  Quantum computation can be performed by encoding logical qubits into the
states of two or more physical qubits, and controlling a single effective
exchange interaction and possibly a global magnetic field. This "encoded
universality" paradigm offers potential simplifications in quantum computer
design since it does away with the need to perform single-qubit rotations. Here
we show that encoded universality schemes can be combined with quantum error
correction. In particular, we show explicitly how to perform fault-tolerant
leakage correction, thus overcoming the main obstacle to fault-tolerant encoded
universality.
