Electronic Structure Calculations and the Ising Hamiltonian,The Journal of Physical Chemistry B

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Electronic Structure Calculations and the Ising Hamiltonian
The Journal of Physical Chemistry B ( IF 2.8 ) Pub Date : 2017-11-20 00:00:00 , DOI: 10.1021/acs.jpcb.7b10371
Rongxin Xia ₁ , Teng Bian ₁ , Sabre Kais _{1,

2,

3}

Affiliation

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 H₂ , He₂ , 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.

中文翻译：

电子结构计算与伊辛哈密顿量

从原子，分子和扩展系统的Schrödinger方程获得精确解仍然是一个“圣杯”问题，自成立以来，理论化学和物理学领域一直在努力解决这一问题。在硬件效率更高的量子优化器和相干Ising机器的开发方面取得了最新突破，这些机器可以模拟具有Ising型哈密顿量的数百个相互作用的自旋。与这些新设备有关的最重要的问题之一是：“这些机器可以用于执行电子结构计算吗？” 在这项工作中，我们回顾了这些设备使用的一般程序，并证明了电子结构哈密顿量和伊辛哈密顿量之间存在精确的映射。此外，我们提供了H变换后的Ising哈密顿量的仿真结果₂  ，He ₂  ，HeH ⁺和LiH分子，它们与精确的数值计算相匹配。这表明，人们可以将分子哈密顿量映射到一个Ising型哈密顿量，可以很容易地在当前可用的量子硬件上实现该哈密顿量。这是在此类化学物理设备上开发通用方法的第一步。

更新日期：2017-11-21

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