Explore a comprehensive theory of Trotter error in quantum computing through this seminar by Yuan Su from the University of Maryland. Delve into the limitations of previous approaches based on Baker-Campbell-Hausdorff expansion truncation and discover a new analysis that directly exploits operator summand commutativity. Learn about improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of various Hamiltonian systems. Examine how product formulas can preserve system locality, leading to simulations of local observables with complexity independent of system size for power-law interacting systems. Gain insights into the accuracy of this new theory in characterizing Trotter error, both in terms of asymptotic scaling and constant prefactor, and understand its implications for quantum simulation and Lieb-Robinson bounds.