Title :
Quantum error correction via codes over GF(4)
Author :
Calderbank, A.R. ; Rains, E.M. ; Shor, P.W. ; Sloane, N. J A
Author_Institution :
AT&T Bell Labs., Murray Hill, NJ, USA
fDate :
29 Jun-4 Jul 1997
Abstract :
The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment. In the present paper the problem of finding quantum-error-correcting codes is transformed into one 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
Keywords :
Galois fields; error correction codes; quantum theory; GF(4); additive codes; coherent quantum superposition; lower bounds; quantum computing; quantum entanglement; quantum error correction codes; self-orthogonal codes; trace inner product; upper bounds; Additives; Error correction; Error correction codes; Quantum computing; Quantum entanglement; Quantum mechanics; Rain; Tensile stress;
Conference_Titel :
Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on
Conference_Location :
Ulm
Print_ISBN :
0-7803-3956-8
DOI :
10.1109/ISIT.1997.613213
