  Universal robust quantum control is essential for performing complex quantum
algorithms and efficient quantum error correction protocols. Geometric phase,
as a key element with intrinsic fault-tolerant feature, can be well integrated
into quantum control processes to enhance control robustness. However, the
current geometric quantum control is still controversial in robust
universality, which leads to the unsatisfactory result that cannot sufficiently
enhance the robustness of arbitrary type of geometric gate. In this study, we
find that the finite choice on geometric evolution trajectory is one of the
main roots that constrain the control robustness of previous geometric schemes,
as it is unable to optionally avoid some trajectory segments that are seriously
affected by systematic errors. In view of this, we here propose a new scheme
for universal robust geometric control based on geometric trajectory
correction, where enough available evolution parameters are introduced to
ensure that the effective correction against systematic errors can be executed.
From the results of our numerical simulation, arbitrary type of geometric gate
implemented by using the corrected geometric trajectory has absolute robustness
advantages over conventional quantum one. In addition, we also verify the
feasibility of the high-fidelity physical implementation of our scheme in
superconducting quantum circuit, and finally discuss in detail the potential
researches based on our scheme. Therefore, our theoretical work is expected to
offer an attractive avenue for realizing practical fault-tolerant quantum
computation in existing experimental platforms.
