  Multi-controlled gates are fundamental components in the design of quantum
algorithms, where efficient decompositions of these operators can enhance
algorithm performance. The best asymptotic decomposition of an n-controlled X
gate with one borrowed ancilla into single qubit and CNOT gates produces
circuits with degree 3 polylogarithmic depth and employs a divide-and-conquer
strategy. In this paper, we reduce the number of recursive calls in the
divide-and-conquer algorithm and decrease the depth of n-controlled X gate
decomposition to a degree of 2.799 polylogarithmic depth. With this optimized
decomposition, we also reduce the depth of n-controlled SU(2) gates and
approximate n-controlled U(2) gates. Decompositions described in this work
achieve the lowest asymptotic depth reported in the literature. We also perform
an optimization in the base of the recursive approach. Starting at 52 control
qubits, the proposed n-controlled X gate with one borrowed ancilla has the
shortest circuit depth in the literature. One can reproduce all the results
with the freely available open-source code provided in a public repository.
