Scaling is now a key challenge in superconducting quantum computing. One solution is to build modular systems in which smaller-scale quantum modules are individually constructed andcalibrated, and then assembled into a larger architecture. This, however, requires the development of suitable interconnects. Here, we report low-loss interconnects based on pure aluminium coaxial cables and on-chip impedance transformers featuring quality factors up to 8.1×105, which is comparable to the performance of our transmon qubits fabricated on single-crystal sapphire substrate. We use these interconnects to link five quantum modules with inter-module quantum state transfer and Bell state fidelities up to 99\%. To benchmark the overall performance of the processor, we create maximally-entangled, multi-qubit Greenberger-Horne-Zeilinger (GHZ) states. The generated inter-module four-qubit GHZ state exhibits 92.0\% fidelity. We also entangle up to 12 qubits in a GHZ state with 55.8±1.8% fidelity, which is above the genuine multipartite entanglement threshold of 1/2. These results represent a viable modular approach for large-scale superconducting quantum processors.