  Entangled qubit can increase the capacity of quantum error correcting codes
based on stabilizer codes. In addition, by using entanglement quantum
stabilizer codes can be construct from classical linear codes that do not
satisfy the dual-containing constraint. We show that it is possible to
construct both additive and non-additive quantum codes using the codeword
stabilized quantum code framework. Nonadditive codes may offer improved
performance over the more common sta- bilizer codes. Like other
entanglement-assisted codes, the encoding procedure acts only the qubits on
Alice's side, and only these qubits are assumed to pass through the channel.
However, errors the codeword stabilized quantum code framework gives rise to
effective Z errors on Bob side. We use this scheme to construct new
entanglement-assisted non-additive quantum codes, in particular, ((5,16,2;1))
and ((7,4,5;4)) codes.
