Master defense by Matt Steinberg

MERA Tensor Networks, Quantum Error Correction, and AdS/CFT

High energy theoretical physics has undergone a radical transformation in the past 20 years due to the AdS/CFT correspondence. Our understanding of spacetime as a geometric construct related to higher dimensional quantum field theories has given us new insight into the nature of the universe. At the same time, quantum information has also undergone a revolution; the advent of quantum error correction and quantum error correction codes has truly revolutionized our understanding of how information is contained and can be manipulated in a quantum state. It was shown that there does indeed exist a connection between these two seemingly disparate fields of theoretical physics in 2006. Since then, there has been a torrent of interest in the theoretical community concerning the reproducibility of the AdS/CFT correspondence.

The aim of this thesis defense is to provide a conceptual overview of not only this connection between quantum information and AdS/CFT, but to showcase the AdS/CFT correspondence as a design principle for so-called holographic quantum error correction codes. Additionally, we propose a new variant from a popular design that may be useful as an effective realization of these new types of quantum error correction codes.