CAREER: Uncertainty Quantification for Quantum Computing Algorithms

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。量子计算利用量子态的性质来实现使用经典计算难以处理的计算。人们普遍认为，在未来，量子计算可以彻底改变人们执行和思考计算的方式，并成为科学发现、工程设计、国家安全和商业发展等突破性新技术的支柱。目前，量子计算发展的关键障碍是硬件中的噪声引起的误差。该项目的研究目标是开发方法来模拟量子计算算法中的错误传播，并过滤结果中产生的噪声。这项研究将有助于提高一般量子计算算法在精度和效率方面的性能。这项工作的教育目标是为学生进行跨学科研究做好准备，并促进STEM参与和代表性不足的群体之间的公平。外联活动也涉及K-12学生。研究人员将在以下四个方向开发新的不确定性量化方法，以理解和减轻噪声对量子计算算法的影响：（1）使用认知不确定性模型描述门误差和读出误差的传播;（2）使用约束优化方法和贝叶斯方法减轻误差;（3）分析误差传播的渐近行为;（4）使用认知不确定性模型描述门误差和读出误差的传播。（4）开发一个开源软件包来实现不确定度量化算法。这些新方法将利用贝叶斯推理方法、张量分解技术、随机微分方程的渐近分析工具和高性能计算包，从概率的角度构建“量子数值分析”框架的基础。这个框架是通用的，它可以用来评估现实世界的量子处理器的性能，并评估特定量子计算硬件架构对广泛应用的适用性。该项目由数学科学部：计算数学计划和计算与通信基础部：新兴技术基础计划共同支持。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Quantum computing harnesses properties of quantum states to enable computations that would be intractable using classical computing. It is widely established that, in the future, quantum computing can revolutionize the way one performs and thinks about computation and serve as the backbone of groundbreaking new technologies for scientific discovery, engineering design, national security, and business development, to name a few. Currently, the key barrier in the development of quantum computing is the error induced by the noise in the hardware. The research goal of this project is to develop methods to model the error propagation in quantum computing algorithms and filter the resulting noise in the outcomes. This study will help enhance the performance of general quantum computing algorithms in terms of accuracy and efficiency. The educational goals of this effort are to prepare students for interdisciplinary research and promote STEM participation and equity among underrepresented groups. Outreach activities also involve K-12 students. The investigator will develop new uncertainty quantification methods in the following four directions to understand and alleviate the effect of noise on quantum computing algorithms: (1) describing propagation of gate error and readout error using epistemic uncertainty models; (2) mitigating errors using constrained optimization methods and Bayesian approaches; (3) analyzing asymptotic behavior of the propagation of the error; (4) developing an open-source software package to implement the uncertainty quantification algorithms. These new methods will leverage Bayesian inference approaches, tensor decomposition techniques, asymptotic analysis tools for stochastic differential equations, and high-performance computing packages to build the foundation of a "quantum numerical analysis" framework from a probabilistic perspective. This framework is general, and it can be used to assess the performance of real-world quantum processors and evaluate the suitability of specific quantum computing hardware architectures for a wide range of applications. This project is jointly supported by the Division of Mathematical Sciences: Computational Mathematics Program and the Division of Computing and Communication Foundations: Foundations of Emerging Technologies Program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.