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Center for Nonlinear Studies |
A physical system is said to be in topological phase if it is invariant under smooth local perturbations. These physical systems have applications in a wide range of disciplines, especially in quantum information science. Quantum computers based on such systems are topologically protected from decoherence. This fault-tolerance removes the need for the expensive error-correcting codes required by the qubit model. These topological phases of matter can be studied through their algebraic avatars, modular categories. Thus, a complete classification of these categories would provide a taxonomy of admissible topological phases. In this talk, we will discuss two paradigms for quantum computation: the qubit model and the topological model. Modular categories will be introduced and the connections between these mathematical constructs and the physical systems that they describe will be explained. We will examine the classification problem for these categories and present a recent solution of a foundational finiteness problem (Wang's Conjecture). Finally, we will discuss the algorithm suggested by this proof and its applications to low-rank classification.
Host: Kevin Buescher XCP-8. 667-1356