Tensor Network Algorithms for Quantum Chemistry

Abstract

High-accuracy quantum chemical calculations are commonly limited to relatively small molecules due to the exponential scaling of the computational cost with the number of involved particles. By leveraging powerful tensor decomposition-based approaches, tensor network algorithms are continuously expanding the scope of wave function-based molecular simulation methods. While tensor network-based methods such as the density matrix renormalization group (DMRG) algorithm are nowadays routinely applied to ground-state electronic structure problems, we aim to target a broader range of molecular many-body quantum systems. In this talk, I will present our versatile tensor network framework, which enables the application of DMRG-based methods also to vibrational and vibronic problems. We extend our framework to excited-states targeting algorithms, and develop time-dependent tensor network approaches to enable large-scale simulations of quantum dynamical phenomena governing a variety of chemical processes. To gain further insights into the correlated wave functions and to optimize the construction of efficient tensor factorizations, we exploit entropic measures from quantum information theory. The combination of powerful tensor-based wave function representations and efficient numerical algorithms paves the way toward the accurate characterization of a large variety of high-dimensional quantum systems.

References

• arxiv.org/abs/2109.08961
• arxiv.org/abs/2405.02031