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Quantum time dynamics (QTD) is considered a promising problem for quantumsupremacy on near-term quantum computers. However, QTD quantum circuits growwith increasing time simulations. This study focuses on simulating the timedynamics of 1-D integrable spin chains with nearest neighbor interactions. Weshow how the quantum Yang-Baxter equation can be exploited to compress andproduce a shallow quantum circuit. With this compression scheme, the depth ofthe quantum circuit becomes independent of step size and only depends on thenumber of spins. We show that the compressed circuit scales quadratically withsystem size, which allows for the simulations of time dynamics of very large1-D spin chains. We derive the compressed circuit representations for differentspecial cases of the Heisenberg Hamiltonian. We compare and demonstrate theeffectiveness of this approach by performing simulations on quantum computers.

Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression