Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fault-tolerant logical gates in holographic stabilizer codes are
  severely restricted   We evaluate the usefulness of holographic stabilizer codes for practical
purposes by studying their allowed sets of fault-tolerantly implementable
gates. We treat them as subsystem codes and show that the set of transversally
implementable logical operations is contained in the Clifford group for
sufficiently localized logical subsystems. As well as proving this concretely
for several specific codes, we argue that this restriction naturally arises in
any stabilizer subsystem code that comes close to capturing certain properties
of holography. We extend these results to approximate encodings,
locality-preserving gates, certain codes whose logical algebras have
non-trivial centers, and discuss cases where restrictions can be made to other
levels of the Clifford hierarchy. A few auxiliary results may also be of
interest, including a general definition of entanglement wedge map for any
subsystem code, and a thorough classification of different correctability
properties for regions in a subsystem code.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex