Simulating quantum dynamics is one of the pioneering applications of quantum computers. To enhance the efficiency of quantum simulations on near-term devices, quantum dynamics compilation has emerged as a critical task, aiming to synthesize multi-qubit target dynamics into circuits with minimal elementary gate usage. In this talk, we demonstrate the power of variational algorithms in advancing quantum dynamics compilation for both Hermitian and non-Hermitian systems. For Hermitian systems, leveraging out-of-distribution generalization results in quantum machine learning, our variational quantum compilation (VQC) algorithm surpasses state-of-the-art methods in terms of both system size and accuracy for both one-dimensional and two-dimensional systems, achieving substantial resource savings compared to standard Trotterization techniques for system sizes up to 30x30. Furthermore, we address the challenges of simulating non-Hermitian dynamics, where traditional Trotterization struggles due to the necessity of postselection. Our works underscore the versatility and efficacy of variational methods in expanding the scope of quantum dynamics simulations, paving the way to practical quantum advantage.

[Refs: arxiv 2409.16346; Nature Communications 16 (1), 3286]