Variational Trotter compression algorithm for quantum dynamics simulations on noisy intermediate-scale quantum computers*

Simulating quantum dynamics of interacting many-body systems is one of the primary potential applications of quantum computing, since the growth of entanglement makes such simulations exponentially hard on classical computers. The shallow circuit requirement of current noisy QPUs, however, limits traditional algorithms based on Trotter product formulas to simulations of the early time dynamics, and instead favors the use of variational quantum algorithms. Here, we present and benchmark an algorithm that combines Trotterized state evolution over short times with a variational compression step that uses the state overlap as a cost function. We implement the algorithm on IBM hardware and show quantum dynamics simulation results for a few site Heisenberg spin chain beyond the coherence time of the device. We discuss the impact of sample and gate noise as well as various error mitigation strategies on the performance and scalability of the algorithm, and present results on noisy and noiseless simulators of systems up to six and eleven sites, respectively.