Dynamic Simulation of the Jaynes-Cummings model ‎using the hybridquantum-classical algorithm

The Jaynes-Cummings model is the canonical model for atom-light interactions, describing ‎a single confined bosonic mode interacting with a two-level system (qubit). This is ‎sufficient to describe a wide range of phenomena in quantum optics and quantum ‎computing. We simulate the dynamics of this model using the hybrid quantum-classical ‎algorithm (HQCA) consisting of quantum and classical computers. The parametric quantum ‎state preparations and quantum measurements are performed on the quantum computer ‎and parameters optimization employ on the classic computer. For implement of hybrid ‎quantum-classical algorithms, the Noisy Intermediate Scale Quantum (NISQ) computer is ‎used. In Noisy Intermediate Scale Quantum computers, we don’t need to error correction.  ‎For this purpose, we transform Hamiltonian to qubit form and using an algorithm to obtain ‎the dynamic of the Jaynes-Cummings model. We obtain occupation probability and ‎transition probability in the Jaynes-Cummings model using the hybrid quantum-classical ‎algorithm. The output of the algorithm is compatible with the exact calculation‎‎‎‎.‎