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Abstract

The numerical simulation of quantum many-body systems constitutes a long-standing and challenging problem, as the 'curse of dimensionality' restricts the applicability of exact methods to systems consisting of only a few particles. Thus approximative techniques that reduce the computational complexity are of high fundamental interest. Simultaneously, there exists a strong desire to benchmark the ever-growing capabilities of quantum simulators, thus strengthening the motivation to research tools that are capable of matching their increasing system sizes.

In this thesis, we, for one, develop and explore such new computational methods by exploiting the rapid developments in machine learning, allowing us to construct highly versatile ansatz functions to model quantum states based on deep artificial neural networks. Building on this, we establish a new numerical technique capable of modeling the dynamics of dissipative many-body quantum systems, relying on an accurate variational description of an informationally complete probability distribution that corresponds to the quantum system of interest. Additionally, we explore the differences in performance in ground state searches between a multitude of different network architectures and thereby shed light on the question of why some networks significantly outperform others.

Secondly, we adapt the developed techniques also for classical systems. This is possible as the only requirement is a probabilistic description with a (closed) evolution equation, thereby emphasizing the wide range of applicability.

Finally, we rely on existing approximative techniques to devise an experimental proposal aimed at observing an area to a volume law transition following a quench in a spin-1 Bose-Einstein condensate. Notably, we herein do not rely on quantum entropies but rather on differential entropies of the phase-space distribution describing the system. These quasi probability distributions are importantly readily accessible in experiments and we demonstrate that their entropies can be reliably estimated from a feasible number of samples without assuming a particular type of distribution, such as a Gaussian.