Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Non-parametric learning in many-body physics.

Rajat Kumar Panda

Published Dec 11, 2023• 0 citations
OpenAlex

Abstract

In this digital age, machine learning (a prominent element within the context of artificial intelligence) has become an integral part of modern life, influencing various aspects of our daily activities.The predictive power of these tools is increasing with the advancements in algorithms, increased computational power, and the availability of large data sets: one basic example of this is language-based models, which have revolutionized our capabilities of transferring and processing information.Data is the foundational element of machine learning, and the quality and relevance of the data sets have a profound impact on the performance and accuracy of machine learning models.Thus "data is the new gold", captures the immense value that data holds in our modern world.With the exponential growth in data, the increasing demand for better machine-learning tools comes as a natural consequence.The field of physics is no exception to this, especially with the rise of big simulations and experiments generating huge amounts of data.Experiments at particle accelerators like the Large Hadron Collider(LHC) and Fermi lab, gravitational waves detector by LIGO and Virgo, climate models and weather simulations, Sloan Digital Sky Survey (SDSS), Cosmic Microwave Background(CMB) radiation providing insights into the early universe; all these studies generate massive data sets.In this context, developing more powerful, accurate, and specialized tools, is essential to meet the evolving needs in physics as well.In this thesis, we aim to study different types of ML tools to characterize the many-body problem in the context of classical and quantum statistical mechanics, with a focus on unbiased and interpretable methods.We use techniques coming from so-called non-parametric learning (NPL), where the analysis is done without specifying a fixed set of parameters in an assumption-free vi manner.NPL is a subset of the broad unsupervised learning category; the algorithm learns from the intrinsic structure of the data set.NPL is particularly valuable in scenarios where data assumptions are uncertain, data distributions are non-standard, or when dealing with complex data sets where relationships are difficult to predict beforehand.This works in our favor as the relation between data sets coming from many-body physics system and their effect on data structures when physical parameters change is not well understood -the simple reason being that the typical physicists mindset is very much focused on performing huge dimensional reduction from microscopic physical information (a canonical example of this being mean field theories, where the behavior of a large number of degrees of freedom is replaced by a single one).The thesis is organized as follows.In Chapter 1, we discuss the theoretical framework behind the NPL methods used.We present basic ideas in our methodologies, which encompass the overarching principles guiding our approach.These include the linkage between statistical physics and data analysis, particularly in relation to intrinsic dimension (Id) and its significance in understanding critical characteristics.Additionally, we delve into the application of Principal Component Analysis (PCA) and introduce the notion of PCA entropy -a witness of information spreading under linear transformation, whose relevance to physical phenomena we start investigating here.In Chapter 2, we describe the data sets we work with; statistical mechanics inspired data sets, such as those generated via sampling classical Ising models through advanced Monte Carlo algorithms, and experimental data of a spinor Bose-Einstein condensate.The following chapters present the applications I worked on.In Chapter 3, we present and thoroughly assess a framework for understanding critical behavior in classical partition functions by employing NPL techniques on data sets containing thermal configurations; provide a robust analysis of phase transitions using different NPL methods.In Chapter 4, we present a theoretical framework for information extraction in synthetic quantum matter for the case of a quantum quench in a spinor Bose-Einstein vii condensate experiment.In Chapter 5, we demonstrate how the field of network science can significantly improve and elevate our assumption-free characterization of various phases of matter.We present compelling evidence that network science offers a transparent and effective set of methods for investigating the properties of distinct phases and phase transitions, enabling us to identify critical points.

Related papers

Augmenting Quantum Mechanics with Artificial Intelligence

Giacomo Torlai

The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.

•Dec 4, 2018•3 citations

Neural networks and quantum many-body physics: exploring reciprocal benefits.

Anna Golubeva

One of the main reasons why the physics of quantum many-body systems is hard \nlies in the curse of dimensionality: \nThe number of states of such systems increases exponentially with the number of degrees of freedom involved. \nAs a result, computations for realistic systems become intractable, \nand even numerical methods are limited to comparably small system sizes. \nMany efforts in modern physics research are therefore concerned with \nfinding efficient representations of quantum states and \nclever approximations schemes that would allow them to characterize physical systems of interest. \n \nMeanwhile, Deep Learning (DL) has solved many non-scientific problems \nthat have been unaccessible to conventional methods for a similar reason. \nThe concept underlying DL is to extract knowledge from data \nby identifying patterns and regularities. \nThe remarkable success of DL has excited many physicists about \nthe prospect of leveraging its power to solve intractable problems in physics. \nAt the same time, DL turned out to be an interesting complex many-body \nproblem in itself. \nIn contrast to its widespread empirical applications, \nthe theoretical foundation of DL is strongly underdeveloped. \nIn particular, as long as its decision-making process and result interpretability remain opaque, \nDL can not claim the status of a scientific tool. \n \nIn this thesis, I explore the interface between DL and quantum many-body physics, \nand investigate DL both as a tool and as a subject of study. \nThe first project presented here is a theory-based study of \na fundamental open question about the role of width and the number of parameters in deep neural networks. \nIn this work, we consider a DL setup for the image recognition task on standard benchmarking datasets. \nWe combine controlled experiments with a theoretical analysis, including analytical calculations for a toy model. \nThe other three works focus on the application of Restricted Boltzmann Machines as generative models \nfor the task of wavefunction reconstruction from measurement data on a quantum many-body system. \nFirst, we implement this approach as a software package, making it available as a tool for experimentalists. \nFollowing the idea that physics problems can be used to characterize DL tools, \nwe then use our extensive knowledge of this setup to conduct a systematic study of \nhow the RBM complexity scales with the complexity of the physical system. \nFinally, in a follow-up study we focus on the effects of parameter pruning techniques \non the RBM and its scaling behavior.

•Aug 3, 2021•0 citations

Disentangling and machine learning the many-fermion problem

Peter Broecker

One of the most intriguing areas of physics is the study of strongly correlated many-body systems. In these kinds of systems, a large number of particles interacts via interactions that are strong enough to play a major role in determining the properties of the system, which is particularly interesting when multiple interaction terms compete and cannot be satisfied simultaneously. Examples of phases they realize range from simple magnetism to puzzling phenomena such as superconductivity or topological order. Of special interest in condensed matter are fermionic models which have an extra layer of complexity added by the possibly intricate sign structure of the wave function. \nHowever, exactly solvable models that exhibit the sought-after phenomena are scarce and Hamiltonians that are supposed to model experiments often elude analytical solutions precisely due to the strong interactions. Numerical methods are thus essential to gain insight into these systems and provide an important link between theoretical models and real world experiments. There are many different methods that in principle allow solving a problem numerically exact, most prominently exact diagonalization, tensor network based methods such as DMRG and (quantum) Monte Carlo. Exact diagonalization is certainly the most straightforward technique which allows measuring any observable of interest but its application to interacting models is severely limited by the exponential growth of the Hilbert space with the system size which only allows studying rather small systems. Tensor network methods excel in the study of gapped, one-dimensional systems and while they have shown some impressive results for two-dimensional systems, they need a lot of fine tuning and careful analysis to be considered reliable in this very important domain. Quantum Monte Carlo, on the other hand, is in principle neither limited by the size of the Hilbert space nor by the strength of the interactions and has thus been a tremendously important tool for studying condensed matter systems which is why it is the focus of this thesis. \nIt is necessary to continuously advance existing and develop new techniques to keep up with theoretical as well as with experimental progress. In this thesis, new methods to identify and characterize conventional and novel phases of matter within quantum Monte Carlo are developed and tested on archetypical models of condensed matter. \nIn the first part of this thesis, a method to study entanglement properties of strongly interacting fermionic models in quantum Monte Carlo is presented. Measurements of this kind are needed because some characteristics of a system remain hidden from conventional approaches based on the calculation of correlation functions. Prime examples are systems that realize so-called topological order entailing long-range entanglement that can be positively diagnosed using entanglement techniques. Realizing such measurements in a concrete algorithm is not straightforward for fermions. A large section of this part is thus devoted to developing a solution to the problem of implementing entanglement measurements and benchmarking the results against known data. \nThe second part is concerned with a truly novel and recent approach to the many-body problem, namely the symbiosis of machine learning and quantum Monte Carlo techniques. Out of the many different possibilities to combine the two, this part is concerne with exploring ways in which machine learning can help to effortlessly explore phase diagrams of hitherto unknown Hamiltonians. \nDespite the power and versatility of quantum Monte Carlo techniques, it does suffer from one significant weakness called the fermion sign problem. At its core related to the peculiar exchange statistics of fermions, it is in principle merely a technical problem of the Monte Carlo procedure but one that actually prohibits the use of Monte Carlo methods for a large number of interesting problems. The sign problem has been known for a long time but remains unsolved to this day. Thus, it is time to approach the problem from a different perspective with the hope of learning something new that can either help to better understand the problem itself or the properties of the models affected by it. Both of the two major research areas, entanglement measures and machine learning, are capable of providing such new perspectives and the sign problem will be revisited in more detail in the context of each of them.

•Jan 1, 2018•0 citations

Explorations in machine learning for interacting many-body systems.

Jonathon Matthew Schulz-Beach

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.

•Sep 3, 2020•0 citations

Machine learning phases in statistical physics

Qi Chen

Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM)\nis closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.

•Jan 1, 2017•0 citations

Machine learning for many-Body physics

Louis-François Arsenault, Alejandro López‐Bezanilla, O. Anatole von Lilienfeld +1 more

Bulletin of the American Physical Society•Mar 5, 2015•0 citations
In this digital age, machine learning (a prominent element within the context of artificial intelligence) has become an integral part of modern life, influencing various aspects of our daily activities.The predictive power of these tools is increasing with the advancements in algorithms, increased computational power, and the availability of large data sets: one basic example of this is language-based models, which have revolutionized our capabilities of transferring and processing information.Data is the foundational element of machine learning, and the quality and relevance of the data sets have a profound impact on the performance and accuracy of machine learning models.Thus "data is the new gold", captures the immense value that data holds in our modern world.With the exponential growth in data, the increasing demand for better machine-learning tools comes as a natural consequence.The field of physics is no exception to this, especially with the rise of big simulations and experiments generating huge amounts of data.Experiments at particle accelerators like the Large Hadron Collider(LHC) and Fermi lab, gravitational waves detector by LIGO and Virgo, climate models and weather simulations, Sloan Digital Sky Survey (SDSS), Cosmic Microwave Background(CMB) radiation providing insights into the early universe; all these studies generate massive data sets.In this context, developing more powerful, accurate, and specialized tools, is essential to meet the evolving needs in physics as well.In this thesis, we aim to study different types of ML tools to characterize the many-body problem in the context of classical and quantum statistical mechanics, with a focus on unbiased and interpretable methods.We use techniques coming from so-called non-parametric learning (NPL), where the analysis is done without specifying a fixed set of parameters in an assumption-free vi manner.NPL is a subset of the broad unsupervised learning category; the algorithm learns from the intrinsic structure of the data set.NPL is particularly valuable in scenarios where data assumptions are uncertain, data distributions are non-standard, or when dealing with complex data sets where relationships are difficult to predict beforehand.This works in our favor as the relation between data sets coming from many-body physics system and their effect on data structures when physical parameters change is not well understood -the simple reason being that the typical physicists mindset is very much focused on performing huge dimensional reduction from microscopic physical information (a canonical example of this being mean field theories, where the behavior of a large number of degrees of freedom is replaced by a single one).The thesis is organized as follows.In Chapter 1, we discuss the theoretical framework behind the NPL methods used.We present basic ideas in our methodologies, which encompass the overarching principles guiding our approach.These include the linkage between statistical physics and data analysis, particularly in relation to intrinsic dimension (Id) and its significance in understanding critical characteristics.Additionally, we delve into the application of Principal Component Analysis (PCA) and introduce the notion of PCA entropy -a witness of information spreading under linear transformation, whose relevance to physical phenomena we start investigating here.In Chapter 2, we describe the data sets we work with; statistical mechanics inspired data sets, such as those generated via sampling classical Ising models through advanced Monte Carlo algorithms, and experimental data of a spinor Bose-Einstein condensate.The following chapters present the applications I worked on.In Chapter 3, we present and thoroughly assess a framework for understanding critical behavior in classical partition functions by employing NPL techniques on data sets containing thermal configurations; provide a robust analysis of phase transitions using different NPL methods.In Chapter 4, we present a theoretical framework for information extraction in synthetic quantum matter for the case of a quantum quench in a spinor Bose-Einstein vii condensate experiment.In Chapter 5, we demonstrate how the field of network science can significantly improve and elevate our assumption-free characterization of various phases of matter.We present compelling evidence that network science offers a transparent and effective set of methods for investigating the properties of distinct phases and phase transitions, enabling us to identify critical points.
The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.
One of the main reasons why the physics of quantum many-body systems is hard \nlies in the curse of dimensionality: \nThe number of states of such systems increases exponentially with the number of degrees of freedom involved. \nAs a result, computations for realistic systems become intractable, \nand even numerical methods are limited to comparably small system sizes. \nMany efforts in modern physics research are therefore concerned with \nfinding efficient representations of quantum states and \nclever approximations schemes that would allow them to characterize physical systems of interest. \n \nMeanwhile, Deep Learning (DL) has solved many non-scientific problems \nthat have been unaccessible to conventional methods for a similar reason. \nThe concept underlying DL is to extract knowledge from data \nby identifying patterns and regularities. \nThe remarkable success of DL has excited many physicists about \nthe prospect of leveraging its power to solve intractable problems in physics. \nAt the same time, DL turned out to be an interesting complex many-body \nproblem in itself. \nIn contrast to its widespread empirical applications, \nthe theoretical foundation of DL is strongly underdeveloped. \nIn particular, as long as its decision-making process and result interpretability remain opaque, \nDL can not claim the status of a scientific tool. \n \nIn this thesis, I explore the interface between DL and quantum many-body physics, \nand investigate DL both as a tool and as a subject of study. \nThe first project presented here is a theory-based study of \na fundamental open question about the role of width and the number of parameters in deep neural networks. \nIn this work, we consider a DL setup for the image recognition task on standard benchmarking datasets. \nWe combine controlled experiments with a theoretical analysis, including analytical calculations for a toy model. \nThe other three works focus on the application of Restricted Boltzmann Machines as generative models \nfor the task of wavefunction reconstruction from measurement data on a quantum many-body system. \nFirst, we implement this approach as a software package, making it available as a tool for experimentalists. \nFollowing the idea that physics problems can be used to characterize DL tools, \nwe then use our extensive knowledge of this setup to conduct a systematic study of \nhow the RBM complexity scales with the complexity of the physical system. \nFinally, in a follow-up study we focus on the effects of parameter pruning techniques \non the RBM and its scaling behavior.
One of the most intriguing areas of physics is the study of strongly correlated many-body systems. In these kinds of systems, a large number of particles interacts via interactions that are strong enough to play a major role in determining the properties of the system, which is particularly interesting when multiple interaction terms compete and cannot be satisfied simultaneously. Examples of phases they realize range from simple magnetism to puzzling phenomena such as superconductivity or topological order. Of special interest in condensed matter are fermionic models which have an extra layer of complexity added by the possibly intricate sign structure of the wave function. \nHowever, exactly solvable models that exhibit the sought-after phenomena are scarce and Hamiltonians that are supposed to model experiments often elude analytical solutions precisely due to the strong interactions. Numerical methods are thus essential to gain insight into these systems and provide an important link between theoretical models and real world experiments. There are many different methods that in principle allow solving a problem numerically exact, most prominently exact diagonalization, tensor network based methods such as DMRG and (quantum) Monte Carlo. Exact diagonalization is certainly the most straightforward technique which allows measuring any observable of interest but its application to interacting models is severely limited by the exponential growth of the Hilbert space with the system size which only allows studying rather small systems. Tensor network methods excel in the study of gapped, one-dimensional systems and while they have shown some impressive results for two-dimensional systems, they need a lot of fine tuning and careful analysis to be considered reliable in this very important domain. Quantum Monte Carlo, on the other hand, is in principle neither limited by the size of the Hilbert space nor by the strength of the interactions and has thus been a tremendously important tool for studying condensed matter systems which is why it is the focus of this thesis. \nIt is necessary to continuously advance existing and develop new techniques to keep up with theoretical as well as with experimental progress. In this thesis, new methods to identify and characterize conventional and novel phases of matter within quantum Monte Carlo are developed and tested on archetypical models of condensed matter. \nIn the first part of this thesis, a method to study entanglement properties of strongly interacting fermionic models in quantum Monte Carlo is presented. Measurements of this kind are needed because some characteristics of a system remain hidden from conventional approaches based on the calculation of correlation functions. Prime examples are systems that realize so-called topological order entailing long-range entanglement that can be positively diagnosed using entanglement techniques. Realizing such measurements in a concrete algorithm is not straightforward for fermions. A large section of this part is thus devoted to developing a solution to the problem of implementing entanglement measurements and benchmarking the results against known data. \nThe second part is concerned with a truly novel and recent approach to the many-body problem, namely the symbiosis of machine learning and quantum Monte Carlo techniques. Out of the many different possibilities to combine the two, this part is concerne with exploring ways in which machine learning can help to effortlessly explore phase diagrams of hitherto unknown Hamiltonians. \nDespite the power and versatility of quantum Monte Carlo techniques, it does suffer from one significant weakness called the fermion sign problem. At its core related to the peculiar exchange statistics of fermions, it is in principle merely a technical problem of the Monte Carlo procedure but one that actually prohibits the use of Monte Carlo methods for a large number of interesting problems. The sign problem has been known for a long time but remains unsolved to this day. Thus, it is time to approach the problem from a different perspective with the hope of learning something new that can either help to better understand the problem itself or the properties of the models affected by it. Both of the two major research areas, entanglement measures and machine learning, are capable of providing such new perspectives and the sign problem will be revisited in more detail in the context of each of them.
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.
Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM)\nis closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.