The paper presents a significant advancement in superconducting qubit technology, demonstrating high-fidelity logic gates in a multi-qubit processor. The authors achieve an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity of up to 99.4%, placing Josephson quantum computing at the fault-tolerant threshold for surface code error correction. The processor consists of five Xmon qubits arranged in a linear array with nearest-neighbour coupling, and the two-qubit controlled-phase (CZ) gate is implemented using a fast adiabatic frequency tuning method. The high-fidelity performance is achieved through highly coherent qubits, a straightforward interconnection architecture, and a novel implementation of the CZ gate. The authors also construct a five-qubit Greenberger-Horne-Zeilinger (GHZ) state, showcasing the ability to create complex quantum states with high fidelity. This work paves the way for fault-tolerant, multi-qubit quantum computing using Josephson quantum devices.The paper presents a significant advancement in superconducting qubit technology, demonstrating high-fidelity logic gates in a multi-qubit processor. The authors achieve an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity of up to 99.4%, placing Josephson quantum computing at the fault-tolerant threshold for surface code error correction. The processor consists of five Xmon qubits arranged in a linear array with nearest-neighbour coupling, and the two-qubit controlled-phase (CZ) gate is implemented using a fast adiabatic frequency tuning method. The high-fidelity performance is achieved through highly coherent qubits, a straightforward interconnection architecture, and a novel implementation of the CZ gate. The authors also construct a five-qubit Greenberger-Horne-Zeilinger (GHZ) state, showcasing the ability to create complex quantum states with high fidelity. This work paves the way for fault-tolerant, multi-qubit quantum computing using Josephson quantum devices.