Compact Wave Functions for Classical and Quantum Computers

用于经典和量子计算机的紧凑波函数

• 批准号: RGPIN-2020-05634
• 负责人: AspuruGuzik, Alán
• 金额: $ 6.85万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=748347
• 关键词: Compact; Wave; Functions; Classical; Quantum

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.

在NSERC DG的支持下，我将能够继续进行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交界处。这一交叉学科领域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的应用，如张量网络，扩大了社区的能力，影响了化学、材料科学和物理的大多数领域。虽然取得了很大进展，但社区中仍存在一些挑战。我的计划旨在解决以下两个具体挑战：a)开发计算机代码，以便在该领域轻松制作新想法的原型；b)开发紧凑波函数，用于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)量子化学以及量子计算领域的双重影响。作为第一个一般性研究领域，受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是一种使用现代自动区分技术的代码，因此开发人员不需要显式编写关于任何参数的任何派生代码。这是由AlgoPy程序包实现的，该程序包受到机器学习中经常使用的技术的启发，用于反向传播。我们开发了该程序，并将其应用于小分子高斯基函数的中心和指数的优化。在有“困难的”或耗时的衍生品编码的地方，代码表现出色，根据我们自己的经验，这可能需要2-3个人年[2]。我们将a)在程序中添加高角动量基函数，并将其链接到libint等快速积分程序；b)使程序更加人性化，并将其应用于获得相关方法的高阶导数，如MP2。我们将使用该代码为它们开发和调整新的密度泛函和函数形式。第二个研究领域将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，这是一个增长非常迅速的领域，自2005年以来，我一直积极帮助开创这一领域。特别是，我们将使用DiffiQult为特定几何位置的特定分子生成定制的基函数，然后使用量子计算机使用我和我的团队引入的变分量子本征解算器(VQE)算法进行关联[3]，该算法最近使我们在量子计算机上模拟LiH。VQE使用量子-经典混合方法来优化紧凑波函数ansatz，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。