| dc.description.abstract | Quantum computation is a proposed model of computation that applies quantum
mechanics to perform information processing and store information in quantum
states. Quantum mechanics applies for many different phenomena, with
many possible systems in which it is possible to model and manipulate the
fundamental quantum information bit - the qubit - and thus there are hypothetically
many ways to construct a quantum computer. One proposed way of
quantum computation is to use non-abelian anyons to model qubits. These are
exotic quasi-particles whose wave functions evolve non-trivially when permuting
their positions. This allows for computation with qubits simply by permuting
anyons, a process called braiding since their trajectories in spacetime resemble
braids. The quantum states associated with the anyons evolve only when the
positions of anyons are permuted and do not depend on the paths the anyons
take. For this reason this model of quantum computation is called topological
quantum computation (TQC). One of the main advantages of TQC is that computations
are inherently fault tolerant: there is no noise due to anyons taking
strange paths since the quantum evolution is path independent. The goal of
this text is to investigate the mathematical framework for this proposed model
of quantum computation. The main results are the possible gates that can be
applied to two one-qubit topological computers. Given the key properties of
the anyons used, Theorem 5.2 states the possible one-qubit gates in an Ising
computer, and Theorem 7.1 states the possible one-qubit gates in a Fibonacci
computer. | |
