Let us start with the quantum computation first. Quantum computing can be realized in many ways but mostly involve physical states like polarized photons or Josephson junction which may not exist in the hot and wet environment of the brain. However, over the last 20 years, new ways to perform computing using topology have been proposed. In so-called topological quantum computing (TQC) information is processed via topological braiding whereby a topological order is imparted to topological defects \cite{Freedman_2002}.
Biological systems contain diversities of topological defects \cite{Kumar_2018,Duclos_2016,Kawaguchi_2017,Saw_2017}. Not only do they contain them, they also  which may also move in a céilí dance fashion \cite{Doostmohammadi_2018}