Lectures on Quantum Tensor Networks

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.

178 page book in LaTeX. Please email me about any mistakes or typos. Current version always available on overleaf, see http://www.overleaf.com/read/jkccbhcdqwnh

References in corpus (19)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Novel schemes for measurement-based quantum computation
• Measurement-based quantum computation beyond the one-way model
• Closed timelike curves via post-selection: theory and experimental demonstration
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• A Simple Proof that Toffoli and Hadamard are Quantum Universal
• The maximally entangled symmetric state in terms of the geometric measure
• Tensor Networks in a Nutshell
• Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins
• Optimum Quantum Error Recovery using Semidefinite Programming
• Density Matrix Renormalization Group in the Heisenberg Picture
• TensorNetwork: A Library for Physics and Machine Learning
• Dynamical simulations of classical stochastic systems using matrix product states
• A 2 rebit gate universal for quantum computing
• Categorical Quantum Circuits
• Solving search problems by strongly simulating quantum circuits
• Charged String Tensor Networks
• Pushing Tensor Networks to the Limit