Efficient quantum time dynamics using the Yang-Baxter equation

This study demonstrates how the Yang-Baxter equation (YBE) can be efficiently utilized to compress and produce a constant depth quantum circuit for efficient time dynamics of 1D lattice spin chains with nearest-neighbor interactions on real quantum devices. We show that the depth of quantum circuits for each time step is independent of time and step size and depends only on the number of spins. The depth of the compressed circuit is a linear function of the system size for the classes of Heisenberg model Hamiltonians studied in this work. We rigorously show that the number of CNOT gates in the compressed circuit only scales quadratically with system size [1]. This allows for simulations of time dynamics of very large 1D spin chains. To demonstrate the efficacy of the developed technique, we have performed time dynamics simulations of three and five spins on an IBM quantum computer and compared the results from both compressed and uncompressed quantum circuits. We have also developed an open-source algebraic compiler (QuYBE) based on this approach to compress quantum circuits [2]. QuYBE is a first step towards making this technique available to the broader community of scientists from multiple domains.