  Quantum computing is an important developing technology with the potential to
revolutionise the landscape of scientific and business problems that can be
practically addressed. The widespread excitement derives from the potential for
a fault tolerant quantum computer to solve previously intractable problems.
Such a machine is not expected to be available until 2030 at least. Thus we are
currently in the so-called NISQ era where more heuristic quantum approaches are
being applied to early versions of quantum hardware. In this paper we seek to
provide a more accessible explanation of many of the more technical aspects of
quantum computing in the current NISQ era exploring the 2 main hybrid
classical-quantum algorithms, QAOA and VQE, as well as quantum annealing. We
apply these methods, to an example of combinatorial optimisation in the form of
a facilities location problem. Methods explored include the applications of
different types of mixer (X, XY and a novel 3XY mixer) within QAOA as well as
the effects of many settings for important meta parameters, which are often not
focused on in research papers. Similarly, we explore alternative parameter
settings in the context of quantum annealing. Our research confirms the broad
consensus that quantum gate hardware will need to be much more capable than is
available currently in terms of scale and fidelity to be able to address such
problems at a commercially valuable level. Quantum annealing is closer to
offering quantum advantage but will also need to achieve a significant step up
in scale and connectivity to address optimisation problems where classical
solutions are sub-optimal.
