A Topological Quantum Calculus

Topological Quantum Computation is based on the existence of two-dimensional particles called anyons, whose statistics substantially differ from what we can observe in a three-dimensional quantum system. The behaviour of anyons can be described via the statistics observed after exchanging one particle with another. In this work we revisit TQC from the perspective of computability theory and investigate the question of computational universality for TQC, namely the definition of a anyonic quantum computer that is able to simulate any program on any other anyonic quantum computer