  We show how to construct a multi-qubit control gate on a quantum register of
an arbitrary size N. This gate performs a single-qubit operation on a specific
qubit conditioned by the state of other N-1 qubits. We provide an algorithm how
to build up an array of networks consisting of single-qubit rotations and
multi-qubit control-NOT gates for the synthesis of an arbitrary entangled
quantum state of N qubits. We illustrate the algorithm on a system of cold
trapped ions. This example illuminates the efficiency of the direct
implementation of the multi-qubit CNOT gate compared to its decomposition into
a network of two-qubit CNOT gates.
