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.