Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules,Journal of Chemical Theory and Computation

当前位置： X-MOL 学术 › J. Chem. Theory Comput. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2024-09-11 , DOI: 10.1021/acs.jctc.4c00483
Mauro Cainelli ₁ , Reo Baba ₁ , Yuki Kurashige _{1,

2,

3}

Affiliation

We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm, in which the multiplication of Ĥ^–k to the reference wave function is replaced by the Fourier transformed multiplication of e^–iλĤ, as a function of the integration parameters and the iteration power k for various systems, including H₂, LiH, BeH₂ and the notorious H₄ molecule at square geometry. We further consider the possibility of employing the Gaussian-quadrature rule as an alternate integration method and compared it to the results employing trapezoidal integration. The Q-Inv algorithm is compared to the inverse iteration method using the Ĥ^–1 inverse (I-Iter) and the exact inverse by lower-upper decomposition. Energy values are evaluated as the expectation values of the Hamiltonian. Results suggest that the Q-Inv method provides lower energy results than the I-Iter method up to a certain k, after which the energy increases due to errors in the numerical integration that are dependent on the integration interval. A combined Gaussian-quadrature and trapezoidal integration method proved to be more effective at reaching convergence while decreasing the number of operations. For systems like H₄, in which the Q-Inv cannot reach the expected error threshold, we propose a combination of Q-Inv and I-Iter methods to further decrease the error with k at lower computational cost. Finally, we summarize the recommended procedure when treating unknown systems.

中文翻译：

小分子量子逆算法的数值研究

我们评估了量子逆 (Q-Inv) 算法的准确性，其中Ĥ ^{– k}与参考波函数的乘法被 e ^{–iλ Ĥ}的傅里叶变换乘法所取代，作为积分参数和各种系统的迭代幂k ，包括 H ₂ 、LiH、BeH ₂和臭名昭著的方形几何分子 H ₄ 。我们进一步考虑采用高斯求积规则作为替代积分方法的可能性，并将其与采用梯形积分的结果进行比较。将 Q-Inv 算法与使用Ĥ ^–1逆 (I-Iter) 的逆迭代方法以及通过下-上分解的精确逆进行比较。能量值被评估为哈密顿量的期望值。结果表明，在一定k范围内，Q-Inv 方法提供的能量结果比 I-Iter 方法低，此后能量由于取决于积分间隔的数值积分误差而增加。事实证明，高斯求积和梯形积分相结合的方法可以更有效地实现收敛，同时减少运算次数。对于像 H ₄这样的系统，Q-Inv 无法达到预期的误差阈值，我们提出了 Q-Inv 和 I-Iter 方法的组合，以较低的计算成本进一步减少k的误差。最后，我们总结了处理未知系统时推荐的程序。

更新日期：2024-09-11

点击分享查看原文

点击收藏

公开下载

阅读更多本刊新发论文本刊介绍/投稿指南