  Each year, the gap between theoretical proposals and experimental endeavours
to create quantum computers gets smaller, driven by the promise of
fundamentally faster algorithms and quantum simulations. This occurs by the
combination of experimental ingenuity and ever simpler theoretical schemes.
This thesis comes from the latter perspective, aiming to find new, simpler ways
in which components of a quantum computer could be built. We first search for
ways to create quantum gates, the primitive building blocks of a quantum
computer. We find a novel, low-control way of performing a two-qubit gate on
qubits encoded in a decoherence-free subspace, making use of many-body
interactions that may already be present. This includes an analysis of the
effect of control errors and magnetic field fluctuations on the gate. We then
present novel ways to create three-qubit Toffoli and Fredkin gates in a single
step using linear arrays of qubits, including an assessment of how well these
gates could perform, for quantum or classical computation, using
state-of-the-art ion trap and silicon donor technology. We then focus on a very
different model from the normal circuit model, combining ideas from
measurement-based quantum computation (MBQC) and holonomic quantum computation,
showing that all MBQC patterns with a property called \emph{gflow} can be
converted into a holonomic computation. The manifestation of the properties of
MBQC in this adiabatically driven model is then explored. Finally, we
investigate ways in which quantum information can be communicated between
distant parties, using minimally engineered spin chains. The viability of using
1D Wigner crystals as a quantum channel is analysed, as well as schemes using
ideal uniform spin chains with next-neighbour interactions, and edge-locking
effects.
