In this work, we utilize the framework of many-body expansion (MBE) to decompose electronic structures into fragments by incrementing virtual orbitals, aiming to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. While our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and its generalization, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules (H₂O and N₂) and calculate the ground and excited state energies of three molecules (LiH, CH⁺, and H₂O). The results demonstrate that our approach can, in principle, provide reliable descriptions in all the tests including strongly correlated systems when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

中文翻译：

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基于变分量子本征解算器和动态相关紧缩的多体展开

在这项工作中，我们利用多体展开（MBE）的框架，通过增加虚拟轨道将电子结构分解为碎片，旨在使用变分量子本征解算器和紧缩算法精确求解每个碎片的基态和激发态能量。虽然我们的方法主要基于酉耦合簇单簇和双簇 (UCCSD) 及其泛化，但我们还引入了修改和近似，通过部分泛化 UCCSD 算子并忽略参考态的松弛来节省 MBE 中的量子资源。作为概念证明，我们研究了两个分子（H ₂ O 和 N ₂ ）基态断键过程的势能面，并计算了三个分子（LiH、CH ⁺、和H ₂ O)。结果表明，当选择适当的近似值时，我们的方法原则上可以在所有测试中提供可靠的描述，包括强相关系统。此外，我们还进行模型模拟来研究散粒噪声对总 MBE 能量的影响，并表明精确的能量估计对于低阶 MBE 碎片至关重要。