Multi-qubit controlled gate with optimal T-count

Abstract

Controlled gates are key components in various quantum algorithms. Improving on the prior work of Gosset et al., we show that, for an allowed error $\epsilon$, $3{\log }_2(1/\epsilon )+o(\log (1/\epsilon ))$ $T$ gates are sufficient to approximate most multi-qubit controlled SU(2)s. We also show that this T-count matches the lower bound when the use of an almost controlled gate is prohibited. As an application, general controlled gate synthesis and efficient SU(4) gate synthesis are given.

15 pages