Applications Of Machine Learning To Studies Of Quantum Phase Transitions
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Applications of Machine Learning to Studies of Quantum Phase Transitions
In the past years Machine Learning has shown to be a useful tool in quantum many-body physics to detect phase transitions. Being able to identify phases via machine learning introduces the question of how did the algorithm learn to classify them, and thus how to interpret the model?s prediction. In this thesis we present a study of the transition from a normal insulator to a topological insulator. We study this quantum phase transition in the framework of the Su-Schrie?er-Heeger model. In the area of Deep Learning, we introduce two models, a normal convolutional neural network and a model based on deep residual learning. In particular, we focus on the interpretability of the model and its prediction by generating class activation maps (CAM) using a global average pooling (GAP) layer. We show the application of this technique by applying it on the model without disorder and with disorder. Here we give further analysis of the detection of states using transfer learning from no disordered to disordered systems. We conclude that the neural network is able to detect edge states when there is no disorder but unable to distinguish between edge states and Anderson localized states when disorder is introduced.
Neural-Network Simulation of Strongly Correlated Quantum Systems
Quantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.
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