  Resource consumption is an important issue in quantum information processing,
particularly during the present NISQ era. In this paper, we investigate
resource optimization of implementing multiple controlled operations, which are
fundamental building blocks in the field of quantum computing and quantum
simulation. We design new quantum circuits for the $n$-Toffoli gate and general
multi-controlled unitary, which have only $O(\log n)$-depth and $O(n)$-size,
and only require $1$ ancillary qubit. To achieve these results, we explore the
potential of ancillary qubits and discover a method to create new conditional
clean qubits from existed ancillary qubits. These techniques can also be
utilized to construct an efficient quantum circuit for incrementor, leading to
an implementation of multi-qubit Toffoli gate with a depth of $O(\log^2n)$ and
size of $O(n)$ without any ancillary qubits. Furthermore, we explore the power
of ancillary qubits from the perspective of resource theory. We demonstrate
that without the assistance of ancillary qubit, any quantum circuit
implementation of multi-qubit Toffoli gate must employ exponential precision
gates. This finding indicates a significant disparity in computational power of
quantum circuits between using and not using ancillary qubits. Additionally, we
discuss the comparison of the power of ancillary qubits and extra energy levels
in quantum circuit design.
