The many-body problem in the age of quantum machine learning

该奖项支持理论和计算研究，旨在开发和应用新的机器学习算法和计算工具，以研究电子-电子相互作用非常强的量子材料的新特性。这些材料可以作为具有半导体范例之外的新功能的器件的构建块。另一方面，这样的系统的数值建模是具有挑战性的，因为它需要处理一个大的配置空间：数据集由所有可能的电子配置组成，不能存储在最大的超级计算机的内存中。因此，从信息处理的角度来看，强相互作用多电子问题可以被解释为“极端数据科学”问题。解决这种复杂性的一个改变游戏规则的想法包括识别模式和压缩数据集，其精神与压缩图像和视频的算法非常相似。在过去的五年里，出现了一个新的研究方向，现在被称为“量子机器学习”，它使用神经网络和机器学习算法来提取有洞察力的信息，并表示量子力学状态中编码的复杂结构。在这个项目中，PI将开发基于量子信息和机器学习思想的新算法，以研究各种强相互作用模型系统和真实材料的电子和磁性。该奖项还支持一些教育和外展活动。PI将(i)与东北大学的STEM教育中心合作，通过研讨会和演讲丰富目前为高中和社区大学学生和教师提供的项目，以及（ii）建立一个广泛的项目，在服务不足的社区，在有大量少数民族学生的社区，对高中进行班级访问，让他们接触科学研究。与此同时，将为想要选择科学职业道路的学生创建一个全年指导计划。此外，PI将继续组织国际量子物质研讨会系列，该研讨会将在Zoom和YouTube上进行直播。最后，PI将继续维护和开发一个开源的程序和库集合，用于模拟强相关量子晶格模型，目前正在被全球数十名研究人员和学生使用。该奖项支持理论和计算研究，旨在开发和应用新的机器学习算法和计算工具，以研究强相关量子材料的新型电子和磁性能。研究主要包括两个方向。在第一个项目中，PI和他的团队将开发几种新的算法来研究基态、激发光谱和量子多体问题的热力学，使用神经网络和高斯过程作为近似器。在第二个重点中，他们将研究具有远程相互作用的相互作用链和阶梯，这些相互作用实现了实际的自发对称破缺和真正的远程秩序，从而使人们能够研究目前无法达到的阶段之间的竞争。该奖项还支持一些教育和外展活动。PI将(i)与东北大学的STEM教育中心合作，通过研讨会和演讲丰富目前为高中和社区大学学生和教师提供的项目，以及（ii）建立一个广泛的项目，在服务不足的社区，在有大量少数民族学生的社区，对高中进行班级访问，让他们接触科学研究。与此同时，将为想要选择科学职业道路的学生创建一个全年指导计划。此外，PI将继续组织国际量子物质研讨会系列，该研讨会将在Zoom和YouTube上进行直播。最后，PI将继续维护和开发用于模拟强相关量子晶格模型的ALPS开源程序和库，目前全球数十名研究人员和学生正在使用这些程序和库。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。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research with an aim to develop and apply new machine learning algorithms and computational tools for investigating novel properties of quantum materials in which the electron-electron interactions are very strong. These materials can serve as building blocks for devices with new functionalities beyond the semiconductor paradigm. Numerical modeling of such systems, on the other hand, is challenging, as it requires dealing with a large configuration space: Datasets are comprised of all possible electronic configurations and cannot be stored in the memory of the largest supercomputer. Hence, the strongly interacting many-electron problem can be interpreted as an “extreme data science” problem from an information processing perspective. A game-changing idea that tackles this complexity consists of identifying patterns and compressing datasets in a spirit very similar to algorithms to compress images and videos. In the past five years, a novel line of research, now referred to as “quantum machine learning”, has emerged that uses neural networks and machine-learning algorithms to extract insightful information and represent the complex structure encoded in quantum mechanical states. In this project, the PI will develop new algorithms based on quantum information and machine-learning ideas to study the electronic and magnetic properties of a variety of strongly-interacting model systems and real materials. This award also supports several educational and outreach activities. The PI will (i) work in collaboration with the Center for STEM Education at Northeastern to enrich current program offerings for high school and community college students and teachers through seminars and presentations, and (ii) establish a broad reaching program of class visits to high schools in underserved communities with a large population of minority students to expose them to scientific research. In conjunction, a year-round mentoring program will be created for students who want to choose a scientific career path. In addition, the PI will continue to organize the International Quantum Matter Seminar series, which is live streamed on Zoom and YouTube. Finally, the PI will continue to maintain and develop an open-source collection of programs and libraries for the simulation of strongly correlated quantum lattice models, that is currently being used by dozens of researchers and students around the globe.TECHNICAL SUMMARYThis award supports theoretical and computational research with an aim to develop and apply new machine learning algorithms and computational tools for investigating novel electronic and magnetic properties of strongly correlated quantum materials. The research consists of two main directions. In the first thrust, the PI and his team will develop several new algorithms to study ground-state, excitation spectra, and thermodynamics of quantum many-body problems using neural networks and Gaussian processes as approximators. In the second thrust, they will study interacting chains and ladders with long-range interactions that realize actual spontaneous symmetry breaking and true long-range order, thus enabling one to study competition between phases that are currently out of reach. This award also supports several educational and outreach activities. The PI will (i) work in collaboration with the Center for STEM Education at Northeastern to enrich current program offerings for high school and community college students and teachers through seminars and presentations, and (ii) establish a broad reaching program of class visits to high schools in underserved communities with a large population of minority students to expose them to scientific research. In conjunction, a year-round mentoring program will be created for students who want to choose a scientific career path. In addition, the PI will continue to organize the International Quantum Matter Seminar series, which is live streamed on Zoom and YouTube. Finally, the PI will continue to maintain and develop the ALPS open-source collection of programs and libraries for the simulation of strongly correlated quantum lattice models, that is currently being used by dozens of researchers and students around the globe.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.