  The prospect of building quantum circuits using advanced semiconductor
manufacturing positions quantum dots as an attractive platform for quantum
information processing. Extensive studies on various materials have led to
demonstrations of two-qubit logic in gallium arsenide, silicon, and germanium.
However, interconnecting larger numbers of qubits in semiconductor devices has
remained an outstanding 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 high-connectivity
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 an important step towards
quantum error correction and quantum simulation with quantum dots.
