Single Temporal-Pulse-Modulated Parameterized Controlled-Phase Gate for Rydberg Atoms

Abstract

We propose an adiabatic protocol for implementing a controlled-phase gate ${\mathrm{CZ}}_{\ensuremath{\theta}}$ with continuous $\ensuremath{\theta}$ 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 $\ensuremath{\theta}$ of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ 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 $\ensuremath{\theta}$, we can obtain the fidelity of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate over 99.7% in less than $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$, in the presence of spontaneous emission from intermediate and Rydberg states. And in particular for $\ensuremath{\theta}=\ensuremath{\pi}$, 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.