Explore recent advancements in quantum simulation through this 51-minute lecture by Nathan Wiebe from Microsoft Research. Delve into the challenges of quantum computation, focusing on dynamical simulation, unitary access, and sparse matrix access. Examine the limitations of Charter Suzuki methods and investigate alternative approaches such as linear combinations, time-dependent evolution, and Taylor series. Learn about randomized compilation techniques and their applications in quantum chemistry and ground state physics. Gain insights into the current problems and potential solutions in the field of quantum simulation.