<!--HTML--> Abstract This talk with cover a foundational understanding of tensor networks, starting with the basics of tensors and their contractions. Students will learn simple forms of tensor networks and their connection to quantum circuits. Additionally, the course gives an example of the application of tensor networks in machine learning. By the end of the course, participants will grasp the core concepts and practical uses of tensor networks. Bio Ema is a computer scientist pursuing PhD in physics at CERN and Universitat Autonoma de Barcelona, specializing in quantum and quantum-inspired algorithms for anomaly detection with applications in high-energy physics and medical imaging. Francesco is a PhD student at CERN and University of the Basque Country. He studied at KTH and Politecnico di Torino and focuses on the simulation of Quantum Matter with Tensor Network Methods and other techniques related to Quantum Computation.
<!--HTML--> Abstract This talk with cover a foundational understanding of tensor networks, starting with the basics of tensors and their contractions. Students will learn simple forms of tensor networks and their connection to quantum circuits. Additionally, the course gives an example of the application of tensor networks in machine learning. By the end of the course, participants will grasp the core concepts and practical uses of tensor networks. Bio Ema is a computer scientist pursuing PhD in physics at CERN and Universitat Autonoma de Barcelona, specializing in quantum and quantum-inspired algorithms for anomaly detection with applications in high-energy physics and medical imaging. Francesco is a PhD student at CERN and University of the Basque Country. He studied at KTH and Politecnico di Torino and focuses on the simulation of Quantum Matter with Tensor Network Methods and other techniques related to Quantum Computation.
<!--HTML-->In recent years, tensor networks have become a viable alternative to Monte Carlo calculations and exact diagonalization for the simulation of many-body systems. As they represent a formulation of quantum mechanical wavefunctions with polynomially many parameters, they make calculations of large systems feasible. They have already found wide application in condensed matter physics and start to be an interesting tool for high energy physics as well. In this lecture series, I will introduce the basic concepts of tensor networks. We will start with an introduction of the necessary basics of quantum mechanics and linear algebra and focus on the algorithmic side of tensor networks in the second lecture.
Discover the foundations of classical and quantum information theory in the digital age with this modern introductory textbook. Familiarise yourself with core topics such as uncertainty, correlation, and entanglement before exploring modern techniques and concepts including tensor networks, quantum circuits and quantum discord. Deepen your understanding and extend your skills with over 250 thought-provoking end-of-chapter problems, with solutions for instructors, and explore curated further reading. Understand how abstract concepts connect to real-world scenarios with over 400 examples, including numerical and conceptual illustrations, and emphasising practical applications. Build confidence as chapters progressively increase in complexity, alternating between classic and quantum systems. This is the ideal textbook for senior undergraduate and graduate students in electrical engineering, computer science, and applied mathematics, looking to master the essentials of contemporary information theory.
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics are covered, including tensor structures and network representations like Matrix Product States (MPS) and Tree Tensor Networks (TTN). These preliminaries provide readers with the core mathematical tools and concepts necessary for quantum physics and quantum computing applications, bridging the gap between multi-linear algebra and complex quantum systems. Part II explores practical applications of tensor networks in simulating quantum dynamics, with a particular focus on the efficiency they offer for systems of high computational complexity. Key topics include Hamiltonian dynamics, quantum annealing, open system dynamics, and optimization strategies using TN frameworks. A final chapter addresses the emerging role of “quantum magic” in tensor networks. It delves into non-stabilizer states and their contribution to quantum computational power beyond classical simulability, featuring methods such as stabilizer-enhanced MPS and the Clifford-dressed TDVP. In presenting tensor networks as tools for understanding quantum complexity, this book aims to foster a deeper collaboration between the many-body physics and quantum computing communities, inviting a broader audience to engage with these recent developments.
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the "quantics" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the "quantics" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.
In this informal course, I intend to give an introduction to Tensor Networks and their use for numerical simulations.The class is targeted towards PhD students and researchers with no background on the subject. The goal is for the audience to be able to concretely use TNs in their research at the end of the course.The first session will start with a quick global introduction to tensor networks, and then focus on the one-dimensional Matrix Product States (Tensor Trains).We will go through their properties, strengths and limitations, and give a few explicit examples. We will then study a few concrete time-evolution and groundstate-search algorithms for finite and infinite systems.
<!--HTML--> Abstract This hands-on session focuses on understanding the fundamental concepts of quantum computing, which are introduced during the presentation, such as superposition and entanglement, as well as one of the most well-known quantum algorithms, Grover's algorithm. The students will explore the practical usage of quantum computing with one of the most commonly used quantum computing languages, Qiskit, and learn how qubits form the foundation of quantum computation. By the end of the session, they should be able to code the quantum algorithm on their own and run it on different quantum simulators. Bio Graduated Master in Physics at EPFL in Switzerland, Su Yeon undertook her research on Quantum Generative Adversarial Networks to simulate High-Energy detectors. She is now working as a PhD student at EPFL and CERN to investigate quantum algorithms, especially focused on quantum machine learning for image classification and generation.