Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holography, cellulations and error correcting codes   Quantum error correction codes associated with the hyperbolic plane have been
explored extensively in the context of the AdS$_3$/CFT$_2$ correspondence. In
this paper we initiate a systematic study of codes associated with holographic
geometries in higher dimensions, relating cellulations of the spatial sections
of the geometries to stabiliser codes. We construct analogues of the HaPPY code
for three-dimensional hyperbolic space (AdS$_4$), using both absolutely
maximally entangled (AME) and non-AME codes. These codes are based on uniform
regular tessellations of hyperbolic space but we note that AME codes that
preserve the discrete symmetry of the polytope of the tessellation do not exist
above two dimensions. We also explore different constructions of stabiliser
codes for hyperbolic spaces in which the logical information is associated with
the boundary and discuss their potential interpretation. We explain how our
codes could be applied to interesting classes of holographic dualities based on
gravity-scalar theories (such as JT gravity) through toroidal reductions of
hyperbolic spaces.

14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio