Erasing Doppler Dephasing Error in Rydberg Quantum Gates

Abstract: The Doppler dephasing error due to residual thermal motion of qubit atoms is a major cause of fidelity loss in neutral-atom quantum gates. Besides cooling and trapping advancements, few effective methods exist to mitigate this error. In the present work, we introduce an error-erasing strategy that utilizes a pair of off-resonant fields to continuously dress the protected Rydberg state with an auxiliary state, which induces an opposite but enhanced sensitivity to the same source of Doppler dephasing error. Combining with an optimal control of laser pulses, we realize a family of Rydberg two-qubit controlled-NOT gates in Rb and Cs atoms that are fully robust to the Doppler dephasing error. We benchmark this gate operation with fidelity $F\approx0.9906$ at ${\it any}$ temperature for a lower-excited auxiliary state, and a higher fidelity of $F\approx0.9965$ can be attained for a ground-state auxiliary state at a temperature of 50 $\mu$K. Our results significantly reduce atomic temperature requirements for high-fidelity quantum gates, and may provide fundamental guidance to practical error-tolerant quantum computing with neutral atoms.