  We present an implementation of multi-controlled quantum gates which provides
significant reductions of cost compared to state-of-the-art methods. The
operator applied on the target qubit is a unitary, special unitary, or the
Pauli X operator (Multi-Controlled Toffoli). The required number of ancilla
qubits is no larger than one, similarly to known linear cost decompositions. We
extend our methods for any number of target qubits, and provide further cost
reductions if additional ancilla qubits are available. For each type of
multi-controlled gate, we provide implementations for unrestricted (all-to-all)
connectivity and for linear-nearest-neighbor. All of the methods use a linear
cost of gates from the Clifford+T (fault-tolerant) set. In the context of
linear-nearest-neighbor architecture, the cost and depth of our circuits scale
linearly irrespective of the position of the qubits on which the gate is
applied. Our methods directly improve the compilation process of many quantum
algorithms, providing optimized circuits, which will result in a large
reduction of errors.
