TY - JOUR A1 - Klus, Stefan A1 - Gelß, Patrick A1 - Peitz, Sebastian A1 - Schütte, Christof T1 - Tensor-based dynamic mode decomposition JF - Nonlinearity Y1 - 2018 U6 - https://doi.org/10.1088/1361-6544/aabc8f VL - 31 IS - 7 PB - IOP Publishing Ltd & London Mathematical Society ER - TY - JOUR A1 - Gelß, Patrick A1 - Klus, Stefan A1 - Knebel, Sebastian A1 - Shakibaei, Zarin A1 - Pokutta, Sebastian T1 - Low-Rank Tensor Decompositions of Quantum Circuits JF - Journal of Computational Physics N2 - Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation, optimization, and physical realization of quantum circuits is of utmost importance for designing novel algorithms. We show how matrix product states (MPSs) and matrix product operators (MPOs) can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers and to gain insight into the underlying structure of the system. We present different examples to demonstrate the advantages of MPO formulations and show that they are more efficient than conventional techniques if the bond dimensions of the wave function representation can be kept small throughout the simulation. Y1 - 2022 ER - TY - JOUR A1 - Gelß, Patrick A1 - Klus, Stefan A1 - Eisert, Jens A1 - Schütte, Christof T1 - Multidimensional Approximation of Nonlinear Dynamical Systems JF - Journal of Computational and Nonlinear Dynamics N2 - A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems. Y1 - 2019 U6 - https://doi.org/10.1115/1.4043148 VL - 14 IS - 6 ER -