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.

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Forum * In 2010 an industrial-academic collaboration commissioned by the National Institute of Information and Communications Technology in Japan implemented the world's fastest network protected by quantum encryption technology on 45 km of metropolitan optical fibre network in Tokyo ** The Canadian company D-Wave Systems advertises its superconducting 128-qubit processor chip as "the first commercial quantum computing system on the market" Heading to market

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From science to technology and back again:state-of-the-art tools developed for quantum technologies, in theory and experiment, are allowing researchers to revisit the foundations of quantum theory and to explore the terra incognita that may lie beyond.