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 $C^N$ 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 $C^3$ 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.

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• Optical quantum information processing
• Quantum computation
• Quantum gates
• Quantum optics