  The promise of quantum computation with quantum dots has stimulated
widespread research. Still, a platform that can combine excellent control with
fast and high-fidelity operation is absent. Here, we show single and two-qubit
operations based on holes in germanium. A high degree of control over the
tunnel coupling and detuning is obtained by exploiting quantum wells with very
low disorder and by working in a virtual gate space. Spin-orbit coupling
obviates the need for microscopic elements and enables rapid qubit control with
Rabi frequencies exceeding 100 MHz and a single-qubit fidelity of 99.3 %. We
demonstrate fast two-qubit CX gates executed within 75 ns and minimize
decoherence by operating at the charge symmetry point. Planar germanium thus
matured within one year from a material that can host quantum dots to a
platform enabling two-qubit logic, positioning itself as a unique material to
scale up spin qubits for quantum information.
