Multiparticle entanglement with quantum logic networks: Application to cold trapped ions

We show how to construct a multiqubit 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 multiqubit control-NOT (CNOT) 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 multiqubit CNOT gate compared to its decomposition into a network of two-qubit CNOT gates.