  Fast and robust quantum gates is the cornerstone of fault-tolerance quantum
computation. In this paper, we propose to achieve quantum gates based on
non-cyclic geometric evolution. Dynamical phase during the evolution is
cancelled by spin-echo process and the adiabatic control can be sped up through
shortcut to adiabatic manner. Different from geometric gates based on cyclic
evolution, the superiority of non-cyclic scheme is that the operation time is
proportional to the rotation angle (but not the geometric phase) of quantum
state. Therefore, the non-cyclic scheme becomes fairly fast in the case of
quantum gates with small rotation angle which will be more insensitive to the
decoherence and leakage to the states outside the computational basis. The
proposed scheme is also robust against random noise due to the geometric
characteristic of projective Hilbert space. Since the refined proposed scheme
is fast and robust, it is an particularly suitable way to manipulate the
physical systems with weak nonlinearity, such as superconucting systems.
