  Quantum manipulation based on geometric phases provides a promising way
towards robust quantum gates. However, in the current implementation of
nonadiabatic geometric phases, operational and/or random errors tend to
destruct the conditions that induce geometric phases, thereby smearing their
noise-resilient feature. In a recent experiment [Y. Xu et al., Phys. Rev. Lett.
124, 230503 (2020)], high-fidelity universal geometric quantum gates have been
implemented in a superconducting circuit, which are robust to different types
of errors under different configurations of the geometric evolution paths.
Here, we apply the path-design strategy to explain in detail why both
configurations can realize universal quantum gates in a single-loop way.
Meanwhile, we purposefully induce our geometric manipulation by selecting the
path configuration that is robust against the qubit-frequency-drift induced
error, which is the dominant error source on realistic superconducting circuits
and has not been deliberately addressed. Moreover, our proposal can further
integrate with the composite scheme to enhance the gate robustness, which is
verified by numerical simulations. Therefore, our scheme provides a promising
way towards practical realization of high-fidelity and robust nonadiabatic
geometric quantum gates.
