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According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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量子化学和MaxCut的桥梁:Hartree-Fock方法的经典性能保证和量子算法

Alexis Ralli1,2,3, Tim Weaving2,3, Peter V Coveney2,4,5

  • 1Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, United States.

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概括

新的自相一致场 (SCF) 算法是从Hartree-Fock理论中衍生出来的,其形式是正方体不受约束的二进制优化 (QUBO) 问题. 这些新的方法,QUBO-SCF和MaxCut-SCF,证明了量子化学计算的稳定性和性能提高.

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科学领域:

  • 量子化学 是一个量子化学.
  • 计算化学的计算化学
  • 量子计算是一种量子计算.

背景情况:

  • 自相一致场 (SCF) 算法是量子化学的基础,提出了复杂的非线性优化挑战.
  • 现有的SCF方法可能存在不稳定性,特别是在具有挑战性的分子系统中.

研究的目的:

  • 以哈特里-福克理论为灵感,开发新的SCF算法,利用正方位不受约束的二进制优化 (QUBO) 和MaxCut图形问题.
  • 提高量子化学计算的稳定性和效率.
  • 探索量子优化算法的应用到SCF问题.

主要方法:

  • 由哈特里-福克 (Hartree-Fock) 引发的SCF算法推导,可以作为二进制不受约束的旋转/二进制优化 (QUSO/QUBO) 问题解决.
  • 重构SCF优化作为MaxCut图形问题,通过半确定的编程解决.
  • 在氧化离子 (OH-) 和分子 (N2) 上进行数值验证,最高可达到220个量子位.
  • 引入了四种混合量子-经典方法 (GAS-SCF,QAOA-SCF,QA-SCF,DQI-SCF).

主要成果:

  • 与传统的SCF方法相比,QUBO-SCF和MaxCut-SCF的内部不稳定性显著降低.
  • 新的算法显示了增强配置交互等单个引用方法的潜力.
  • 已成功应用于多达220个自旋轨道系统.

结论:

  • 在量子化学中,QUBO-SCF和MaxCut-SCF方法为解决SCF问题提供了强大的替代方案.
  • 这些方法提供了性能保证和更好的稳定性.
  • 混合量子-经典算法显示了未来量子计算化学的前景.