The main goal of this paper is to apply the Yang-Baxter-Rowell equation in topological quantum
computation, using the symbolic computational software Maple. Initially, using Maple, I reproduced the Dye
classification of the 4x4 unitary solutions of the Yang-Baxter equation. Then, also using Maple, I reproduced
the solutions given by Rebecca Chen to the Yang-Baxter-Rowell equation. Finally, the obtained solutions
were applied to the problem of topological quantum categorification of the chromatic polynomial for graphs.
It was claimed that the Yang-Baxter-Rowell operators, considered as quantum gates, can be incorporated in
quantum circuit models and quantum games, such as the Grover algorithm and the game Battle of the Sexes.
It is expected that a future investigation can provide a more complete classification of the solution to the
Yang-Baxter-Rowell equation and its possible applications on topological quantum computation.