There are many quantum algorithms that exhibit an advantage over known classical algorithms. Such a diversity of results can make it difficult to express the computational capability of a quantum computer in a clear and faithful manner to someone new to quantum computing. In this recent paper, we address a large family of quantum algorithms that are often used as the main subroutine in many important applications. In particular we consider quantum algorithms that apply some smooth function of a Hermitian matrix to an input state. Examples of algorithms of this type include Hamiltonian simulation used in a variety of applications including quantum chemistry, the Quantum Linear Systems or matrix inversion algorithm used in quantum machine learning applications, and sampling from Gibbs distributions used in the recent quantum semi-definite programming (SDP) solvers. The full paper can be found here.