  Nonadiabatic holonomic quantum computation has received increasing attention
due to its robustness against control errors as well as high-speed realization.
Several schemes of its implementation have been put forward based on various
physical systems, each of which has some particular merits. In this paper, we
put forward an alternative scheme of nonadiabatic holonomic quantum
computation, in which a universal set of quantum gates is realized based on
Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that
allows for only a single Rydberg excitation shared by many atoms within a
blockade radius and can be used to generate the collective states to encode the
qubits. In our scheme, the qubit is encoded into two collective ground states
of Rydberg superatoms and the interaction between two long-range Rydberg
superatoms is mediated by a microwave cavity with the aid of two additional
collective Rydberg states. Different from the previous schemes,which are based
on the systems in the microscope scale, the present scheme is based on atomic
ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic
holonomic quantum computation such as the robustness and the speediness, the
Rydberg-superatom-based scheme has the following particular merits: the long
coherence time of Rydberg states and the operability of the mesoscopic systems.
