  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 $50\;{\rm ns}$, 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.
