Fig. 2: Beamsplitting with the differentially-driven SQUID.

a Beamsplitting implements an effective driven Rabi evolution in the Bloch sphere of the dual-rail qubit formed by the single photon subspace Alice and Bob, where decay can be detected by monitoring the vacuum state. b Resonant evolution of a single-photon prepared in Bob. The data is normalized for readout infidelity, and state preparation fidelity is shown as a dashed gray line (Supplementary Note 10). The fast coherent oscillations (black dots) between the cavities are fitted to Eq. (6) (green lines show envelope) to obtain the decay and dephasing time-scales. The evolution for the first 1.5 μs is plotted separately to better illustrate the oscillations, and fit to a sinusoid to extract g_BS. c Sweeping both drive amplitudes simultaneously and repeating experiment (a) lets us quantify g_BS (blue crosses), and the decoherence limit on beamsplitter infidelity (red diamonds) at various drive strengths. We choose a drive strength with simultaneously low infidelity and high beamsplitter rate as our operating point (yellow dashed line). d The coupler’s driven excitation (P_c) after evolving for 10 swaps is directly quantified through a dedicated on-chip readout mode. We observe no monotonic correlation with respect to drive amplitude, and driven populations mostly remain within the range of the undriven population (gray region). e Coupler population as a function of number of swaps at the operational driving point. The heating rate is nearly immeasurable, with a fitted (pink line) slope of (1.2 ± 2.4) × 10⁻⁵ excitation per swap, which is within expectation for our natural thermal background (γ_c,↑ ~ (3.3 ms)⁻¹). The non-zero offset of the fit arises from preparation and readout infidelities. Error bars in both (d) and (e) represent fit errors from the protocol described in ref. ⁴⁶.