Fibonacci Model Unitary Subgroup Structure

A permutation quantum computer model is used to describe a modern quantum computer. This approach suggests the use of knot theory as mathematics describing the processes of this model. To connect this model with the existing mathematics of special unitary operators, the idea was expressed to correlate special unitary operators with quaternions and introduce node algebra already on quaternions. Kauffman and Lomonaco described this approach by posing the question of the density of the resulting subgroup in a special unitary group.