Tensor product methods and entanglement optimization for ab initio quantum chemistry

By Szilárd Szalay, Max Pfeffer, V. Murg, Gergely Barcza, Frank Verstraete, Reinhold Schneider, Ors Legeza. 2014

322 citations recorded by the source corpus.

The treatment of high-dimensional problems such as the Schrodinger 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, February 18–21, 2014, Mariapfarr, Austria. © 2015 Wiley Periodicals, Inc.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Mathematics

View Paper: https://www.semanticscholar.org/paper/217944a8dc26d22f237ae402e54aabd157eba6fa

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Citations in the corpus

Quantum Chemistry in the Age of Quantum Computing. (2018, background): “ynamics. The resulting quantum Hamiltonian describing the electronic system, in atomic units, can be written as Helec= X i r2 r i 2 X i;j Z i jRi rjj + X i;j>i ZZj jRi Rjj + X i;j>i 1 jri rjj ; (100) where ri are the position coordinates of the electrons, which parametrically depend on the xed”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “MPS and TTN have also been applied to problems in quantum chemistry, yielding very promising results, although there are still open questions about the suitability of different tensor networks for different chemical structures (Chan and Sharma, 2011; Szalay et al., 2015; White and Martin, 1999).”