  High-fidelity quantum gates are an essential prerequisite for large-scale
quantum computation. When manipulating practical quantum systems,
environmentally and operationally induced errors are inevitable, and thus, in
addition to being fast, it is preferable that operations should be
intrinsically robust against different errors. Here, we propose a general
protocol for constructing geometric quantum gates with on-demand trajectories
by modulating the applied pulse shapes that define the system's evolution
trajectory. Our scheme adopts reverse engineering of the target Hamiltonian
using smooth pulses, which also eliminates the difficulty of calculating
geometric phases for an arbitrary trajectory. Furthermore, because a particular
geometric gate can be induced by various different trajectories, we can further
optimize the gate performance under different scenarios; the results of
numerical simulations indicate that this optimization can greatly enhance the
quality of the gate. In addition, we present an implementation of our proposal
using superconducting circuits, showcasing substantial enhancements in gate
performance compared with conventional schemes. Our protocol thus presents a
promising approach for high-fidelity and strong-robust geometric quantum gates
for large-scale quantum computation.
