Quantum time dynamics (QTD) is considered a promising problem to solve on near-term quantum computers. However, quantum circuits for QTD grow with increasing time simulation. This study focuses on simulating the time dynamics of one-dimensional (1-D) integrable spin chains with nearest-neighbor interactions. We show how the Yang-Baxter equation can be exploited to compress a quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and depends only on the number of spins. The compressed circuit scales quadratically with system size, which allows for the simulations of time dynamics of very large 1-D spin chains. In addition, each time step of the simulation can run independently in parallel. We show the implementation of this scheme on an IBM quantum device and demonstrate the impact of our compression scheme on the fidelity of calculations.