Quantum computational tensor network on string-net condensate

The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, “how useful is the string-net condensate in quantum information processing?”, we consider the most basic example of the string-net condensate, namely the $Z_2$ gauge string-net condensate on the two-dimensional hexagonal lattice, and show that the universal measurement-based quantum computation (in the sense of the quantum computational webs) is possible on it by using the framework of the quantum computational tensor network. This result implies that even the most basic example of the string-net condensate is equipped with the correlation space that has the capacity for the universal quantum computation.