Compact Wave Functions for Classical and Quantum Computers

在NSERC DG的支持下，我将能够继续量子化学方法的基础研究。该领域位于化学，物理，应用数学和计算机科学的界面。这个跨学科领域已经导致了社区可用的复杂计算机代码的开发，用于计算原子，分子和材料的电子结构和相关性质，并取得了巨大成功。从密度泛函理论到新的相关方法（如张量网络）的方法的应用扩大了社区影响化学，材料科学和物理学大部分领域的能力。虽然取得了很大进展，但社区中仍然存在一些挑战。我的计划旨在解决以下两个具体的挑战：a）计算机代码的发展，以方便原型的新想法在该领域，和B）的发展紧凑的波函数的量子计算机模拟分子。这将导致在“经典”（在使用经典计算机的意义上）量子化学和量子计算领域的双重影响。作为研究的第一个一般领域，支持的计划将使我的研究小组能够继续开发开源DiffiQult包[1]。DiffiQult是一种采用现代自动微分技术的代码，因此开发人员不需要显式编码任何参数的任何导数。这是由AlgoPy软件包实现的，该软件包的灵感来自机器学习中经常采用的技术，用于反向传播。我们开发的代码，并将其应用于小分子高斯基函数的中心和指数的优化。代码在有“困难”或耗时的衍生代码的地方表现出色，根据我们自己的经验，这可能需要2-3人年[2]。我们将a）向代码中添加更高角动量的基函数，并将其链接到快速积分代码（如libint）; B）使程序更加用户友好，并将其应用于获得相关方法（如MP2）的高阶导数。我们将使用代码来开发和调整新的密度泛函和函数形式。第二个研究领域是开发非常紧凑的波函数，用于在量子计算机上模拟量子化学，这是一个发展非常迅速的领域，自2005年以来，我一直积极帮助开拓。特别是，我们将使用DiffiQult为特定几何形状的特定分子生成自定义基函数，然后使用量子计算机使用变分量子本征解算器（VQE）算法进行关联，我和我的团队介绍了[3]，最近我们在量子计算机上模拟了LiH [4]。VQE使用混合量子-经典方法来优化紧致波函数，其中波函数在量子计算机中准备，并且由经典计算机基于哈密顿量的期望值的测量来更新参数。

Supported by the NSERC DG, I will be able to continue fundamental research in quantum chemistry methods. The field lies at the interface of chemistry, physics, applied math, and computer science. This interdisciplinary area has led to development of community-available complex computer codes for calculation of the electronic structure & associated properties of atoms, molecules, and materials with great success. Application of methods that range from density functional theory to novel correlated approaches such as; tensor networks has expanded the ability of community to impact most areas of chemistry, materials science, and physics. Although much progress has been made, several challenges in the community remain. My program aims to address the following two specific challenges: a) the development of computer code for easy prototyping of new ideas in the field, and b) the development of compact wave functions for quantum computer simulation of molecules. This will lead to dual impact both in the area of "classical" (in the sense of employing classical computers) quantum chemistry as well as quantum computing. As a first general area of research, the supported program will enable my research group to continue developing open-source DiffiQult package[1]. DiffiQult is a code that employs modern automatic differentiation techniques so the developer does not need to explicitly code any derivative with respect to any parameter. This is enabled by the AlgoPy package inspired by technology often employed in machine learning, for back propagation. We developed the code and applied it for optimization of centers and exponents of Gaussian basis functions for small molecules. The code excels where there are "difficult" or time-consuming derivatives to code, which can take, in our own experience 2-3 person-years[2]. We will a) add higher-angular momentum basis functions to the code, and link it to fast integrals codes such as libint; b) make the program more user-friendly, and apply it to obtaining higher-order derivatives of correlated methods such as MP2. We will employ the code to develop and tune new density functionals and functional forms for them. Second area of research would be development of very compact wave functions for simulation of quantum chemistry on quantum computers, a very rapidly-growing field that I have actively helped to pioneer, since 2005. In particular, we will use DiffiQult to generate custom basis functions for particular molecules at particular geometries that then will be correlated using quantum computer using Variational Quantum Eigensolver (VQE) algorithm that my group and I introduced[3] and that recently led us to simulate LiH on a quantum computer[4]. VQE optimizes a compact wave function ansatz using a hybrid quantum-classical approach where the wave function is prepared in the quantum computer and the parameters updated by the classical computer based on the measurement of expectation values of the Hamiltonian.