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Though algorithms for quantum simulation of Quantum Harmonic Oscillator (QHO)have been proposed, still they have not yet been experimentally verified. Here,for the first time, we demonstrate a quantum simulation of QHO in the presenceof both time-varying and constant force field for both one and two dimensionalcase. New quantum circuits are developed to simulate both the one andtwo-dimensional QHO and are implemented on the real quantum chip "ibmqx4".Experimental data, clearly illustrating the dynamics of QHO in the presence oftime-dependent force field, are presented in graphs for different frequencyparameters in the Hamiltonian picture.

Experimental Demonstration of Force Driven Quantum Harmonic Oscillator in IBM Quantum Computer