Abstract: The generation and control of quantum states of light constitute fundamental tasks in cavity quantum electrodynamics (QED). The superconducting realization of cavity QED, circuit QED (refs 11, 12, 13, 14), enables on-chip microwave photonics, where superconducting qubits control and measure individual photon states. A long-standing issue in cavity QED is the coherent transfer of photons between two or more resonators. Here, we use circuit QED to implement a three-resonator architecture on a single chip, where the resonators are interconnected by two superconducting phase qubits. We use this circuit to shuffle one- and two-photon Fock states between the three resonators, and demonstrate qubit-mediated vacuum Rabi swaps between two resonators. By shuffling superposition states we are also able to demonstrate the high-fidelity phase coherence of the transfer. Our results illustrate the potential for using multi-resonator circuits as photon quantum registers and for creating multipartite entanglement between delocalized bosonic modes.