Machine learning has gained in popularity over recent years.It shows great power in many real-world problems, including Computer Vision, Natural Language Processing and Speech Recognition.However, a clear theoretical mechanism is still lacked behind many machine learning algorithms, such as Deep Learning.Good theoretical analysis can not only explain the current success of machine learning, but also reveal new approaches to future advancements.In last few years, more and more physicists contributed good works that provided novel insights and philosophy for machine learning communities.Due to two reasons, we believe physical approaches can be very promising.First, we think machine learning share some similar theoretical mechanism with physical theories, particularly quantum physics and statistical physics.We may employ physical languages to study machine learning models in some physical frameworks.Second, real-world problems and information itself must obey some fundamental laws, which are often physical laws for our universe.Good physical prior knowledge which may be helpful to reduce model complexity and improve generalization.The physical perspective deserve more attention.In this thesis, we review a few related works on the physics based approach and related traditional machine learning.It helps us understand how physics may interact with machine learning.We propose quantum interpretations for machine learning and a class of original physics-inspired machine learning algorithms, named Quantum-Inspired Forest.Both theoretical proof and empirical analysis are presented in details.The success of quantum-inspired machine learning encourages us to pay attention to multiple physical viewpoints.Even without solid theoretical analysis, important prior knowledge and heuristics may be obtained from physical models.The proposed algorithm is an example that illustrates how to combine physics and machine learning together.We in particular discuss a physical perspective on machine learning.We hope our physical analysis on machine learning would inspire more novel works in near future.
Machine learning has gained in popularity over recent years.It shows great power in many real-world problems, including Computer Vision, Natural Language Processing and Speech Recognition.However, a clear theoretical mechanism is still lacked behind many machine learning algorithms, such as Deep Learning.Good theoretical analysis can not only explain the current success of machine learning, but also reveal new approaches to future advancements.In last few years, more and more physicists contributed good works that provided novel insights and philosophy for machine learning communities.Due to two reasons, we believe physical approaches can be very promising.First, we think machine learning share some similar theoretical mechanism with physical theories, particularly quantum physics and statistical physics.We may employ physical languages to study machine learning models in some physical frameworks.Second, real-world problems and information itself must obey some fundamental laws, which are often physical laws for our universe.Good physical prior knowledge which may be helpful to reduce model complexity and improve generalization.The physical perspective deserve more attention.In this thesis, we review a few related works on the physics based approach and related traditional machine learning.It helps us understand how physics may interact with machine learning.We propose quantum interpretations for machine learning and a class of original physics-inspired machine learning algorithms, named Quantum-Inspired Forest.Both theoretical proof and empirical analysis are presented in details.The success of quantum-inspired machine learning encourages us to pay attention to multiple physical viewpoints.Even without solid theoretical analysis, important prior knowledge and heuristics may be obtained from physical models.The proposed algorithm is an example that illustrates how to combine physics and machine learning together.We in particular discuss a physical perspective on machine learning.We hope our physical analysis on machine learning would inspire more novel works in near future.
Machine learning, especially deep learning, has achieved remarkable success in a wide range of applications.It is one of today' s most rapidly growing fields in science and technology.In recent years, the interplay between machine learning and physics has attracted tremendous attention, giving rise to a new interdisciplinary research frontier.On the one hand, we may utilize machine learning methods to tackle certain intricate physical problems that are beyond the capability of traditional approaches.On the other hand, certain concepts, ideas, and methods originated in physics can also be exploited to enhance the study of machine learning.Without a doubt, the fusion of machine learning and physics will bring us new opportunities and challenges, and significantly advance the studies in both fields.This special topic contains several review papers written by experts working actively in this emergent interdisciplinary field.These papers review a number of hot topics and some latest progresses, covering adversarial learning in quantum artificial intelligence, quantum generative models, machine learning based on waves and diffusions, automatic differentiation, machine learning assisted quantum adiabatic algorithm design, state preparation in quantum machine learning, experimental progress of quantum machine learning based on spin systems, etc.We hope this special topic can help readers gain a primary picture of the research content, basic ideas and methods, the latest developments, and the challenges and opportunities faced in the intersection of machine learning and physics.Meanwhile, we also hope this special topic can provide some inspiration to readers, and attract more researchers to join this exciting interdisciplinary field.
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 intersection of machine learning and quantum computing has been one of the greatest scientific projects in current time. With quantum computing in the offing, the assurance of using quantum mechanical effects in computational learning to transform the world has never been closer. The publication of this book comes at a critical time, when theoretical models are shouldering maturity with capabilities of experimentation, that has brought about great possibilities to implement computational benefits that quantum systems can provide in performing machine learning tasks. Quantum machine learning is one field which has rapidly changed in the last ten years. What was originally viewed as mere theoretical conjecture has now evolved into a living research community which includes rigorous mathematical modeling, novel algorithm design, and more and more complex experimental realisations on the near-term quantum computers. Such change can be characterised by the increasing sophistication of our theory in as well as the revolutionary advances in quantum computing technology, and by the noisy intermediate-scale quantum (NISQ) era. Chapters in this book chronologically discuss the complex nature of quantum machine learning, including theoretical principles and challenges of practice. All the chapters cover a very important aspect in this growing area leaving the reader not only with an in-depth analysis but also a wide enough point of view to traverse this somewhat complicated inter-disciplinary area. The book is organized in such a way that that it takes the reader through more advanced parts of the quantum machine learning theory and practice. We start by explaining quantum feature maps, and kernel-type methods and laying the mathematical background on which quantum-enhanced learning is based. There we discuss computational complexity, trainability issues, neural network architectures, scaling of resources, sample complexity limits and the issue critical of quantum data encoding. This book has a variety of audience. The works will also offer exhaustive proposals of key concepts, methodologies and open problems to graduate students and researchers venturing into the field. Individuals who operate quantum computing platforms will have an understanding of the options available when it comes to designing an algorithm and the resources needed, as well as the expectations of its performance. The systematic approach of tackling complexity theorist-foundations and rigorous mathematical analyses will be appreciated by the theorists. Quantum machine learning is interdisciplinary and requires the services and knowledge of quantum physics, computer science, mathematics, and statistics. Although we do not expect our readers to have the basic knowledge of quantum computing and classical machine learning, we give adequate background and references to accommodate other readers of varying technical background. By 2026, quantum machine learning will be on a important crossroads. NISQ has also provided its own stunning demonstrations and harsh lessons on the difficulty of obtaining useful quantum advantage. Other phenomena like barren plateaus have changed the minds of us on the nature of variational quantum algorithm trainability. Resource-efficient quantum learning has been transformed by the advanced measurement protocols, such as classical shadow tomography. The frontier of the implementable quantum algorithms is constantly being pushed by hardware advances. The book reflects the picture of the field in this dynamic time, including the latest theoretical developments, their experiments, and new optimal practices. We admit that quantum machine learning is a fast-developing science, and there are certain spheres of our knowledge that will surely become more profound in the nearest future. The transformative potential of quantum machine learning is still achievable only with further achievements in many dimensions: the theory of when and why quantum algorithms are effective, algorithmic innovations to overcome the limitations of near-term hardware, hardware engineering to overcome qubit quality and system scale, and discovering applications when quantum algorithms and methods and methods offer significant superior practical performance. Hopefully, this book will provide useful guidance to all the existing knowledge and guide to the future innovations. The opportunities are out of the world, yet the challenges are significant. With the ongoing development of quantum hardware capabilities and an ever-increasing theoretical basis, it is quite possible that quantum machine learning will transform the world of approaching the problem of complex computational learning.
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessible way, and discusses the potential of a future theory of quantum learning.
Neural network approaches to machine learning problems rely on statistical frameworks that are designed to generalize to many situations, whereas traditional physics-based approaches to quantum problems stem from specific physical laws that govern the behavior of certain classes of systems. While quantum physics and machine learning have been largely disparate fields for most of their history, their interplay has gained considerable attention in recent years, primarily driven by the premise that the most powerful computational models are those whose foundations stem from both physical and statistical principles. Two overarching strategies in this area include building physics-based machine learning models from the ground up, or alternatively, looking for hidden ways that statistical models include aspects of physical systems. Many-body quantum systems turn out to be a useful testing ground for both of these approaches, due to the complex behavior that arises from simple fundamental rules. Here, we present several ways that neural networks can represent many-body spin states, which enables the exploration into the underlying nature of neural networks, as well as gaining insight into how effective different classes of models are for simulating physical systems. The main focus areas of this thesis are (1) connecting convolutional neural networks to maximum-entropy distributions when applied to spin systems, (2) using generative models to gain physical insights into experimental tomographic data, and (3) applying inverse reinforcement learning to probe the nature of agent-based quantum circuit design.