  Scalable quantum computing is based on realizable accurate quantum gates. For
neutral atoms, it is an outstanding challenge to design a high-fidelity
two-qubit entangling gate without resorting to difficult techniques like
shaping laser pulses or cooling atoms to motional ground states. By using spin
echo to suppress the blockade error, we propose an easily realizable
controlled-phase Rydberg quantum gate of high intrinsic fidelity. In the
context of spin echo, we show that the fundamental blockade error of the
traditional Rydberg gate, on the order of $\epsilon\sim10^{-3}$, actually
results from two `clockwise' rotations of Rabi frequencies $\bar\Omega_\pm=V\pm
\sqrt{V^2+\Omega^2}$. In our `echo' sequence, such an error can be suppressed
to the order of $\epsilon^2$ by adding two `anticlockwise' rotations with
frequencies $-\bar\Omega_\pm$. With the blockade error effectively removed, the
error caused by Rydberg state decay becomes the final fundamental limit to the
gate accuracy, which in principle, can be reduced beyond the level of
$10^{-5}$. Furthermore, due to the small population $\epsilon$ involved in the
`echo' process, the spin-echo gate is robust against the variation of Rydberg
blockade caused by the drift of the qubits, so that it can still be much more
accurate than that of a traditional Rydberg gate even for qubits cooled only to
the sub-mK regime.
