Trapped-ion two-qubit gates with >99.99% fidelity without ground-state cooling

We introduce the 'smooth gate', an entangling method for trapped-ion qubits where residual spin-motion entanglement errors are adiabatically eliminated by ramping the gate detuning. We demonstrate electronically controlled two-qubit gates with an estimated error of 8.4(7)×10⁻⁵ without ground-state cooling. We further show that the error remains ≲5×10⁻⁴ for ions with average phonon occupation up to n_bar=9.4(3) on the gate mode. These results indicate that trapped-ion quantum computation can achieve high fidelity at temperatures above the Doppler limit, which enables faster and simpler device operation.