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Geometric phases are robust to local noises and the nonadiabatic ones canreduce the evolution time, thus nonadiabatic geometric gates have strongrobustness and can approach high fidelity. However, the advantage of geometricphase has not being fully explored in previous investigations. Here, we proposea scheme for universal quantum gates with pure nonadiabatic and noncyclicgeometric phases from smooth evolution paths. In our scheme, only geometricphase can be accumulated in a fast way, and thus it not only fully utilizes thelocal noise resistant property of geometric phase but also reduces thedifficulty in experimental realization. Numerical results show that theimplemented geometric gates have stronger robustness than dynamical gates andthe geometric scheme with cyclic path. Furthermore, we propose to constructuniversal quantum gate on superconducting circuits, with the fidelities ofsingle-qubit gate and nontrivial two-qubit gate can achieve $99.97\%$ and$99.87\%$, respectively. Therefore, these high-fidelity quantum gates arepromising for large-scale fault-tolerant quantum computation.

State-independent geometric quantum gates via nonadiabatic and noncyclic evolution