We show that the use of shaped pulses improves the fidelity of a Rydberg-blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical derivative removal by adiabatic gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade, we generate Bell states with a fidelity of
F>0.9999 in a 300 K environment for a gate time of only
50ns, which is an order of magnitude faster than previous protocols. These results establish the potential of neutral atom qubits with Rydberg-blockade gates for scalable quantum computation.