  We solve the fundamental quantum error correction problem for bi-unitary
channels on two-qubit Hilbert space. By solving an algebraic compression
problem, we construct qubit codes for such channels on arbitrary dimension
Hilbert space, and identify correctable codes for Pauli-error models not
obtained by the stabilizer formalism. This is accomplished through an
application of a new tool for error correction in quantum computing called the
``higher-rank numerical range''. We describe its basic properties and discuss
possible further applications.
