Clifford subsystem codes

Abstract

Subsystem codes are a generalization of decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. The known constructions of subsystem codes from classical codes are limited to quantum systems that all have the same dimension, and this dimension must be a power of a prime. It is shown that one can remove these restrictions and obtain subsystem codes in quantum systems of arbitrary finite dimension from classical codes that are subgroups of an abelian group. The constructions are derived from Clifford codes over abstract error groups with abelian index groups.