Schleich Philipp, Kottmann Jakob S, Aspuru-Guzik Alán
Department of Computer Science, University of Toronto, Canada.
Applied and Computational Mathematics, Department of Mathematics, RWTH Aachen University, Aachen, Germany.
Phys Chem Chem Phys. 2022 Jun 8;24(22):13550-13564. doi: 10.1039/d2cp00247g.
We provide an integration of the universal, perturbative explicitly correlated [2]-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. The proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in the VQE. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE + [2] approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]. In particular the combination of MRA-PNOs with [2] has turned out to be very promising - persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a complexity.
我们在变分量子本征求解器（VQE）的背景下，对通用的、微扰显式相关的[2]校正进行了整合。这种方法能够显著提高基础参考方法的精度，同时无需额外的量子资源。所提出的方法仅需要知道参考波函数的单粒子和双粒子约化密度矩阵（RDM）；这些可以在VQE达到收敛后进行测量。这种计算的成本与电子数的六次方成正比。我们使用传统的高斯基组和我们最近提出的通过多分辨率分析获得的直接确定的对自然轨道（MRA - PNOs）来探索VQE + [2]方法的性能。在[2]的计算中，高斯轨道和PNOs都作为一组潜在的互补基函数进行了研究。特别是MRA - PNOs与[2]的结合已被证明非常有前景——在我们所有的数据中始终如此，这使得在最小基组的量子成本下能够进行非常精确的模拟。此外，我们发现将PNOs作为互补基进行部署，可以在复杂度上大大减少进入校正计算的互补基函数的数量。
