Nonadiabatic geometric quantum gates with on-demand trajectories

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.