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978-3-8439-1918-0, Reihe Mathematik

Konrad Waldherr Numerical Linear and Multilinear Algebra in Quantum Control and Quantum Tensor Networks

423 Seiten, Dissertation Technische Universität München (2013), Softcover, B5

Quantum control and quantum simulation play a key role in several applications, including quantum information processing, nanotechnology, and spectroscopy. The computational treatment of quantum problems typically involves basic tasks of numerical linear algebra. However, calculating relevant quantities of large quantum systems is a computationally demanding task as the dimension of the underlying Hilbert space (and thus also the resource requirements) grow exponentially with the size of the quantum system, in contrast to a classical configuration space just growing linearly. Therefore, classical numerical matrix approaches, which act on the entire Hilbert space, soon reach a limit, even on high-capacity hardware architectures. In order to be able to deal with larger systems and to exploit the power of today's supercomputers, numerical approaches to simulate large quantum systems require both efficient algorithms based on problem-adapted data structures and powerful hardware of (massively) parallel processors.

We address selected topics in quantum information theory from a computational perspective and exploit inherent properties of these problems in the corresponding multilinear formulation in order to develop tailored approaches and algorithms, leading to faster convergence and higher accuracy.