Algebraic theory of topological quantum information

The algebraic theory of topological quantum information is a collection of algebraic techniques developed and applied to topological aspects of condensed matter physics and quantum information. Often, this revolves around using categorical structures or cohomology theories to classify and describe various topological phases of matter, such as topological order and symmetry-protected topological order.

Often, the application of categorical models to topological systems comes from the fact that the objects the categories describe some sort of quasiparticles, and the structures on the category encode the ways in which these quasiparticles can interact with one another.

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