Fig. 1: Device design and characterization.

a Schematic diagram showing a lossy resonator with linewidth κ coupled to a qutrit-qubit system via three parametric drives. Rabi drives resonant with the 0–1 transition are also applied to both the qutrit and the qubit. b Circuit realization of the scheme in a showing two superconducting transmons (green and turquoise) and central resonator (orange), as well as the dedicated readout resonators (gray). The transmons and central resonator share a SQUID that implements parametric couplings (\({g}_{k}^{n,n+1}\)). c Optical micrographs of the device layout (left) and a magnified view of the junctions and the SQUID coupler (right). The external bias line used to pump the SQUID can be seen at the bottom of the device. The resonator consists of an array of 10 Josephson junctions, each having a critical current I_ac ≈ 540 nA, in series with a fixed capacitor. d Measured 0–1 transition frequency for each transmon and resonator center frequency as a function of flux through the SQUID loop. The operating flux bias is indicated with a dashed-black line. e Time-domain parametric swaps measured as a function of pump frequency for each of the three parametric drives in Eq. (1). From left to right, the transmons are initialized in \(\left|10\right\rangle\), \(\left|20\right\rangle\), and \(\left|01\right\rangle\) respectively. f Parametric coupling rates measured as a function of pump amplitude. Solid lines are linear fits to the data; the nonlinear response of \({g}_{l}^{12}\) at higher drive amplitude is due to enhanced mixer saturation at the corresponding IF frequency of 150 MHz, as compared to the other drives, which use 50 MHz.