  Quantum computing promises to provide the next step up in computational power
for diverse application areas. In this review, we examine the science behind
the quantum hype and breakthroughs required to achieve true quantum advantage
in real world applications. Areas that are likely to have the greatest impact
on high performance computing (HPC) include simulation of quantum systems,
optimisation, and machine learning. We draw our examples from materials
simulations and computational fluid dynamics which account for a large fraction
of current scientific and engineering use of HPC. Potential challenges include
encoding and decoding classical data for quantum devices, and mismatched clock
speeds between classical and quantum processors. Even a modest quantum
enhancement to current classical techniques would have far-reaching impacts in
areas such as weather forecasting, engineering, aerospace, drug design, and
realising "green" materials for sustainable development. This requires
significant effort from the computational science, engineering and quantum
computing communities working together.
