Simulation of material's properties are one of the most natural applications of quantum computers. Using classical methods, scientists have developed methods to treat large materials using compressed representations called impurity models. Increasing the size of these models gives a way of interpolating between the large complicated material and a smaller representation that can capture the correct physics.  While in practice simulating these systems at scale is challenging, it is not known if these models are truly beyond the scope of classical computations. In our work we provide evidence that this class of systems is indeed universal for quantum computation, meaning that, unless strongly held assumptions about the power of a quantum computer collapse, simulating these family of models is very challenging classically.