ABSTRACT. We study Topological Quantum Computing (TQC) from the perspective of computability theory with the aim of definining a formal system which is able to capture the computational features of TQC. We discuss the mathematical model for TQC, namely Modular Tensor Categories, and their suitability for the construction of a domain of denotational objects similar to the Scott domain of the lambda calculus. This leads us to believe that a formalism similar to the classical lambda calculus can be defined also for TQC.