Suppression of Measurement-Induced State Transitions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>cos</mml:mi> <mml:mo></mml:mo> <mml:mi>φ</mml:mi> </mml:math> -Coupling Transmon Readout

Drive-induced unwanted state transitions (DUST) are limiting both for microwave readout and parametric operations of superconducting qubits. Among them, measurement-induced state transitions (MIST) are due to intrinsic resonances described by the readout Hamiltonian. They were previously studied with a qubit linearly coupled to its readout mode, which constitutes the usual readout Hamiltonian. Since MIST can appear even at moderate powers, they limit the readout signal-to-noise ratio and the quantum non-demolition readout fidelity. In this work, we study the high-power readout regime in a different transmon readout scheme, implementing a nonlinear coupling called the cos φ -coupling. This coupling stems from a transmon molecule circuit and has symmetry properties that suppress nonparity-conserving MIST. We succeed in performing multistate single-shot readout up to the fifth excited state of the transmon, which enables us to identify leakage pathways from the computational subspace. The measurements indicate that the system is free of MIST up to high powers, with more than 300 photons in the readout mode. The MIST can be controllably turned on by breaking the parity symmetry of the coupling using flux-tuning. These experimental results are corroborated by branch analysis and simulations of the classical chaotic dynamics, showing that the cos φ -coupling is very robust to readout photons compared to the usual transverse coupling.