Tensor product methods and entanglement optimization for ab initio quantum chemistry

TL;DR

This paper introduces tensor product and entanglement-based methods for high-dimensional quantum chemistry problems, demonstrating their theoretical foundations and numerical benefits in optimizing wavefunctions and tackling complex quantum systems.

Contribution

It provides a pedagogical overview of entanglement optimization techniques and their application to quantum chemistry, integrating concepts from many-body physics and tensor approximations.

Findings

Entanglement-based methods improve high-dimensional quantum problem solving.

Numerical examples demonstrate the effectiveness of the approaches.

Theoretical background supports future developments in quantum chemistry algorithms.

Abstract

The treatment of high-dimensional problems such as the Schr\"odinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods, -- developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools -- can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic "New wavefunction methods and entanglement optimizations in quantum chemistry" at the Workshop on Theoretical Chemistry, 18 - 21 February 2014, Mariapfarr, Austria.