The quantum circuit model is the most widely used model of quantum
computation. It provides both a framework for formulating quantum algorithms
and an architecture for the physical construction of quantum computers.
However, several other models of quantum computation exist which provide useful
alternative frameworks for both discovering new quantum algorithms and devising
new physical implementations of quantum computers. In this thesis, I first
present necessary background material for a general physics audience and
discuss existing models of quantum computation. Then, I present three results
relating to various models of quantum computation: a scheme for improving the
intrinsic fault tolerance of adiabatic quantum computers using quantum error
detecting codes, a proof that a certain problem of estimating Jones polynomials
is complete for the one clean qubit complexity class, and a generalization of
perturbative gadgets which allows k-body interactions to be directly simulated
using 2-body interactions. Lastly, I discuss general principles regarding
quantum computation that I learned in the course of my research, and using
these principles I propose directions for future research.
