Lectures on Quantum Tensor Networks

TL;DR

This book provides a comprehensive overview of tensor network theory, emphasizing its applications in quantum information processing and its role as a reasoning tool across physics, computer science, and mathematics.

Contribution

It consolidates contemporary practices in tensor networks, integrating foundational concepts with advanced applications like matrix product states and entanglement in a unified diagrammatic language.

Findings

Covers tensor network applications in quantum states and operators

Includes practical tools for graphical reasoning in quantum information

Provides educational material suitable for graduate students

Abstract

Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing. This book aims to present the best contemporary practices in the use of tensor networks as a reasoning tool, placing quantum states, operators and processes on the same compositional footing. The book has 7 parts and over 40 subsections which took shape in over a decade of teaching. In addition to covering the foundations, the book covers important applications such as matrix product states, open quantum systems and entanglement $-$ all cast into the diagrammatic tensor network language. The intended audience includes those in quantum information science wishing to learn about tensor networks. It includes scientists who have employed tensor networks in their modeling codes who have interest in the tools graphical reasoning capacity. The audience further includes the graduate student researcher, whom with some effort, should find this book accessible. I would appreciate it if you emailed me about any mistakes or typos you find.