  It has been known that quantum error correction via concatenated codes can be
done with exponentially small failure rate if the error rate for physical
qubits is below a certain accuracy threshold. Other, unconcatenated codes with
their own attractive features-improved accuracy threshold, local
operations-have also been studied. By iteratively distilling a certain
two-qubit entangled state it is shown how to perform an encoded Toffoli gate,
important for universal computation, on CSS codes that are either
unconcatenated or, for a range of very large block sizes, singly concatenated.
