  Nonadiabatic geometric quantum computation is dedicated to the realization of
high-fidelity and robust quantum gates, which are necessary for fault-tolerant
quantum computation. However, it is limited by cyclic and mutative evolution
path, which usually requires longer gate-time and abrupt pulse control,
weakening the gate performance. Here, we propose a scheme to realize geometric
quantum gates with noncyclic and nonadiabatic evolution via invariant-based
shortcuts, where universal quantum gates can be induced in one step without
path mutation and the gate time is also effectively shortened. Our numerical
simulations show that, comparing with the conventional dynamical gates, the
constructed geometric gates have stronger resistance not only to systematic
errors, induced by both qubit-frequency drift and the deviation of the
amplitude of the driving fields, but also to environment-induced decoherence
effect. In addition, our scheme can also be implemented on a superconducting
circuit platform, with the fidelities of single-qubit and two-qubit gates are
higher than 99.97$\%$ and 99.84$\%$, respectively. Therefore, our scheme
provides a promising way to realize high-fidelity fault-tolerant quantum gates
for scalable quantum computation.
