Fetching the paper…
Reading the bibliography…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel.
Low Density Parity-Check Codes
R. Gallager · 1963
Earlier work this paper cites.
Graphs and Hypergraphs
C. Berge · 1973
Earlier work this paper cites.
The critical probability of bond percolation on the square lattice equals 1/2
H. Kesten · 1980
Earlier work this paper cites.
G. Grimmett, Percolation
1989
Earlier work this paper cites.
Elements of Information Theory
T. M. Cover and J. A. Thomas · 1991
Earlier work this paper cites.
Matroid Theory
J. G. Oxley · 1992
Earlier work this paper cites.
Percolation beyond ℤ d \mathbb{Z}^{d} , many questions and a few answers
I. Benjamini and O. Schramm · 1996
Earlier work this paper cites.
Good quantum error-correcting codes exist
A. R. Calderbank and P. W. Shor, · 1996
Earlier work this paper cites.
A. Steane, Multiple particle interference and quantum error correction, Proc. Roy. Soc. Lond. A
1996
Earlier work this paper cites.
Capacities of quantum erasure channels
C. H. Bennett, D. P. DiVincenzo, and J. A. Smolin · 1997
Earlier work this paper cites.
Codes for the quantum erasure channel
M. Grassl, T. Beth, and T. Pellizzari · 1997
Earlier work this paper cites.
Fault-tolerant quantum computation by anyons
A. Y. Kitaev · 1997
Earlier work this paper cites.
Quantum error correction via codes over G F ( 4 ) GF(4)
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1998
Earlier work this paper cites.
Quantum information and computation, 1998
J. Preskill · 1998
Cited alongside, same era.
Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
Cited alongside, same era.
Triangle group representations and constructions of regular maps
J. Širáň · 2000
Cited alongside, same era.
Upper bounds on the rate of LDPC codes
D. Burshtein, M. Krivelevich, S. Litsyn, and G. Miller · 2002
Cited alongside, same era.
Topological quantum memory
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill · 2002
Cited alongside, same era.
Algorithmic aspects of quantum error-correcting codes
M. Grassl · 2002
Cited alongside, same era.
Sparse-graph codes for quantum error correction
A class of quantum LDPC codes: construction and performances under iterative decoding
T. Camara, H. Ollivier, and J-P. Tillich · 2007
Later among the works it cites.
Quantum quasi-cyclic LDPC codes
M. Hagiwara and H. Imai · 2007
Later among the works it cites.
A class of quantum LDPC codes constructed from finite geometries
S.A. Aly · 2008
Later among the works it cites.
Modern Coding Theory
T. Richardson and R. Urbanke · 2008
Later among the works it cites.
Asymmetric quantum ldpc codes
K.P. Sarvepalli, M. Rötteler, and A. Klappenecker · 2008
Later among the works it cites.
Percolation on hyperbolic lattices
S. K. Baek, P. Minnhagen, and B. J. Kim · 2009
Later among the works it cites.
Analytic Combinatorics
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
D.J.C. MacKay, G. Mitchison, and P.L. McFadden · 2004
Cited alongside, same era.
Topological quantum distillation
H. Bombin and M. A. Martin-Delgado · 2006
Cited alongside, same era.
Generatingfunctionology
H. S. Wilf · 2006
Cited alongside, same era.
A class of quantum LDPC codes derived from latin squares and combinatorial objects
S.A. Aly · 2007
Cited alongside, same era.
Exact topological quantum order in d = 3 d=3 and beyond: Branyons and brane-net condensates
H. Bombin and M. A. Martin-Delgado · 2007
Cited alongside, same era.
Homological error correction: Classical and quantum codes
H. Bombin and M. A. Martin-Delgado · 2007
Cited alongside, same era.
P. Flajolet and R. Sedgewick · 2009
Later among the works it cites.
Quantum LDPC codes with positive rate and minimum distance proportional to n 1 / 2 n^{1/2} ;
J.-P. Tillich and G. Zémor · 2009
Later among the works it cites.
On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction
G. Zémor · 2009
Later among the works it cites.
Quantum erasure-correcting codes and percolation on regular tilings of the hyperbolic plane
N. Delfosse and G. Zémor · 2010
Later among the works it cites.
A construction of quantum LDPC codes from Cayley graphs
A. Couvreur, N. Delfosse, and G. Zémor · 2011
Later among the works it cites.
Crossing on hyperbolic lattices, 2011
H. Gu and R. M. Ziff · 2011
Later among the works it cites.