Wisconsin Quantum Institute
There are many practical and theoretical challenges in the emerging area of quantum information processing, which seeks to optimally use the information embedded in the state of a quantum system to solve previously intractable computational problems and revolutionize simulation. The engineering goal is to develop scalable quantum hardware that circumvents the physical limits on the computational power of existing technologies, which are ultimately constrained by energy dissipation as the physical size of the components is reduced to the nanometer scale. In parallel with such “practical” difficulties, new theory is required to understand the limitations of quantum media and capitalize on the advantages of quantum superposition and entanglement. This includes the creation of new quantum algorithms that are targeted toward real-world problems, e.g., in finance, chemistry, and medicine; a study of the required resources to achieve a particular outcome, as well as methods to efficiently characterize such resources; and the development of novel protocols for secure quantum-enhanced communication, as well as classical ‘post-quantum encryption’ methods that are immune to quantum hacking. For all of these, quantum information theory relies on and draws inspiration from many different aspects of mathematics and theoretical computer science, including geometry, group theory, functional analysis, number theory, operator theory, probability theory, topology, complexity theory, and learning theory. Furthermore, the recent resolution of Connes’ embedding conjecture using quantum information-theoretic methods shows that ideas and results from quantum information theory can also influence research in pure mathematics.