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Abstract One of the primary challenges in realizing large-scale quantum processors is the realization of qubit couplings that balance interaction strength, connectivity, and mode confinement. Moreover, it is very desirable for the device elements to be detachable, allowing components to be built, tested, and replaced independently. In this work, we present a microwave quantum state router, centered on parametrically driven, Josephson-junction based three-wave mixing, that realizes all-to-all couplings among four detachable quantum modules. We demonstrate coherent exchange among all four communication modes, with an average full-iSWAP time of 764 ns and average inferred inter-module exchange fidelity of 0.969, limited by mode coherence. We also demonstrate photon transfer and pairwise entanglement between module qubits, and parallel operation of simultaneousiSWAP exchange across the router. Our router-module architecture serves as a prototype of modular quantum computer that has great potential for enabling flexible, demountable, large-scale quantum networks of superconducting qubits and cavities.