We propose an adiabatic protocol for implementing a controlled-phase gate ${\mathrm{CZ}}_{\theta }$ with continuous $\theta$ of neutral atoms through a symmetrical two-photon excitation process via the second resonance line, $6P$ in ${}^{87}\mathrm{Rb}$, with a single-temporal-modulation-coupling of the ground state and intermediate state. Relying on different adiabatic paths, the phase factor $\theta$ of the ${\mathrm{CZ}}_{\theta }$ gate can be accumulated on the logic qubit state $|11⟩$ alone by calibrating the shape of the temporal pulse where strict zero amplitudes at the start and end of the pulse are not needed. For a wide range of $\theta$, we can obtain the fidelity of the ${\mathrm{CZ}}_{\theta }$ gate over 99.7% in less than $1\mu \mathrm{s}$, in the presence of spontaneous emission from intermediate and Rydberg states. And in particular for $\theta =\pi$, we benchmark the performance of the CZ gate by taking into account various experimental imperfections, such as Doppler shifts, fluctuation of Rydberg-Rydberg interaction strength, inhomogeneous Rabi frequency, and noise of driving fields, etc., and show that the predicted fidelity is able to maintain at about 98.4% after correcting the measurement error. This gate protocol provides a robustness against the fluctuation of pulse amplitude and a flexible way for adjusting the entangling phase, which may contribute to the experimental implementation of near-term noisy intermediate-scale quantum computation and algorithm with neutral-atom systems.

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• Quantum algorithms
• Quantum computation
• Quantum control
• Quantum gates
• Rydberg atoms & molecules
• Adiabatic approximation