Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Cosystolic Expanders from Tensors Imply Explicit Quantum LDPC Codes
  with $\Omega(\sqrt{n}\log^kn)$ Distance   In this work we introduce a new notion of expansion in higher dimensions that
is stronger than the well studied cosystolic expansion notion, and is termed
{\em Collective-cosystolic expansion}.
  We show that tensoring two cosystolic expanders yields a new cosystolic
expander, assuming one of the complexes in the product, is not only cosystolic
expander, but rather a collective cosystolic expander.
  We then show that the well known bounded degree cosystolic expanders, the
Ramanujan complexes are, in fact, collective cosystolic expanders. This enables
us to construct new bounded degree cosystolic expanders, by tensoring of
Ramanujan complexes.
  Using our new constructed bounded degree cosystolic expanders we construct
{\em explicit} quantum LDPC codes of distance $\sqrt{n} \log^k n$ for any $k$,
improving a recent result of Evra et. al. \cite{EKZ}, and setting a new record
for distance of explicit quantum LDPC codes.
  The work of \cite{EKZ} took advantage of the high dimensional expansion
notion known as cosystolic expansion, that occurs in Ramanujan complexes. Our
improvement is achieved by considering tensor product of Ramanujan complexes,
and using their newly derived property, the collective cosystolic expansion.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas