Decoding in Hyperbolic Spaces: LDPC Codes With Linear Rate and Efficient Error Correction

Built on

R. J. Lipton and R. E. Tarjan, ”A separator theorem for planar graphs”, SIAM Journal on Applied Mathematics 36
1979
Earlier work this paper cites.
L. Aleksandrov and H. Djidjev, “Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus”, SIAM Journal of Discrete Mathematics 9
Original
1996
Earlier work this paper cites.
M. Freedman, D. Meyer, and F. Luo, “ Z 2 Z_{2} systolic freedom and quantum codes”, Mathematics of Quantum Computation, Chapman & Hall/CRC, 287-320 (2002)
2002
Earlier work this paper cites.

E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory”, J. Math. Phys. 43
2002
Cited alongside, same era.
A. Kitaev, “Fault-tolerant quantum computation by anyons”, Ann. Phys. 303
2003
Cited alongside, same era.
J-P Tillich and G. Zémor, “Quantum ldpc codes with positive rate and minimum distance proportional to n 1 / 2 n^{1/2} ”, IEEE International Symposium on Inf. Theory
2009
Cited alongside, same era.
L. Guth and A. Lubotzky, “Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds”, arXiv:1310.5555
Original
Cited in the paper.
D. Gottesman, “What is the Overhead Required for Fault-Tolerant Quantum Computation?”, arXiv:1310.2984
Original
Cited in the paper.

W. Breslin, “Thick Triangulations of Hyperbolic n n -manifolds”, Pac. J. Math. 24
2009
Later among the works it cites.
A. A. Kovalev and L. P. Pryadko, “Improved quantum hypergraph-product LDPC codes”, IEEE International Symposium on Inf. Theory
2012
Later among the works it cites.
“Quantum Systems on Non- k k -Hyperfinite Complexes: A Generalization of Classical Statistical Mechanics on Expander Graphs”, M. H. Freedman and M. B. Hastings, arXiv:1301.1363, QIC 14
Original
2014
Closest in time.