Erasing Doppler dephasing error in Rydberg quantum gates

The Doppler dephasing error due to residual thermal motion of atoms is a major cause of infidelity in neutral-atom quantum gates. Besides cooling and trapping advancements, few effective methods exist to mitigate this error. In the present work, we first propose an error-erasing strategy that utilizes a pair of off-resonant fields to continuously dress the protected Rydberg state with an auxiliary state, which can induce an opposite but enhanced sensitivity to the same source of Doppler dephasing error. Combining with the optimal control of laser pulses, we have realized a family of Rydberg two-qubit controlled-NOT gates in Rb and Cs atoms that are fully immune to the Doppler dephasing error. We numerically simulate this gate operation with fidelity F ≈ 0.9906 at any temperature for a lower-excited auxiliary state, and a higher fidelity of F ≈ 0.9960 can be attained for a ground auxiliary state even at a temperature of 500 µK. Finally, we predict a super-high fidelity of F > 0.9999 for 50 μ K is possible by using the robust pulses with a larger amplitude. Our results significantly reduce atomic temperature requirements for high-fidelity quantum gates, and may provide fundamental guidance to practical fault-tolerant quantum computing with neutral atoms.