Explorations in machine learning for interacting many-body systems.

Most interacting many-body systems in physics are not analytically solvable. Instead, numerical methods are needed for the study of these complex and high-dimensional problems. At present, there are many interesting problems in strongly correlated systems that remain unsolved with current methods. At the heart of this problem is finding an efficient representation that incorporates symmetries, correlations and general features. In the context of computer science, machine learning techniques have had astonishing success at reducing the dimensionality of data. The leading method is through the use of artificial neural networks. These networks have been enormously successful at sifting through vast amounts of data to find patterns and regularities. In a sense, neural networks are themselves a statistical system whose properties are adjusted to mimic the features of the data. By finding an effective low-dimensional representation of the data, machine learning has greatly subdued the curse of dimensionality found in many real-world problems. In this Thesis, we apply several machine learning techniques to the study of interacting many-body systems in classical and quantum statistical physics. We explore supervised classification of phases of matter with an emphasis on physical interpretation of the net- work. In doing so, we design a custom network architecture that possesses rotational symmetry as an inductive bias. We further investigate connections between the renormalization group and deep learning through applying a super-resolving neural network to the classical Ising model. Towards experimental efforts, we also repurpose generative machine learning to quantum state tomography for the calibration and testing of quantum devices. We conclude with a latent variable model inspired by near-term quantum algorithms. This maps to a variational Monte Carlo ansatz that produces samples efficiently for interacting quantum systems

Second order relative entropy in holographic theories

Recently, there has been growing recognition that the tools from quantum information theory might be well-suited to studying quantum gravity in the context of the gauge/gravity correspondence. It is exploring this connection that is the main motivation for the work in this thesis. In particular, we focus on holographic field theories which possess classical spacetime duals. The aim is that certain conditions on the classical duals will narrow down the types of field theories that can be holographic. This will give a better understanding of the limitations and robustness of the gauge/gravity correspondence. We do so by computing the canonical energy for general perturbations around anti-de Sitter spacetime, which is dual to quantum Fisher information in the field theory. We go on to prove the positivity of canonical energy and discuss the addition of matter fields. We further show that our result can be interpreted as an interaction between scalar fields living in an auxiliary de Sitter spacetime. We concluded with a summary of progress and future challenges for this program.Science, Faculty ofPhysics and Astronomy, Department ofGraduat