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Tensor product methods and entanglement optimization for ab initio quantum chemistry

International journal of quantum chemistry, 2015-10, Vol.115 (19), p.1342-1391 [Peer Reviewed Journal]

2015 Wiley Periodicals, Inc. ;ISSN: 0020-7608 ;EISSN: 1097-461X ;DOI: 10.1002/qua.24898 ;CODEN: IJQCB2

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  • Title:
    Tensor product methods and entanglement optimization for ab initio quantum chemistry
  • Author: Szalay, Szilárd ; Pfeffer, Max ; Murg, Valentin ; Barcza, Gergely ; Verstraete, Frank ; Schneider, Reinhold ; Legeza, Örs
  • Subjects: DMRG ; entanglement ; quantum infromation ; tensor networks ; tensor product approximation
  • Is Part Of: International journal of quantum chemistry, 2015-10, Vol.115 (19), p.1342-1391
  • Description: The treatment of high‐dimensional problems such as the Schrödinger 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. Building on research performed in the past decade, entanglement‐based methods—developed for different purposes in distinct communities—have matured into tools that can be employed to attack highly challenging problems in quantum chemistry. For example, controlled manipulation of quantum entanglement in tensor product approximations yields a novel approach to treat high‐dimensional optimization problems and time‐dependent equations, such as the Schrödinger equation.
  • Publisher: Hoboken: Blackwell Publishing Ltd
  • Language: English;French;German
  • Identifier: ISSN: 0020-7608
    EISSN: 1097-461X
    DOI: 10.1002/qua.24898
    CODEN: IJQCB2
  • Source: Alma/SFX Local Collection
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