Quantum computers, a rapidly developing technology in recent years, utilize quantum bits (qubits) based on quantum entanglement for computation. This paper aims to use quantum computers to calculate the time evolution operator for a harmonic oscillator. First, we find out the appropriate matrix size, spatial step ∆x, mass (m), and angular frequency (ω) for the oscillator's operator and express the time evolution operator matrix in the position basis. After designing and simplifying the quantum circuit, we use IBM's quantum computer to simulate and compute the numerical values. By applying matrix correction to reduce readout errors , we achieve more accurate results. The simulation results within a single time unit closely match theoretical values. In the future, we hope to apply this quantum circuit to find eigenvalues of matrices or simulate larger systems.