Abstract: I will discuss the application of classical algorithms in quantum simulation and give examples of state-of-the-art simulations drawn from the group’s work, in one or more of the following areas: correlated quantum materials (Kondo physics and high Tc superconductivity), biochemistry (metalloenzymes), and Hamiltonian and circuit quantum dynamics. If time permits, I will also discuss conjectures about the role of classical algorithms in quantum simulation and the computational power of classical heuristics.