Topological quantum computation aims to solve the decoherence problem by encoding quantum information in a topologically invariant way. The foremost example uses anyon braiding in two-dimensional topological phases of matter. The algebraic models for these anyon systems are tensor categories, a mathematical structure with a wide range of applications from representation theory to low-dimensional topology. In this talk, I will discuss some recent results in the theory of tensor categories, motivated by this connection with topological quantum computation.

Researchers should cite this work as follows:

• Qing Zhang (2019), "The Algebra of Topological Quantum Computing," https://nanohub.org/resources/31752.

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1. quantum
2. quantum computing
3. quantum science and information
4. topological quantum computing