Experimental signatures of a $\hat{Z}\hat{X}$ beam-splitter interaction between a Kerr-cat and transmon qubit
Quantum error correction (QEC) requires ancilla qubits to extract error syndromes from data qubits which store quantum information. However, ancilla errors can propagate back to the data qubits, introducing additional errors and limiting fault-tolerance. In superconducting quantum circuits, Kerr-cat qubits (KCQs), which exhibit strongly biased noise, have been proposed as ancillas to suppress this back-action and enhance QEC performance. Here, we experimentally demonstrate a beamsplitter interaction between a KCQ and a transmon, realizing an effective $\hat{Z}_{cat}\hat{X}_q$ coupling that can be employed for parity measurements in QEC protocols. We characterize the interaction across a range of cat sizes and drive amplitudes, confirming the expected scaling of the interaction rate. These results establish a step towards hybrid architectures that combine transmons as data qubits with noise-biased bosonic ancillas, enabling hardware-efficient syndrome extraction and advancing the development of fault-tolerant quantum processors.