Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term computers. However, QTD circuits grow with increasing simulations. This study focuses simulating the of one-dimensional (1D) integrable spin chains nearest-neighbor interactions. We have proved existence reflection symmetry in circuit employed evolution certain classes 1D Heisenberg model Hamiltonians by virtue Yang-Baxter equation, and how this can be exploited to compress produce shallow circuit. With compression scheme, depth becomes independent step size only depends number spins. show that compressed rigorously linear function system studied present work. As consequence, CNOT gates scales quadratically size, which allows simulations very large chains. derive representations different special cases Hamiltonian. compare demonstrate effectiveness approach performing