  High-fidelity two-qubits gates are essential for the realization of
large-scale quantum computation and simulation. Tunable coupler design is used
to reduce the problem of parasitic coupling and frequency crowding in
many-qubit systems and thus thought to be advantageous. Here we design a
extensible 5-qubit system in which center transmon qubit can couple to every
four near-neighbor qubit via a capacitive tunable coupler and experimentally
demonstrate high-fidelity controlled-phase (CZ) gate by manipulating center
qubit and one near-neighbor qubit. Speckle purity benchmarking (SPB) and cross
entrophy benchmarking (XEB) are used to assess the purity fidelity and the
fidelity of the CZ gate. The average purity fidelity of the CZ gate is
99.69$\pm$0.04\% and the average fidelity of the CZ gate is 99.65$\pm$0.04\%
which means the control error is about 0.04\%. Our work will help resovle many
chanllenges in the implementation of large scale quantum systems.
