QNC B201
Speaker
Sumit
Sijher
Department
of
Applied
Mathematics,
University
of
Waterloo
Title
Topological Quantum Computation and Protected gates
Abstract
This thesis serves to give a mathematical overview of topological quantum computation and to apply the theory to characterize desirable fault-tolerant operations called protected gates. Topological quantum computation is a novel paradigm for quantum computation which seeks to harness certain exotic quantum systems known as topological phases of matter that exhibit unique physical phenomenon such as the manifestation of quasiparticle excitations called anyons. The low energy effective field theories of these systems can be expressed by certain topological quantum field theories, which in turn are described in terms of a unitary modular tensor categories that capture the essential properties of a topological phase of matter and its corresponding anyon model. An overview of the relevant category theoretic concepts is given, and the axioms of a unitary modular tensor category are made explicit.