Quantum Circuits, Cellular Automata and Tensor Networks - Ignacio Cirac

Explore quantum circuits, cellular automata, and tensor networks in this comprehensive lecture by Ignacio Cirac. Delve into the composition of quantum computers using quantum gates acting on near neighbors according to spatial geometry. Examine quantum cellular automata (QCA) and their representation through tensor networks in various spatial dimensions. Discover how QCAs obey an area law for entanglement entropy creation. Investigate generalizations of these concepts, including the replacement of unitary operators with quantum channels and the inclusion of local measurements assisted by classical communication. Learn about the implications of these generalizations on area law compliance for mutual information creation and the challenges in expressing them as tensor networks. Gain insights into how these concepts relate to unitary dynamics and the limitations of describing them in terms of QCA.

Introduction
Setup
Quantum Circuits
Questions
Quantum Cellular Automata
Tensor Networks
Infinite Bond Space
Transfer Metrics
Quantum Channels
Defining Quantum Channels