We propose the use of machine learning techniques to address the problem of local measurements in quantum field theory. In particular we discuss how neural networks can efficiently process measurement outcomes from local probes to determine both local and non-local features of the quantum field. As toy examples we show: a) how a particle detector distinguishes boundary conditions imposed on the field without the need of signals propagating from them, and b) how detectors can determine the temperature of the quantum field without thermalizing with it. We discuss how the formalism proposed can be used for any kind of local measurement on a quantum field and, by extension, to local measurements of non-local features in many-body quantum systems.
We propose the use of machine learning techniques to address the problem of local measurements in quantum field theory. In particular we discuss how neural networks can efficiently process measurement outcomes from local probes to determine both local and non-local features of the quantum field. As toy examples we show: a) how a particle detector distinguishes boundary conditions imposed on the field without the need of signals propagating from them, and b) how detectors can determine the temperature of the quantum field without thermalizing with it. We discuss how the formalism proposed can be used for any kind of local measurement on a quantum field and, by extension, to local measurements of non-local features in many-body quantum systems.
Abstract We demonstrate how one can use machine learning techniques to bypass the technical difficulties of designing an experiment and translating its outcomes into concrete claims about fundamental features of quantum fields. In practice, all measurements of quantum fields are carried out through local probes. Despite measuring only a small portion of the field, such local measurements have the capacity to reveal many of the field’s global features. This is because, when in equilibrium with their environments, quantum fields store global information locally, albeit in a scrambled way. We show that neural networks can be trained to unscramble this information from data generated from a very simple one-size-fits-all local measurement protocol. To illustrate this general claim we will consider three non-trivial features of the field as case studies: a) how, as long as the field is in a stationary state, a particle detector can learn about the field’s boundary conditions even before signals have time to propagate from the boundary to the detector, b) how detectors can determine the temperature of the quantum field even without thermalizing with it, and c) how detectors can distinguish between Fock states and coherent states even when the first and second moments of all their quadrature operators match. Each of these examples uses the exact same simple fixed local measurement protocol and machine-learning ansatz successfully. This supports the claim that the framework proposed here can be applied to nearly any kind of local measurement on a quantum field to reveal nearly any of the field’s global properties in a one-size-fits-all manner.
In this thesis, we use detector models to study various properties of quantum fields. One such property is the correlations present in fields. It is known that two uncorrelated detectors, upon coupling to a quantum field, can become correlated, i.e. they harvest correlations from the field. In this work, we study the effect of the presence of extra detectors in correlation harvesting protocols. Our first main result is that a single interloper detector can sabotage the harvesting of classical and quantum correlations. \n \nThe second main result in this thesis is that machines can learn to extract different features of a quantum field by processing the outcomes of local probes. As proof-of-principle, we show how a neural network can distinguish a field's boundary conditions, predict the temperature of a field and of how it can distinguish between a Fock state and a phase-averaged coherent state.
Within the past decade, machine learning algorithms have been proposed as a po-tential solution to a variety of research problems which emerge within physics. As this cross-fertilization matures, one is able to investigate if the efficiency of machine learning algorithms can be increased by interpreting them physically and if there exist fundamental connections that can be established between the two research fields. In this thesis, we pursue research directions intimately related to the above questions.First, we investigate the practical implications of interpreting machine learning functions as statistical-mechanical observables. Through this perspective, we explore if we can extend the classification capabilities of machine learning algorithms and if we are able to include neural networks within Hamiltonians to induce phase transitions in systems. A related direction concerns the use of machine learning to construct inverse renormalization group transformations to arbitrarily increase the size of a system. These techniques are then utilized to study the infinite volume limit of discrete spin systems and of quantum field theories, in order to investigate if machine learning is a powerful tool to study phase transitions.In another research direction we explore the derivation of machine learning algo-rithms from quantum field theories. We investigate if the φ4 scalar field theory satisfies the Hammersley-Clifford theorem and if it can be recast as a Markov random field. We then explore if φ4 neural networks can be derived that generalize a certain class of standard neural network architectures, and we present relevant numerical appli-cations. Finally, we discuss how this research direction opens up the opportunity to investigate machine learning within quantum field theory and how it solidifies a rig-orous connection between the research fields of machine learning, probability theory, statistical mechanics, lattice and constructive quantum field theory.
Reconstructing a system Hamiltonian through measurements on its eigenstates is an important inverse problem in quantum physics. Recently, it was shown that generic many-body local Hamiltonians can be recovered by local measurements without knowing the values of the correlation functions. In this work, we discuss this problem in more depth for different systems and apply supervised learning method via neural networks to solve it. For low-lying eigenstates, the inverse problem is well-posed, neural networks turn out to be efficient and scalable even with a shallow network and a small data set. For middle-lying eigenstates, the problem is ill-posed, we present a modified method based on transfer learning accordingly. Neural networks can also efficiently generate appropriate initial points for numerical optimization based on the BFGS method.
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. \n \nIn 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. \n \nIn 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.
Abstract The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature extraction and dimensionality reduction of high-dimensional datasets. Recent studies have revealed that neural networks are further suitable for the determination of macroscopic phases of matter and associated phase transitions as well as efficient quantum state representation. In this work, we address quantum phase transitions in quantum spin chains, namely the transverse field Ising chain and the anisotropic XY chain, and show that even neural networks with no hidden layers can be effectively trained to distinguish between magnetically ordered and disordered phases. Our neural network acts to predict the corresponding crossovers finite-size systems undergo. Our results extend to a wide class of interacting quantum many-body systems and illustrate the wide applicability of neural networks to many-body quantum physics.