  A great part of the mathematical foundations of topological quantum
computation is given by the theory of modular categories which provides a
description of the topological phases of matter such as anyon systems. In the
near future the anyonic engineering will provide the anyonic devices from which
the topological quantum computers will be constructed. From other side the
string anyons are interesting topological phases of matter which can be
described using mathematical constructions such as Frobenius algebras and
open-closed string topological quantum field theories which are based on
cobordism categories. Recently was proposed that is possible to obtain
representations of cobordism categories using modular categories. In the
present work, the modular categories resulting as representations of the 3
dimensional bordism 2 category are used with the aim to construct a new model
of topological quantum computation. Such new model is named Sanyon Topological
Quantum Computation and it is is theoretically performed by evolving non
abelian string anyons (sanyons) using the Loop Braid Group and the open closed
cobordism category. The output of the computation uniquely depends on how the
sanyons have been braided by the Loop Braid Group and operated by the
generators of the cobordism category. Small disturbances do not unravel the
loop braids and the cobordisms, making the computation resistant to errors and
decoherence.
