I will give an overview of the range of algorithms for simulating Hamiltonian evolution on a quantum computer. These include Lie-Trotter-Suzuki product formulae, quantum walks, linear combinations of unitaries, Taylor series, Dyson series, quantum signal processing and qubitisation. I will discuss the relations between these approaches, as well as how they can be applied to quantum chemistry. The talk will also cover a new log-depth technique for antisymmetrising states to use for quantum chemistry.
