Using Matrix-Free Tensor-Network Optimizations To Construct a Reduced-Scaling and Robust Second-Order Mo̷ller-Plesset...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Canonical Polyadic Decomposition (CPD) and Tensor Hyper-Contraction (THC) are advanced tensor decomposition techniques.
• Efficient computation of electronic structure methods is crucial for advancing quantum chemistry.
• The Laplace transform (LT) second-order Møller-Plesset (MP2) method offers an accurate yet computationally intensive approach.

Purpose of the Study:

• To develop and investigate an efficient combination of CPD and THC for electronic structure calculations.
• To create a novel, low-cost CPD solver utilizing THC factorization for order-4 tensors.
• To apply the combined CPD and THC approximations to the LT MP2 method for improved computational performance.

Main Methods:

• Developed a novel low-cost CPD solver with O(N R^2) scaling, leveraging precomputed THC factorization.
• Employed a matrix-free, THC-based optimization strategy for CPD of order-4 two-electron integral tensors.
• Investigated the combined CPD and THC approximation of the LT MP2 method, enabling efficient switching between factorizations.

Main Results:

• Achieved efficient CPD factorization of two-electron integral tensors using the combined approach.
• Demonstrated that modest THC and CPD ranks preserve the accuracy of the LT MP2 method.
• Showcased a significant performance advantage of the CPD + THC LT MP2 strategy over the canonical LT MP2 method in terms of speed and memory.

Conclusions:

• The synergistic combination of CPD and THC provides a computationally efficient and accurate approach for electronic structure methods.
• The developed CPD + THC LT MP2 strategy offers substantial reductions in computational wall-times and memory requirements.
• This work paves the way for more scalable and resource-efficient quantum chemistry calculations.