Quantum Codes from High-Dimensional Manifolds

R. A. Rankin, “On positive definite quadratic forms”, J. London Math. Soc., 28

1953

Earlier work this paper cites.

H. Federer, and W.H. Fleming, “Normal and integral currents”, Ann. of Math. 72

1960

Earlier work this paper cites.

“Asymptotic Formulae for Point Lattices of Bounded Determinant and Subspaces of Bounded Height”, W. M. Schmidt, Duke Math. J. 35

1968

Earlier work this paper cites.

J. Milnor, D. Husemoller, Symmetric Bilinear Forms

1973

Earlier work this paper cites.

F. R. Harvey and B. Lawson, “Calibrated geometries”, Acta Math. 148

1982

Earlier work this paper cites.

J.H. Conway and N.J. Sloane, Sphere Packings, Lattices and Groups

1988

Earlier work this paper cites.

R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist”, Phys. Rev. A, 54

1996

Earlier work this paper cites.

R. Coulangeon, “Minimal vectors in the second exterior power of a lattice ”, J. of Algebra, 194

1997

Earlier work this paper cites.

I Babenko and M Katz, “Systolic freedom of orientable manifolds”, Ann. Sci. Ecole Norm. Sup. 4

1998

Cited alongside, same era.

R. Gallager, “Low-density parity-check codes”. IRE Trans. on Inf. Theory, 8(1)

1999

Cited alongside, same era.

M. Freedman and D. Meyer, “Projective plane and planar quantum codes”, Foundations of Computational Mathematics, 1

2001

Cited alongside, same era.

M.H. Freedman, D. Meyer, and F. Luo, “Z2-systolic freedom and quantum codes”, Mathematics of quantum computation, Chapman & Hall/CRC, pages 287-320, 2002

2002

Cited alongside, same era.

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. of Phys., 303

D. Poulin, “Stabilizer Formalism for Operator Quantum Error Correction”, Phys. Rev. Lett. 95

2005

Later among the works it cites.

U. Erez, S. Litsyn, and R. Zamir, “Lattices which are good for (almost) everything,” IEEE Trans. Inf. Theory, 51

2005

Later among the works it cites.

N. Gama, N. Howgrave-Graham, H. Koy, and P. Q. Nguyen, “Rankin’s Constant and Blockwise Lattice Reduction”, Advances in Cryptology - CRYPTO 2006, vol. 4117 of Lecture Notes in Computer Science, p. 112-130, Springer-Verlag (2006)

2006

Later among the works it cites.

H. Bombin and M.A. Martin-Delgado, “Homological error correction: classical and quantum codes”, J. Math. Phys., 48

2007

Later among the works it cites.

Sergey Bravyi, Matthew B. Hastings, “Homological Product Codes”, Proc. of the 46th ACM Symposium on Theory of Computing (STOC 2014), pp. 273-282 (2014)

2014