Quantum Error Correction via Codes over GF(4)
Abstract
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 1996
- arXiv:
- arXiv:quant-ph/9608006
- Bibcode:
- 1996quant.ph..8006C
- Keywords:
-
- Quantum Physics
- E-Print:
- Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor errors