any reversible gate can be implemented on a quantum computer, and hence the toffoli gate is also a quantum operator. however, the toffoli gate can not be used for universal quantum computation, though it does mean that a quantum computer can implement all possible classical computations. the toffoli gate has to be implemented along with some inherently quantum gate(s) in order to be universal for quantum computation. in fact, any single-qubit gate with real coefficients that can create a nontrivial quantum state suffices.