Holography from Quantum Error Correction

Abstract

In recent years, there has been growing interest in investigating the connection between quantum error correction and areas of physics like the AdS/CFT correspondence and the real-space renormalization group. In this thesis, we mainly focus on how ideas from holography have an interpretation in terms of quantum error-correcting codes. We begin by recounting how the three qutrit code that protects encoded quantum information from erasure is a useful toy model for realizing some important features of holography, like subregion duality, radial commutativity, and the Ryu-Takayanagi formula. Furthermore, generalizations of this analogy through the means of operator algebra quantum error correction will be discussed as well. Finally, we shall investigate some explicit and simple quantum codes for holographic properties and try to figure out whether they are functional and understand the reasons behind their success or failure when it comes to correcting erasures.