Abstract: Fault tolerance is required to run useful quantum computations at scale. Quantum codes form the basis for fault tolerant quantum operations. Codes based on topological phases of quantum matter have been the focus of research in this area for decades, and small examples have recently been implemented in experiments. On the other hand, recent theoretical research has shifted to focus on more efficient codes that require a higher degree of connectivity. In this talk I will present several results at the interface of quantum codes and quantum matter. The first uses progress on quantum codes to find new states of topological quantum matter. The second applies ideas from topological gauge theories to design better fault-tolerant quantum logic gates.
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