Both Toffoli and Controlled-NOT need little help to universal quantum computing (pp084-092)
        Y-Y Shi
          doi: https://doi.org/10.26421/QIC3.1-7
Abstracts: What additional gates are needed for a set of classical universal gates to do universal quantum computation? We prove that any single-qubit real gate suffices, except those that preserve the computational basis. The Gottesman-Knill Theorem implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its like) are universal for quantum computing. Previously only a generic gate, namely a rotation by an angle incommensurate with \pi, is known to be sufficient in both problems, if only one  single-qubit gate is added.
Key words: quantum circuit, universal quantum computation, universal basis, Toffoli controoed-NOT