  Nonadiabatic holonomic quantum computation (NHQC) is implemented by fast
evolution processes in a geometric way to withstand local noises. However,
recent works of implementing NHQC are sensitive to the systematic noise and
error. Here, we present a path-optimized NHQC (PONHQC) scheme based on the
non-Abelian geometric phase, and find that a geometric gate can be constructed
by different evolution paths, which have different responses to systematic
noises. Due to the flexibility of the PONHQC scheme, we can choose an optimized
path that can lead to excellent gate performance. Numerical simulation shows
that our optimized scheme can greatly outperform the conventional NHQC scheme,
in terms of both fidelity and robustness of the gates. In addition, we propose
to implement our strategy on superconducting quantum circuits with
decoherence-free subspace encoding with the experiment-friendly two-body
exchange interaction. Therefore, we present a flexible NHQC scheme that is
promising for the future robust quantum computation.
