Trapped-ion two-qubit gates with 99.99% fidelity without ground-state cooling - Part 1: Theory

We introduce the "smooth gate'': a novel entangling gate method for trapped-ion qubits where residual spin-motion entanglement errors are adiabatically eliminated by ramping the gate detuning. We demonstrate the power of this technique by performing electronically controlled two-qubit gates with an estimated error of 8.4(7)e-5 without the use of ground-state cooling. We further show that the error remains 5e-4 for ions with average phonon occupation numbers of up to nbar = 9.4(3) on the gate mode. These results show that trapped-ion quantum computation can be performed with high fidelity at temperatures above the Doppler limit, allowing for significantly faster and simpler device operation.