Cat-state qubits formed by photonic cat states have a biased noise channel, i.e., one type of error dominates over all the others. We demonstrate that such biased-noise qubits are also promising for error-tolerant simulations of the quantum Rabi model (and its varieties) by coupling a cat-state qubit to an optical cavity. Using the cat-state qubit can effectively enhance the counterrotating coupling, allowing us to explore several fascinating quantum phenomena relying on the counterrotating interaction. Moreover, another benefit from biased-noise cat qubits is that the two main error channels (frequency and amplitude mismatches) are both exponentially suppressed. Therefore, the simulation protocols are robust against parameter errors of the parametric drive that determines the projection subspace. We analyze three examples: (i) collapse and revivals of quantum states; (ii) hidden symmetry and tunneling dynamics; and (iii) pair-cat-code computation.
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