Quantum Integrability

该奖项资助了迈阿密大学物理系Rafael Nepomechie教授的研究活动。这个项目位于两个重要发展项目的交汇处。一方面，基本粒子标准模型的提出是20世纪最伟大的科学成就之一。然而，这个模型，以及许多其他的数学模型，不能用来对涉及强相互作用的过程做出准确的预测，因为相应的方程变得太难解了。所谓的量子可积模型位于理论物理学的“甜蜜点”：它们足够复杂，可以描述有趣的物理学，但它们又足够简单，可以对一些有趣的物理量进行精确的分析计算。因此，可积性已成为当代理论物理学的主要指导原则之一。另一方面，以量子比特为基础的量子计算机（不像传统计算机那样以0和1为基础）正以惊人的速度发展。事实上，这种装置的发展和应用是国家的优先事项。量子系统的模拟被广泛认为是量子计算机在经济上有用的应用的最佳镜头之一。在这项资助下，Nepomechie教授将在量子计算机上模拟量子可积模型。他还将研究量子可积性的基础和应用。预计该项目还将产生更广泛的重大影响。Nepomechie教授将通过教学和指导，为迈阿密的高中生、本科生和研究生以及非洲数学科学研究所（AIMS）各中心的学生提供科学培训，为下一代科学家提供科学培训。他还将继续进行公开演讲并参与其他推广活动，并将继续担任Journal of Physics A的编辑委员会和SciPost Physics编辑学院的成员。从技术上讲，Nepomechie教授和他的同事将开发算法，用于在量子计算机上准备迪克态及其推广，并探索它们的性质。这些高度纠缠态是准备贝特态的一些算法的起点，而且它们本身也很有趣。他还将开发用于准备可积模型的精确特征态的算法。Nepomechie教授还将继续研究量子可积性的基础和应用。他将与欧洲的同事一起研究可积量子自旋链，其连续极限由所谓的黑洞共形场论描述，具有非紧化自由度。他还将研究二部纠缠熵的计算、量子谱曲线（QSC）和高阶链的代数贝特分析。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。

This award funds the research activities of Professor Rafael Nepomechie in the Department of Physics at the University of Miami.This project lies at the intersection of two important developments. On the one hand, the formulation of the Standard Model of elementary particles is one of the greatest scientific accomplishments of the 20th century. However, this model, as well as many other mathematical models, cannot be used to make accurate predictions of processes involving strong interactions, as the corresponding equations become too difficult to solve. So-called quantum integrable models lie in the "sweet spot” of theoretical physics: they are sufficiently complicated to describe interesting physics, yet they are sufficiently simple to allow for exact analytical computations of some quantities of physical interest. Integrability has therefore become one of the main guiding principles in contemporary theoretical physics. On the other hand, quantum computers, which operate on quantum bits (unlike conventional computers, which operate on 0's and 1's), are advancing at an astonishing rate. Indeed, the development and application of such devices are national priorities. The simulation of quantum systems is widely regarded as one of the best shots at an economically useful application of quantum computers. Under this grant award, Professor Nepomechie will work on the simulation of quantum integrable models on quantum computers. He will also work on the foundations and applications of quantum integrability. This project is also envisioned to have significant broader impacts. Professor Nepomechie will provide scientific training to the next generation of scientists through teaching and mentoring, reaching Miami high-school, undergraduate, and graduate students, as well as students in Africa at centers of the African Institute for Mathematical Sciences (AIMS). He will also continue to give public lectures and engage in other outreach activities, and will continue serving on the Editorial Board of Journal of Physics A and in the Editorial College of SciPost Physics.More technically, Professor Nepomechie and his coworkers will develop algorithms for preparing Dicke states and their generalizations on quantum computers, and explore their properties. These highly-entangled states are the starting points of some algorithms for preparing Bethe states, and are also of interest in their own right. He will also develop algorithms for preparing exact eigenstates of integrable models. Professor Nepomechie will also continue working on the foundations and applications of quantum integrability. Together with coworkers in Europe, he will investigate integrable quantum spin chains whose continuum limits are described by so-called black-hole conformal field theories, with non-compact degrees of freedom. He will also work on computations of bipartite entanglement entropies, the Quantum Spectral Curve (QSC), and algebraic Bethe ansatz for higher-rank chains.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.