  We introduce a purely graph-theoretical object, namely the coding clique, to
construct quantum errorcorrecting codes. Almost all quantum codes constructed
so far are stabilizer (additive) codes and the construction of nonadditive
codes, which are potentially more efficient, is not as well understood as that
of stabilizer codes. Our graphical approach provides a unified and classical
way to construct both stabilizer and nonadditive codes. In particular we have
explicitly constructed the optimal ((10,24,3)) code and a family of 1-error
detecting nonadditive codes with the highest encoding rate so far. In the case
of stabilizer codes a thorough search becomes tangible and we have classified
all the extremal stabilizer codes up to 8 qubits.

Quantum Physics