High-On-Off-Ratio Beam-Splitter 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 three-wave-mixing coupling element to engineer a programmable beam-splitter 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 beam-splitter interaction g_{bs} is fast relative to the time scale of oscillator decoherence, enabling over 10^{3} beam-splitter operations per coherence time and approaching the typical rate of the dispersive coupling χ 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}≈χ, 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%±0.2%.