  Simulating quantum mechanics is known to be a difficult computational
problem, especially when dealing with large systems. However, this difficulty
may be overcome by using some controllable quantum system to study another less
controllable or accessible quantum system, i.e., quantum simulation. Quantum
simulation promises to have applications in the study of many problems in,
e.g., condensed-matter physics, high-energy physics, atomic physics, quantum
chemistry and cosmology. Quantum simulation could be implemented using quantum
computers, but also with simpler, analog devices that would require less
control, and therefore, would be easier to construct. A number of quantum
systems such as neutral atoms, ions, polar molecules, electrons in
semiconductors, superconducting circuits, nuclear spins and photons have been
proposed as quantum simulators. This review outlines the main theoretical and
experimental aspects of quantum simulation and emphasizes some of the
challenges and promises of this fast-growing field.
