Non-Archimedean Holography

We propose a discretization of the AdS/CFT correspondence with bulk space the $p$-adic Bruhat-Tits trees.
In addition to a consistent description of field theory on the boundary and gravity on the bulk, this approach
allows for a natural interpretation of the more recent viewpoint on holography, where bulk geometry emerges
from quantum entanglement on the boundary, in terms of a construction of holographic classical and quantum
codes on the Bruhat-Tits trees.