The eventual success of a quantum computer relies on our ability to robustly initialise, manipulate, and measure quantum bits, or qubits, in the presence of the inevitable occurrence of errors. This requires us to encode quantum information redundantly in systems that are suitable for Quantum Error Correction (QEC). One promising implementation is to use three dimensional (3D) superconducting microwave cavities coupled to one or more non-linear ancillae in the circuit quantum electrodynamics (cQED) framework. Such systems have the advantage of good intrinsic coherence properties and large Hilbert space, making them ideal for storing redundantly encoded quantum bits. Recent progress has demonstrated the universal control and realisation of QEC beyond the break-even point on a logical qubit encoded in a mulit-photon state of a single cavity. This thesis presents the first experiments in implementing quantum operations between multi-photon states stored in two separate cavities. We first explore the ability to create complex two-mode entangled states and perform full characterisation in a novel multi-cavity architecture. Subsequently, we demonstrate the capability to implement conditional quantum gates between two cavity modes, assisted by a single ancilla. In addition, we develop a direct, tunable coupling between two spectrally separated cavities and use it to study complex multiphoton interference between stationary bosonic states. Combining this with robust single cavity controls, we construct a universal entangling gate between multi-photon states. The results presented in this thesis demonstrate the vast potential of 3D superconducting systems as robust, error-correctable quantum modules and the techniques developed constitute an important toolset towards realising universal quantum computing on error-corrected qubits.
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