In the noisy intermediate-scale quantum era, quantum devices can only execute shallow-depth circuits to maintain acceptable fidelity. This poses a significant challenge in implementing quantum algorithms that require interactions between nonadjacent qubits, especially on superconducting platforms with limited qubit connectivity. In conventional methods, swap gates are often employed to bridge distant qubits, at the cost of increased circuit depth and reduced overall fidelity. In this paper, we propose a scheme for implementing a controlled-$Z$ gate between next-nearest-neighbor qubits ($N^3\text{−}\mathrm{C}Z$), which enables direct high-fidelity entanglement between nonadjacent qubits without disturbing the intermediate qubit. Implemented on fixed-frequency and fixed-coupler superconducting qubits via simultaneous cross-resonance drives, the $N^3\text{−}\mathrm{C}Z$ gate achieves an average gate fidelity of 99.0% under realistic decoherence conditions, which is further confirmed by quantum process tomography with a fidelity of 98.9%. Moreover, we demonstrate that the $N^3\text{−}\mathrm{C}Z$ gate significantly reduces circuit depth and gate count in key quantum applications and circuit components, including quantum error correction, the quantum fan-out gate, the Toffoli gate, quantum ripple-carry adder, and graph state preparation. These results highlight the potential of the $N^3\text{−}\mathrm{C}Z$ gate as an efficient and hardware-friendly primitive for scalable quantum computation.

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• Open quantum systems & decoherence
• Quantum algorithms & computation
• Quantum circuits
• Quantum communication, protocols & technology
• Quantum computation
• Superconducting qubits