| Independent of the developments in quantum physics and quantum chemistry, tensor decomposition approaches to high dimensional problems have recently been analyzed in the mathematics community. We recently analyzed the geometric structure of the MPS format (called TT in mathematician's nomenclature), as a special case of the more general Hierarchical Tucker format due to W. Hackbusch, paralleling the development of tree tensor networks in quantum applications. I will give an overview of our results and indicate how they can be used for the treatment and theoretical understanding of optimization tasks, e.g., computation of the smallest eigenvalue of a Hamiltonian system, or of time-dependent equations. |
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