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在量子计算机的子空间基于激发状态方法中的一般化自身价值问题.

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量子化学的量子子空间扩张 (QSE) 方法是不稳定的,因为在一般化固有值问题中的错误放大. 量子运动方程 (qEOM) 方法在量子计算机上的激发状态计算中更稳定.

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科学领域:

  • 量子计算在化学中的应用.
  • 为化学问题开发量子算法.

背景情况:

  • 量子计算机为解决复杂的量子化学问题提供了有前途的应用.
  • 像QSE和qEOM这样的基于子空间的量子算法适用于预故障耐受性量子设备.
  • 这些算法通常涉及使用量子计算解决通用自值方程.

研究的目的:

  • 分析基于子空间的量子算法中的稳定性和错误传播,用于激发状态量子化学.
  • 在现实的量子计算错误条件下比较QSE,qEOM和量子自相一致的运动方程 (q-sc-EOM) 方法的性能.

主要方法:

  • 标准和通用自值问题的分析和数值分析.
  • 调查错误放大与重叠矩阵的条件数相关的错误.
  • 对不良条件方程的值技术的评估和由此产生的激发状态的评估.

主要成果:

  • 固有价值中的错误在一般化固有价值问题中随着条件数的增加而大大放大,破坏QSE和qEOM的稳定.
  • 高条件数使QSE的工作方程变得不良条件,需要值,这可能会忽略关键激发状态.
  • 使用标准自值方程的兴奋状态方法,如q-sc-EOM,更稳定,对条件数不那么敏感.

结论:

  • 由于误差放大,QSE和qEOM方法在激发状态量子化学计算中容易产生不稳定性.
  • 量子自相一致的运动方程 (q-sc-EOM) 显示出更大的稳定性,是化学中近期量子计算的更合适候选者.
  • 仔细考虑固有值问题条件对于开发化学强大的量子算法至关重要.