A hybrid approach to quantum dynamics based on the integration of quantum calculations and machine learning

量子力学提供了对分子动力学的最准确描述，分子动力学决定了微观化学反应以及量子材料的结构和功能。然而，复杂分子系统的完全量子描述是困难的。本工作旨在利用量子动力学理论和机器学习的最新发展，以开发量子动力学的新方法。其目标是开发如下量子方法：(1)比目前确定的方法需要更少的计算资源；(2)不仅产生量子可观测数据，而且还产生由于求解薛定谔方程的困难而造成的这些可观测数据的不确定性；(3)将分子动力学的量子理论与实验观测相结合，以改进对微观分子相互作用的描述；(4)对目前严格的量子理论无法企及的系统和实验条件做出精确的量子可观测数据预测。这些目标将通过将贝叶斯机器学习(ML)整合到量子计算方法中来实现。这将产生一个灵活的量子动力学计算框架。这个框架的核心将是核薛定谔方程。然而，薛定谔方程的输入将由ML模型设计，而量子计算的结果将由另一个ML模型处理。这将大大减少精确预测动力学性质所需的量子计算数量。此外，这将允许解决目前不可行的新问题。具体地说，我们将致力于解决量子分子动力学中的以下主要挑战：(I)逆散射问题，旨在从实验观测数据中获得微观分子相互作用的准确势。(2)超高维系统(最多100维)全球势能面的系统不可知性构造。(Iii)通过将对近似结果进行内插和推广的机器学习模型与推断近似结果与严格或实验结果之间的差异的机器学习模型相结合，提高基于近似动力学方法的量子预测的准确性。(Iv)了解如何将新兴的量子计算设备用于分子动力学应用。我们的工作将提供通用工具，为更大的系统做出量子预测，并具有比目前可行的更高的精度。这可能是从药物设计到催化，再到化学动力学等众多研究领域的关键进展。我们的工作将把新兴的量子计算技术和分子动力学联系起来，为量子技术的新应用铺平道路。这将有助于保持加拿大在实用量子计算行业的领先地位。

Quantum mechanics provides the most accurate description of molecular dynamics that determine microscopic chemical reactions and the structure and functionality of quantum materials. However, the fully quantum description of complex molecular systems is difficult. The present work aims to capitalize on recent developments in quantum dynamics theory and in machine learning in order to develop new approaches to quantum dynamics. The goal is to develop quantum approaches that will (1) require less computational resources than currently established approaches; (2) produce not only quantum observables but also the uncertainties of these observables stemming from limitations imposed by the difficulty of solving the Schrodinger equation; (3) combine quantum theory of molecular dynamics with experimental observations in order to produce improved descriptions of microscopic molecular interactions; (4) make accurate predictions of quantum observables for systems and experimental conditions that are currently out of reach of rigorous quantum theory. These goals will be achieved by integrating Bayesian machine learning (ML) into the methodology of quantum calculations. This will produce a flexible framework for quantum dynamics calculations. The core of this framework will be the nuclear Schrodinger equation. However, the inputs into the Schrodinger equation will be designed by ML models and the results of the quantum calculations will be processed by another ML model. This will dramatically reduce the number of quantum calculations required for accurate predictions of dynamical properties. Moreover, this will allow for new, currently unfeasible, problems to be solved.   Specifically, we will aim to address the following major challenges in quantum molecular dynamics: (i) The inverse scattering problem aiming to obtain accurate potentials for microscopic molecular interactions from experimental observables. (ii) System-agnostic construction of global potential energy surfaces for very high-dimensional systems (up to 100 dimensions).    (iii) Improving the accuracy of quantum predictions based on approximate dynamical approaches by combining the machine learning models that interpolate and generalize approximate results with machine learning models that infer the difference between the approximate results and rigorous or experimental results. (iv) Understand how to use emerging quantum computing devices for applications in molecular dynamics.  Our work will provide general tools to make quantum predictions for bigger systems and with better accuracy than currently feasible. This could be a key advance for numerous research fields, ranging from drug design, to catalysis, to chemical kinetics. Our work will link emerging quantum computing technologies and molecular dynamics, paving a way for a new application for quantum technologies. This will contribute to maintaining Canada's leadership position in practical quantum computing industry.