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One hurdle to performing reliable quantum computations is overcoming noise.One possibility is to reduce the number of particles needing to be protectedfrom noise and instead use systems with more states, so called qudit quantumcomputers. In this paper we show that codes for these systems can be derivedfrom already known codes, and in particular that degenerate stabilizer codescan have their distance also promised upon sufficiently large local-dimension,as well as a new bound on the local-dimension required to preserve the distanceof local-dimension-invariant codes, which is a result which could prove to beuseful for error-corrected qudit quantum computers.

Degenerate Local-dimension-invariant Stabilizer Codes and an Alternative Bound for the Distance Preservation Condition