Jump Codes and Other Quantum Codes
by
Chris Charnes
Deakin University, Burwood, Victoria

Jump codes were developed for purpose of stabilization of errors in quantum computations in the context of quantum optics. The initial research on Jump codes concentrated mainly on their constructions and proving various bounds. Several ad hoc constructions of Jump codes were obtained in a combinatorial setting. But so far no single construction principle has emerged for these codes, such as the group theoretic setting of Calderbank, Rains, Shor and Sloane. Nor has the relation between Jump codes and other quantum error correcting codes been satisfactorily explained.

In this talk we explore the connections between Jump codes, the Pauli error group and topological quantum codes. A group theoretic result accounts for several previously constructed Jump codes and we explain a suggestive relation between the Pauli group error group and Jump codes. This mechanism seems analagous to the group theoretic construction of of Calderbank et al.

Date received: September 22, 2003