Quantum error correction via codes over GF(4)

The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment. In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.