  One of the most promising suggested applications of quantum computing is
solving classically intractable chemistry problems. This may help to answer
unresolved questions about phenomena like: high temperature superconductivity,
solid-state physics, transition metal catalysis, or certain biochemical
reactions. In turn, this increased understanding may help us to refine, and
perhaps even one day design, new compounds of scientific and industrial
importance. However, building a sufficiently large quantum computer will be a
difficult scientific challenge. As a result, developments that enable these
problems to be tackled with fewer quantum resources should be considered very
important. Driven by this potential utility, quantum computational chemistry is
rapidly emerging as an interdisciplinary field requiring knowledge of both
quantum computing and computational chemistry. This review provides a
comprehensive introduction to both computational chemistry and quantum
computing, bridging the current knowledge gap. We review the major developments
in this area, with a particular focus on near-term quantum computation.
Illustrations of key methods are provided, explicitly demonstrating how to map
chemical problems onto a quantum computer, and solve them. We conclude with an
outlook for this nascent field.
