EAGER: Quantum Algorithms for Solving Computational Mechanics Problems in Hybrid Quantum Computers

量子计算在过去几年中受到了国内外的极大关注。这是因为物理学、数学和计算机科学的研究，以及硬件和软件技术已经取得了几个关键的里程碑，这些里程碑证明了量子计算在改变我们在工程、科学等领域如何计算和计算什么的许多方面的潜力。尽管取得了如此重大的进步，但用量子计算解决重要的工程问题仍然是一个遥远的前景，从硬件和软件以及量子算法发展的角度来看，仍有几个基础研究问题有待解决。这个探索性研究（EAGER）研究奖将探索解决工程材料和结构的机械响应的量子算法。有限元法是预测材料和结构力学行为最成功和最常用的方法。本研究的重点是研究新型量子有限元算法在求解力学问题时是否以及如何优于经典有限元算法。作为拨款的一部分，还将开发教育内容，向工程界的广大领域介绍量子计算在解决经典工程问题中的应用。这项EAGER研究的目标是设计和研究量子计算算法，用于解决今天可用或即将可用的噪声中等规模量子计算机中的连续介质力学问题。本研究将建立并分析评估静态加载条件下线弹性问题的算法。实现既定目标的具体研究目标是：(1)基于变分量子线性求解器方法开发量子有限元方法的算法结构框架；(2)分析量子算法相对于经典算法在复杂度、精度和收敛性方面的计算性能；(3)使用基于门的架构和量子计算模拟器的现有量子计算机验证和验证所提出的量子框架的性能。由于有限元方法的一些求解过程要么需要要么更适合经典计算机，而且由于目前可用的量子计算机在其可以执行的操作中受到限制，因此本研究将研究适合混合（经典-量子）计算机的算法。该奖项反映了美国国家科学基金会的法定使命，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。

Quantum computing has received tremendous national and international attention in the past few years. This is because research in physics, mathematics, and computer science, as well as hardware and software technology have achieved several critical milestones that demonstrate the potential of quantum computing in revolutionizing many aspects of how and what we compute in engineering, science, and beyond. Despite such significant advancements, solving important engineering problems with quantum computing remains a distant prospect with several fundamental research questions remain to be addressed from the hardware and software, and from the quantum algorithm development perspectives. This Early-Concept Grants for Exploratory Research (EAGER) research award will explore quantum algorithms for solving the mechanical response of engineering materials and structures. The finite element method is the most successful and commonly used approach to predict the mechanical behavior of materials and structures. The focus of this research is to study whether and how novel quantum finite element algorithms could outperform classical finite element algorithms in solving mechanics problems. As part of the grant, educational content will also be developed to introduce the use of quantum computing in solving classical engineering problems to a broad section of the engineering community. The objective of this EAGER research is to devise and investigate quantum computing algorithms for solving continuum mechanics problems in Noisy Intermediate-Scale Quantum computers that are available today or will be available soon. This research will establish and analyze algorithms for evaluating linear elasticity problems subjected to static loading conditions. The specific research objectives to achieve the stated goal are: (1) to develop a framework for the algorithmic structure of quantum finite element method based on the Variational Quantum Linear Solver approach; (2) to analyze the computational performance of the quantum algorithms relative to classical algorithms in terms of complexity, accuracy and convergence; and (3) to verify and validate the performance of the proposed quantum framework using existing quantum computers with gate-based architectures and quantum computing simulators. Since some of the solution procedures for the finite element method either require or are better suited for classical computers, and since currently available quantum computers are limited in the operations they can perform, this research will study algorithms suitable for hybrid (classical-quantum) computers.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.