A 3-wave mixing beamsplitter between two bosonic modes

Quantum information processing using the bosonic modes of high-Q cavities aims to leverage long intrinsic lifetimes, while extending logical lifetimes by encoding information in the large Hilbert space provided and correcting for errors. In many bosonic encodings, a cavity-cavity beamsplitter interaction enables gates between multiple logical qubits. Gate performance using a transmon as a mixing element between cavities has been limited by unwanted Hamiltonian terms such as cross-Kerr arising from the transmon's 4th-order nonlinearity. A proposed solution is to use the 3rd-order nonlinearity of a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) to mediate the interaction while suppressing unwanted 4th-order terms. We present an experimental implementation of a 3-wave mixing beamsplitter between high-Q cavities and benchmark its performance.