Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry protected self correcting quantum memory in three space
  dimensions   Whether self correcting quantum memories can exist at non-zero temperature in
a physically reasonable setting remains a great open problem. It has recently
been argued [1] that symmetry protected topological (SPT) systems in three
space dimensions subject to a strong constraint -- that the quantum dynamics
respect a 1-form symmetry -- realize such a quantum memory. We illustrate how
this works in Walker-Wang codes, which provide a specific realization of these
desiderata. In this setting we show that it is sufficient for the 1-form
symmetry to be enforced on a sub-volume of the system which is measure zero in
the thermodynamic limit. This strongly suggests that the `SPT' character of the
state is not essential. We confirm this by constructing an explicit example
with a trivial (paramagnetic) bulk that realizes a self correcting quantum
memory. We therefore show that the enforcement of a 1-form symmetry on a
measure zero sub-volume of a three dimensional system can be sufficient to
stabilize a self correcting quantum memory at non-zero temperature.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics