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普遍求解量子多体系统的能力将给人类带来前所未有的后果，使我们能够在计算机芯片上设计和精确计算在化学、生物医学和材料科学中具有重要应用的复杂分子，而不是在昂贵的实验实验室。虽然我们还没有完全做到这一点，但有希望的技术已经出现，可以将当前的理论方法扩大到每个分子几个以上的原子。 在过去的五年里，新不伦瑞克大学(QuNB)最近重新定位的量子化学小组及其合作者提出了一种易于计算的双子理论：一种基于Lewis电子对的前提而不是分子轨道的强关联分子的电子结构方法。Gemina项目产生于理论化学和数学/核物理之间卓有成效的交叉培养，其想法来自可积性和优先方案。尽管Geminal波函数ansatz中编码了很强的量子关联，但该方法具有很好的计算伸缩性，因此其他研究小组目前正在对更大的系统进行研究。 虽然Gemina理论的数学公式目前在加拿大二级研究教席的框架内进行研究，但目前的发现赠款提案超越了传统的电子结构方法，采用了对该领域具有颠覆性潜力的新技术。在三个工作包(WP)中，我们将探索、开发和建立 WP1(GemQC)：量子计算设计完全相关双子理论的能力； WP2(ML-DMET)：机器学习与密度矩阵嵌入理论之间的联系 WP3(e-FMD)：费米子分子动力学作为阿秒激光场探测的电子成键和动力学的直观经典图像。 拟议的研究计划将为3名博士生、2名硕士学生和几名本科生提供绝佳的HQP硬技能和软技能培训机会。理论电子结构理论带来的困难技能是数学抽象和数值建模，这两项技能在学术界和工业界都很受欢迎。在《儿童权利公约》研究小组内的安排将使人们能够在高度尊重公平多样性和包容性的情况下，就(国际)合作和独立等重要软技能进行高质量的培训。 加拿大在机器学习和量子计算的基础和应用方面处于全球领先地位，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)计算机软件包以及该领域的HQP培训来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.