Abstract
Toffoli gates are an important primitive in reversible Boolean logic. In quantum computation, these Toffoli gates are composed using other elementary gates, most notably the Clifford+T basis. However, in fault-tolerant implementations of quantum circuits, a non-transversal gate like the T gate incurs extra cost relative to transversal gates like the S and CNOT gates. Relative-phase Toffoli Gates (RTOF) have been proposed as a way to minimize this "T-depth" at the cost of incurring a relative phase that could skew the final quantum states. While previous research has proposed a way to use transversal S gates to eliminate this relative phase, this paper proposes a novel form of the RTOF that incorporates S gates in order to simplify generation of the logic to return the phase