A high on-off ratio beamsplitter interaction for gates on bosonically encoded qubits

Encoding a qubit in a high quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device, but presents a challenge: how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a 3-wave mixing coupling element to engineer a programmable beamsplitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beamsplitter interaction \(g_\text{bs}\) is fast relative to the timescale of oscillator decoherence, enabling over \(10^3\) beamsplitter operations per coherence time, and approaching the typical rate of the dispersive coupling \(\chi\) used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed \(10^5\). We then introduce a new protocol to realize a hybrid controlled-SWAP operation in the regime \(g_{bs}\approx\chi\), in which a transmon provides the control bit for the SWAP of two bosonic modes. Finally, we use this gate in a SWAP test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of \(95.5\% \pm 0.2\%\).