A four-qubit germanium quantum processor.

The prospect of building quantum circuits1,2 using advanced semiconductor manufacturing makes quantum dots an attractive platform for quantum information processing3,4. Extensive studies of various materials have led to demonstrations of two-qubit logic in gallium arsenide5, silicon6-12 and germanium13. However, interconnecting larger numbers of qubits in semiconductor devices has remained a challenge. Here we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable coupling along both directions. Qubit logic is implemented all-electrically and the exchange interaction can be pulsed to freely program one-qubit, two-qubit, three-qubit and four-qubit operations, resulting in a compact and highly connected circuit. We execute a quantum logic circuit that generates a four-qubit Greenberger-Horne-Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are a step towards quantum error correction and quantum simulation using quantum dots.