time, a systematic uncertainty quantification (UQ) framework into quantum computation by formulating the problem as a statistical inference task. By integrating tools from probabilistic modeling, Bayesian inference, stochastic analysis, and sensitivity analysis, the study establishes a novel paradigm for error characterization and algorithm design tailored to noisy intermediate-scale quantum (NISQ) devices. The proposed uncertainty-aware framework is not only scalable but also provides a unified and mathematically rigorous foundation for error verification, characterization, and mitigation strategies.

Abstract

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.

Problem

• Uncertainty Quantification
• Quantum Computing
• Noise
• Error Propagation
• Reliability

Innovation

• Uncertainty Quantification
• Quantum Computing
• Probabilistic Modeling
• Bayesian Inference
• Error Mitigation