  The nonadiabatic holonomic quantum computation based on three-level systems
has wide applicability experimentally due to its simpler energy level structure
requirement and inherent robustness from the geometric phase. However, in
previous conventional schemes, the states of the calculation subspace have
always leaked to the noncomputation subspace, resulting in less robustness than
anticipated. Recent efforts to address this problem are at the cost of
excessively long gate time, which will lead to more decoherence-induced errors.
Here, we propose a solution to the problem without the severe limitation of the
much longer gate time. Specifically, we implement arbitrary holonomic gates via
a three-segment Hamiltonian, where the gate time depends on the rotation angle,
and the smaller the rotation angle, the shorter the gate time will be. Compared
with the previous solutions, our numerical simulations indicate that the
decoherence-induced gate errors of our scheme are greatly decreased and the
robustness of our scheme is also better, particularly for small-angle rotation
gates. Moreover, we provide a detailed physical realization of our proposal on
a two-dimensional superconducting quantum circuit. Therefore, our protocol
provides a promising alternative for future fault-tolerant quantum computation.
