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A great part of the mathematical foundations of topological quantumcomputation is given by the theory of modular categories which provides adescription of the topological phases of matter such as anyon systems. In thenear future the anyonic engineering will provide the anyonic devices from whichthe topological quantum computers will be constructed. From other side thestring anyons are interesting topological phases of matter which can bedescribed using mathematical constructions such as Frobenius algebras andopen-closed string topological quantum field theories which are based oncobordism categories. Recently was proposed that is possible to obtainrepresentations of cobordism categories using modular categories. In thepresent work, the modular categories resulting as representations of the 3dimensional bordism 2 category are used with the aim to construct a new modelof topological quantum computation. Such new model is named Sanyon TopologicalQuantum Computation and it is is theoretically performed by evolving nonabelian string anyons (sanyons) using the Loop Braid Group and the open closedcobordism category. The output of the computation uniquely depends on how thesanyons have been braided by the Loop Braid Group and operated by thegenerators of the cobordism category. Small disturbances do not unravel theloop braids and the cobordisms, making the computation resistant to errors anddecoherence.

Topological Quantum Computation from the 3-dimensional Bordism 2-Category