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 singlequbit 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.Gate-defined quantum dots were recognized early on as a promising platform for quantum information [1] and a plethora of materials stacks has been investigated as host material. Initial research mainly focused on the low disorder semiconductor gallium arsenide [2,3]. Steady progress in the control and understanding of this system culminated in the initial demonstration and optimization of spin qubit operations [4,5] and the realization of rudimentary analog quantum simulations [6]. However, the omnipresent hyperfine interactions in group III-V materials seriously deteriorate the spin coherence, despite attempts to mitigate this by nuclear polarization [7]. Drastic improvements to the coherence times could be achieved by switching to the group IV semiconductor silicon, in particular when defining spin qubits in isotopically purified host crystal with vanishing concentrations of nonzero nuclear spin [8]. This enabled single qubit rotations with fidelities beyond 99.9% [9] and the execution of two-qubit logic gates with fidelities up to 98% [10-13], underlining the potential of spin qubits for quantum computation. Nevertheless, quantum dots in silicon are often formed at unintended locations and control over the tunnel coupling determining the strength of two-qubit interactions is limited. Moreover, the absence of a sizable spin-orbit coupling for electrons requires the inclusion of microscopic components such as onchip striplines or nanomagnets close to each qubit, which seriously complicates the design of large and dense 2D-structures. This, combined with the limited control over the location and coupling of the dots, remains an outstanding challenge for the scalability of these systems and a platform that can overcome these limitations would be highly desirable. * These two authors contributed equally to this work Hole states in semiconductors typically exhibit strong spinorbit coupling, which has enabled the demonstration of fast single qubit rotations [14,15] and additionally, unlike electrons, holes do not suffer from nearby valley states. In silicon, unfavorable band alignment...

Quantum dots take a shortcut toward practical quantum information.

Superconductors and semiconductors are crucial platforms in the field of quantum computing. They can be combined to hybrids, bringing together physical properties that enable the discovery of new emergent phenomena and provide novel strategies for quantum control. The involved semiconductor materials, however, suffer from disorder, hyperfine interactions or lack of planar technology. Here we realise an approach that overcomes these issues altogether and integrate gate-defined quantum dots and superconductivity into germanium heterostructures. In our system, heavy holes with mobilities exceeding 500,000 cm2 (Vs)−1 are confined in shallow quantum wells that are directly contacted by annealed aluminium leads. We observe proximity-induced superconductivity in the quantum well and demonstrate electric gate-control of the supercurrent. Germanium therefore has great promise for fast and coherent quantum hardware and, being compatible with standard manufacturing, could become a leading material for quantum information processing.