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超越半导体范式的新功能的器件的构建块。另一方面，这类系统的数值建模具有挑战性，因为它需要处理大的配置空间：数据集由所有可能的电子配置组成，无法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，出现了一种新的研究方向，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见地的信息，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的材料的电子和磁性。该奖项还支持一些教育和推广活动。 PI将（i）与东北部STEM教育中心合作，通过研讨会和演讲丰富高中和社区大学学生和教师的现有课程，以及（ii）建立一个广泛的课程访问计划，在服务不足的社区，有大量少数民族学生的高中，让他们接触科学研究。 此外，PI还将继续组织国际量子物质研讨会系列，并在Zoom和YouTube上进行直播。最后，PI将继续维护和开发用于强相关量子晶格模型模拟的程序和库的开源集合，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，以研究新的电子和磁性。强相关量子材料的性质。研究包括两个主要方向。在第一个推力中，PI和他的团队将开发几种新的算法，使用神经网络和高斯过程作为近似器来研究量子多体问题的基态，激发光谱和热力学。在第二个推力中，他们将研究具有长程相互作用的相互作用链和梯子，实现实际的自发对称性破缺和真正的长程有序，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推广活动。 PI将（i）与东北部STEM教育中心合作，通过研讨会和演讲丰富高中和社区大学学生和教师的现有课程，以及（ii）建立一个广泛的课程访问计划，在服务不足的社区，有大量少数民族学生的高中，让他们接触科学研究。 此外，PI还将继续组织国际量子物质研讨会系列，并在Zoom和YouTube上进行直播。最后，PI将继续维护和开发ALPS开源程序集和库，用于强相关量子晶格模型的模拟，目前地球仪的数十名研究人员和学生正在使用该程序集和库。该奖项反映了NSF的法定使命，并通过使用基金会的智力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.