Abstract: Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics, and the growth of entanglement is a major challenge for classical simulation methods. We explore the relationship between quantum entanglement and quantum simulation, showing that product-formula approximations can perform better for entangled systems. In particular, we establish a tighter upper bound for the algorithmic error in terms of entanglement entropy. This shows that entanglement is not only an obstacle to classical simulation, but also a feature that can accelerate quantum algorithms. Based on joint work with Qi Zhao and You Zhou (arXiv:2406.02379)