  Nonadiabatic holonomic quantum computation (NHQC) has attracted significant
attention due to its fast evolution and the geometric nature induced resilience
to local noises. However, its long operation time and complex physical
implementation make it hard to surpass the dynamical scheme, and thus hindering
its wide application. Here, we present to implement NHQC with the shortest path
under some conditions, through the inverse Hamiltonian engineering technique,
which posseses higher fidelity and stronger robustness than previous NHQC
schemes. Meanwhile, the gate performance in our scheme can be further improved
by using the proposed composite dynamical decoupling pulses, which can
efficiently improve both the gate fidelity and robustness, making our scheme
outperform the optimal dynamical scheme in certain parameters range.
Remarkably, our scheme can be readily implemented with Rydberg atoms, and a
simplified implementation of the controlled-not gate in the Rydberg blockade
regime can be achieved. Therefore, our scheme represents a promising progress
towards future fault-tolerant quantum computation in atomic systems.
