Quantum Error Correction and Orthogonal Geometry
Quantum Physics
2009-01-23 v3
Abstract
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.
Cite
@article{arxiv.quant-ph/9605005,
title = {Quantum Error Correction and Orthogonal Geometry},
author = {A. R. Calderbank and E. M Rains and P. W. Shor and N. J. A. Sloane},
journal= {arXiv preprint arXiv:quant-ph/9605005},
year = {2009}
}
Comments
RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have changed the statement of Theorem 2 to correct it -- we now get worse rates than we previously claimed for our quantum codes. Minor changes have been made to the rest of the paper