Compact Wave Functions for Classical and Quantum Computers

点击翻译按钮获取中文摘要

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.