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We consider design of the quantum stabilizer codes via a two-step,low-complexity approach based on the framework of codeword-stabilized (CWS)codes. In this framework, each quantum CWS code can be specified by a graph anda binary code. For codes that can be obtained from a given graph, we giveseveral upper bounds on the distance of a generic (additive or non-additive)CWS code, and the lower Gilbert-Varshamov bound for the existence of additiveCWS codes. We also consider additive cyclic CWS codes and show that these codescorrespond to a previously unexplored class of single-generator cyclicstabilizer codes. We present several families of simple stabilizer codes withrelatively good parameters.

Low-complexity quantum codes designed via codeword-stabilized framework