  Quantum computation has demonstrated advantages over classical computation
for special hard problems, where a set of universal quantum gates is essential.
Geometric phases, which have built-in resilience to local noise, have been used
to construct quantum gates with excellent performance. However, this advantage
has been smeared in previous schemes. Here, we propose a state-independent
nonadiabatic geometric quantum-gate scheme that is able to realize a more fully
geometric gate than previous approaches, allowing for the cancelation of
dynamical phases accumulated by an arbitrary state. Numerical simulations
demonstrate that our scheme has significantly stronger gate robustness than the
previous geometric and dynamical ones. Meanwhile, we give a detailed physical
implementation of our scheme with the Rydberg atom system based on the Rydberg
blockade effect, specifically for multiqubit control-phase gates, which exceeds
the fault-tolerance threshold of multiqubit quantum gates within the considered
error range. Therefore, our scheme provides a promising way for fault-tolerant
quantum computation in atomic systems.
