An application of machine learning to statistical physics: from the phases of quantum control to satisfiability problems
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This dissertation presents a study of machine learning methods with a focus on applications to statistical and condensed matter physics, in particular the problem of quantum state preparation, spin-glass and constraint satisfiability. We will start by introducing the core principles of machine learning such as overfitting, bias-variance tradeoff and the disciplines of supervised, unsupervised and reinforcement learning. This discussion will be set in the context of recent applications of machine learning to statistical physics and condensed matter physics. We then present the problem of quantum state preparation and show how reinforcement learning along with stochastic optimization methods can be applied to identify and define phases of quantum control. Reminiscent of condensed matter physics, the underlying phases of quantum control are identified via a set of order parameters and further detailed in terms of their universal implications for optimal quantum control. In particular, casting the optimal quantum control problem as an optimization problem, we show that it exhibits a generic glassy phase and establish a connection with the fields of spin-glass physics and constraint satisfiability problems. We then demonstrate how unsupervised learning methods can be used to obtain important information about the complexity of the phases described. We end by presenting a novel clustering framework, termed HAL for hierarchical agglomerative learning, which exploits out-of-sample accuracy estimates of machine learning classifiers to perform robust clustering of high-dimensional data. We show applications of HAL to various clustering problems.