Interference between microwave quantum memories*

The ability to generate arbitrary quantum states on-demand, detect them with high fidelity, and excellent coherence properties of 3D cQED systems make them ideal platforms to solve boson sampling problems and implement linear-optics quantum computation (LOQC). In order to realise such protocols, we need robust beamsplitter and phase-shifting operations between cQED elements. Here, we use an RF-driven, frequency-converting beamsplitter between two superconducting memories to implement cascaded Mach-Zehnder interferometers. We use the dispersive coupling to perform phase control on the memory and demonstrate in-situ manipulation of the interference between two microwave photons at different frequencies. We show that this implementation is directly extended to multiphoton states and hence, can be applied to simulate complex high dimensional boson statistics. It is also compatible with qubits encoded in multi-photon states of cavities for quantum error correction, making such operations valuable for implementing logical gates between protected qubits.