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通过单元进化和随机抽样来确定减少密度矩阵的N表示性
Gustavo E Massaccesi1,2, Ofelia B Oña3, Pablo Capuzzi4,5
1Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Journal of chemical theory and computation
|November 14, 2024
概括
本研究引入了一种混合量子-随机算法,以解决减少密度矩阵 (p-RDMs) 的N-可表示性问题. 该方法有效地取代了复杂的N-可表示性条件,从而能够准确地确定基本状态.
科学领域:
- 计算量子化学 计算量子化学
- 多体物理多体物理
- 量子信息理论 量子信息理论
背景情况:
- N-可表示性问题决定了p-body矩阵是否可以从N-body密度矩阵中导出.
- 解决这个问题对于通过受约束最小化找到量子系统的确切基本状态至关重要.
- 由于指数式约束增长,对于大型系统来说,现有的N-可表示性条件在计算上变得难以处理.
研究的目的:
- 引入一种新的混合量子-随机算法,以规避传统N-可表示性条件的计算限制.
- 开发一种方法,可以确定给定的p-body矩阵是否是N-可表示的,评估其质量并纠正它.
- 为各种量子模型创建适用于哈密尔顿独立的方法.
主要方法:
- 一种混合量子-静态算法,将自适应衍生组装伪旋转器 (ADAPT) 方法与模拟回火相结合.
- 该算法反复地将单元进化运算符,以随机过程为指导,应用于初始的N体密度矩阵.
- 该过程旨在将p体子系统的减少密度矩阵演变为目标p体矩阵.
主要成果:
- 拟议的混合 ADAPT 算法成功地接近了 N-可表示性条件.
- 该方法在各种模型中证明了1和2降密度矩阵 (1-RDM和2-RDM) 的预期行为.
- 该算法有效地将初始矩阵演变为指定的目标矩阵,验证了其适用性.
结论:
- 混合量子-随机算法为传统的N-可表示性条件提供了一个有效和计算可行的替代方案.
- 这种方法提供了一个可靠的标准来评估和纠正p-RDMs的N-代表性.
- 该算法的哈密尔顿独立性扩大了其在量子化学和凝聚物质物理学中的适用性.
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