Multiqubit quantum logical gates between distant quantum modules in a network

We study multiqubit quantum logical gates between distant quantum modules in a network, which are appealing in quantum computation by offering advantages including faster execution and higher fidelity. We provide a protocol to implement the fan-out multiqubit controlled -NOT gate CN with one control qubit and N -1 target qubits at a distance, which obviates the need for a direct coherent quantum interaction. We present a proof-of-principle experimental demonstration of the C3 gate in a photonic quantum network with a fidelity of 0.86 and exploit this quantum gate to map representative qubit states to generalized three-qubit Greenberger-Horne-Zeilinger states with an average fidelity of 0.83, demonstrating a crucial step to implement the three-qubit quantum error correction codes in distributed quantum computation. We expect that the nonlocal multiqubit quantum gates may contribute critically to the development of distributed quantum computation.