A four-qubit germanium quantum processor

The prospect of building quantum circuits 1 , 2 using advanced semiconductor manufacturing makes quantum dots an attractive platform for quantum information processing 3 , 4 . Extensive studies of various materials have led to demonstrations of two-qubit logic in gallium arsenide 5 , silicon 6 – 12 and germanium 13 . 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. Using germanium quantum dots, a four-qubit processor capable of single-, two-, three-, and four-qubit gates, demonstrated by the creation of four-qubit Greenberger−Horne−Zeilinger states, is the largest yet realized with solid-state electron spins.