  The Toffoli gate serving as a basic building block for reversible quantum
computation, has manifested its great potentials in improving the
error-tolerant rate in quantum communication. While current route to the
creation of Toffoli gate requires implementing sequential single- and two-qubit
gates, limited by longer operation time and lower average fidelity. We develop
a new theoretical protocol to construct a universal $(n+1)$-qubit Toffoli gate
sphere based on the Rydberg blockade mechanism, by constraining the behavior of
one central target atom with $n$ surrounding control atoms. Its merit lies in
the use of only five $\pi$ pulses independent of the control atom number $n$
which leads to the overall gate time as fast as $\sim$125$n$s and the average
fidelity closing to 0.999. The maximal filling number of control atoms can be
up to $n=46$, determined by the spherical diameter which is equal to the
blockade radius, as well as by the nearest neighbor spacing between two
trapped-atom lattices. Taking $n=2,3,4$ as examples we comparably show the gate
performance with experimentally accessible parameters, and confirm that the
gate errors mainly attribute to the imperfect blockade strength, the
spontaneous atomic loss and the imperfect ground-state preparation. In contrast
to an one-dimensional-array configuration it is remarkable that the spherical
atomic sample preserves a high-fidelity output against the increasing of $n$,
shedding light on the study of scalable quantum simulation and entanglement
with multiple neutral atoms.
