Strong electron correlations in quantum chemistry: new approaches from machine learning, quantum computing and time-dependent quantum control

以低计算成本高精度地普遍求解量子多体系统的能力将对人类产生前所未有的影响，使我们能够在计算机芯片上设计和精确计算复杂的分子，在化学、生物医学和材料科学中具有重要应用，而不是在昂贵的实验实验室中。虽然我们还没有完全做到这一点，但有希望的技术即将出现，可以将当前的理论方法扩展到每个分子的几个原子以上。在过去的五年里，新不伦瑞克大学（University of New Brunswick）最近搬迁的量子化学小组（QuNB）及其合作者提出了一种计算上易于处理的gemini理论：一种基于刘易斯电子对前提的强相关分子的电子结构方法，而不是基于分子轨道。Geminal项目产生于理论化学和数学/核物理之间富有成效的交叉受精，其思想来自可积性和年资计划。尽管在Geminal波函数ansatz中编码了很强的量子相关性，但该方法具有良好的计算缩放性，因此其他研究小组目前正在研究更大的系统。虽然目前在加拿大二级研究主席的框架内研究了Geminal理论的数学公式，但目前的发现资助提案超越了传统的电子结构方法，采用了具有颠覆潜力的新兴技术。在三个工作包（WP）中，我们将探索、发展和建立WP1(GemQC)：量子计算设计完全相关的Geminal理论的能力；WP2(ML-DMET)：机器学习与密度矩阵嵌入理论的结合WP3(e-FMD)：费米子分子动力学是由阿秒激光场探测的电子成键和动力学的直观经典图像。该项目将为3名博士生、2名硕士生和多名本科生提供优秀的HQP软硬技能培训机会。理论电子结构理论的硬技能是数学抽象和数值建模，这两种技能在学术界和工业界都有很高的需求。嵌入CRC研究小组将允许对重要软技能（如（国际）合作和独立性）进行高质量培训，同时强烈尊重公平、多样性和包容性。加拿大在机器学习和量子计算的基础和应用方面都处于全球领先地位，因此该研究计划将通过提供在顶级学术期刊上发表的新理论方法，实现这些方法的开源（量子）计算机软件包，作为HQP在该领域的培训，增强加拿大的领先地位。

The ability to universally solve quantum many-body systems at high accuracy with low computational cost would have unprecedented consequences for human kind, allowing us to design and accurately compute sophisticated molecules with important applications in chemical, bio-medical, and material science on computer chips, rather than in expensive experimental laboratories. While we are not quite there yet, promising techniques are on the horizon to scale up current theoretical methods to more than a few atoms per molecule. In the past five years, the recently relocated quantum chemistry group at the University of New Brunswick (QuNB), and collaborators have proposed a computationally tractable Geminal theory: an electronic structure method for strongly correlated molecules based on the premises of Lewis electron pairs, rather than molecular orbitals. The Geminal project emerged from a fruitful cross fertilization between theoretical chemistry and mathematical/nuclear physics with ideas from integrability and the seniority scheme. Notwithstanding the strong quantum correlations encoded in the Geminal wavefunction ansatz, the method has a good computational scaling, so other research groups are currently investigating it for larger systems. While the mathematical formulation of Geminal theory is currently investigated in the framework of a Tier-2 Canada Research Chair, the present Discovery Grant proposal goes beyond traditional electronic structure methods by embracing newly emerged technologies with disrupting potential to the field. In three Work Packages (WP), we will explore, develop and establish WP1(GemQC): the power of Quantum Computing to design a fully correlated Geminal theory; WP2(ML-DMET): the connection between Machine Learning and Density Matrix Embedding Theory; WP3(e-FMD): Fermionic Molecular Dynamics as an intuitive classical picture of electron bonding and dynamics probed by attosecond laser fields. The proposed research program will provide excellent HQP training opportunities in both hard and soft skills for 3 PhD students, 2 MSc students and several undergraduate students. The hard skills that come with theoretical electronic structure theory are mathematical abstraction and numerical modeling, both skills that are in high demand in academia and industry. The embedding within a CRC research group will allow for high-quality training on important soft skills such as (international) collaboration and independence, with strong respect for Equity Diversity and Inclusion. Canada is a global leader in both the fundamentals and applications of Machine Learning and Quantum Computing, so this research program will enhance Canada's leading position, both by delivering new theoretical methods published in top-tier academic journals, open source (quantum) computer software packages that implement those methods, as the training of HQP in that area.