Distilling one-qubit magic states into Toffoli states

For certain quantum architectures and algorithms, most of the required resources are consumed during the distillation of one-qubit magic states for use in performing Toffoli gates. I show that the overhead for magic-state distillation can be reduced by merging distillation with the implementation of Toffoli gates. The resulting routine distills eight one-qubit magic states directly to a Toffoli state, which can be used without further magic to perform a Toffoli gate.