Xia Rongxin, Bian Teng, Kais Sabre
Department of Physics , Purdue University , West Lafayette , Indiana 47907 , United States.
Department of Chemistry and Birck Nanotechnology Center , Purdue University , West Lafayette , Indiana 47907 , United States.
J Phys Chem B. 2018 Apr 5;122(13):3384-3395. doi: 10.1021/acs.jpcb.7b10371. Epub 2017 Nov 20.
Obtaining exact solutions to the Schrödinger equation for atoms, molecules, and extended systems continues to be a "Holy Grail" problem which the fields of theoretical chemistry and physics have been striving to solve since inception. Recent breakthroughs have been made in the development of hardware-efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins with an Ising-type Hamiltonian. One of the most vital questions pertaining to these new devices is, "Can these machines be used to perform electronic structure calculations?" Within this work, we review the general procedure used by these devices and prove that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. Additionally, we provide simulation results of the transformed Ising Hamiltonian for H , He , HeH, and LiH molecules, which match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware. This is an early step in developing generalized methods on such devices for chemical physics.
自创立以来，理论化学和物理学领域一直致力于解决的一个“圣杯”问题是，获得原子、分子和扩展系统的薛定谔方程的精确解。在硬件高效量子优化器和能够用伊辛型哈密顿量模拟数百个相互作用自旋的相干伊辛机的开发方面，最近取得了突破。与这些新设备相关的最重要问题之一是：“这些机器能否用于进行电子结构计算？” 在这项工作中，我们回顾了这些设备使用的一般程序，并证明电子结构哈密顿量与伊辛哈密顿量之间存在精确映射。此外，我们提供了H₂、He₂、HeH和LiH分子的变换后的伊辛哈密顿量的模拟结果，这些结果与精确的数值计算结果相符。这表明可以将分子哈密顿量映射到一个伊辛型哈密顿量上，该哈密顿量可以很容易地在当前可用的量子硬件上实现。这是在这类设备上开发化学物理通用方法的早期步骤。
