First- and Second-Order Digital Quantum Simulation of Three-Level Jaynes-Cummings Dynamics on Superconducting Quantum Processors

Abstract

This work presents a digital quantum simulation of a three-level atomic system interacting with a single-mode electromagnetic field based on the Jaynes-Cummings model, implemented on IBM Quantum superconducting processors. A qutrit is encoded using two physical qubits to represent the atomic states, while an additional qubit encodes the truncated field mode, enabling the realization of effective $Λ$-type atomic dynamics.The continuous-time light-matter interaction is implemented in a digital form by discretizing the evolution using Suzuki-Trotter decomposition. In contrast to an analog realization, the digital simulation replaces the continuous evolution with a sequence of quantum gates whose parameters are explicitly controlled. Phase evolution arising from the interaction Hamiltonian is digitally encoded using calibrated $R_Z$ gates, whose rotation angles are fixed by the physically relevant coupling scale and the chosen Trotter time step.State preparation is achieved using Hadamard and parametrized rotation gates, while the interaction dynamics are implemented through controlled operations. A comparative analysis between first- and second-order Trotter implementations reveals a trade-off between digital accuracy and hardware-induced noise. Overall, the results demonstrate that calibrated gate operations and noise-aware circuit design enable reliable digital simulation of multi-level light-matter interactions on noisy intermediate-scale quantum platforms.