Quantum information and the structure of spacetime

We will review how quantum information has influenced the study of quantum gravity. This starts from the connection between entropy and black holes in the 1970s, and later involves the gravitational fine grained entropy formula of Ryu and Takayanagi, as well as the connection between entanglement and spacetime geometry. We will see how tensor networks and quantum error correction are very useful tools to think about gravitational holography.