  Hole spin qubits in semiconductor quantum dots (QDs) are promising candidates
for quantum information processing due to their weak hyperfine coupling to
nuclear spins, and to the strong spin-orbit coupling which allows for rapid
operation time. We propose a coherent control on two heavy-hole spin qubits in
a double QD by a fast adiabatic driving protocol, which helps to achieve higher
fidelities than other experimentally commonly used protocols as linear ramping,
$\pi$-pulses or Landau-Zener passages. Using fast quasiadiabatic driving via
spin-orbit coupling, it is possible to reduce charge noise significantly for
qubit manipulation and achieve high robustness for the qubit initialization. We
also implement one and two-qubit gates, in particular, NOT, CNOT, and SWAP-like
gates, of hole spins in a double QD achieving fidelities above $99\%$,
exhibiting the capability of hole spins to implement universal gates for
quantum computing.
