Fig. 1.

Digital-analogue quantum Rabi simulation using phase-controlled parameter tuning. a Parity dynamics of the ideal quantum Rabi model in the degenerate-qubit case $\left({\omega }_{\mathrm{q}}^{\mathrm{R}}=0\right)$ for qubit (green) and resonator (red) in coupling regimes: $r=g^{\mathrm{R}}\mathrm{∕}{\omega }_{\mathrm{r}}^{\mathrm{R}}=0.1$ (dotted), 0.5 (dashed) and 1.0 (solid). In this example, g was chosen to match the experimentally observed value of g/2π = 1.79 MHz. b Two-transmon, three-resonator cQED chip (detailed description in Supplementary Notes 2 and 3). c Sequence schematic for second-order Trotterisation. The rotating frame defining the simulated resonator frequency (ω _r) is controlled via the Q _R bit-flip pulse phases. d Example simplified experimental pulse sequence for 5 Trotter steps followed by a photon parity measurement.