As many other descriptions in physics and beyond, the description of quantum systems is not scalable. That is, the general description based on Hilbert spaces works well for a few qubits, but very quickly becomes too complicated. Tensor networks are a tool to provide efficient descriptions of quantum states. They work very well for pure states, especially in one spatial dimension, but their application to mixed states presents some new challenges. One of them is the so-called positivity problem, which is the difficulty of representing the positivity of the state locally. 

Our team works on various aspects of the positivity problem. For this research topic we enjoy the collaboration with Tim Netzer. 

At the heart of the theory of computer science there is the notion of universal computers---a programmable device that can carry out any algorithm. This encapsulates the insight that programs can run other programs, which underlies the very existence of software. It was early realized that very simple machines are already universal, that is, that only a few simple operations are needed in order to run any possible algorithm. 

Recently, a similar notion of universality has been shown in physics (see here). Physicists use since decades very simplified models of condensed matter systems, often called spin models, which are capable of describing rich physics---the paradigmatic example being the Ising model. The universality results unveiled the fact that some extremely simple models, such as the Ising model, can in fact reproduce the physics of all other models. 

Our team investigates connections between these two notions of universality.