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Video abstract for the article 'Quantum-circuit design for efficient simulations of many-body quantum dynamics' by Sadegh Raeisi, Nathan Wiebe and Barry C Sanders (Sadegh Raeisi et al 2012 New J. Phys. 14 103017). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/14/10/103017/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. Quantum simulation is an important area of study within the field of quantum computing. Its aim is to provide accurate answers efficiently to computational questions concerning the dynamical evolution of states or the properties of the operators that induce the evolution. Many algorithms have been developed for standard (non-quantum) computers, but classical simulations are generically intractable. A quantum computer could, however, make valuable classes of computational problems tractable. As quantum simulation has a much lower time and space cost compared to the requirements for practical use of other quantum algorithms, it is currently undergoing intensive experimental study. Main results. We have developed a circuit-design algorithm for simulating a large class of physically relevant Hamiltonian evolutions. These Hamiltonians are sums of tensor products of Pauli spin operators. The circuit-design algorithm runs efficiently on a classical computer and yields a quantum-computer circuit that efficiently simulates the evolution of an arbitrary input state. For any small error tolerance for the output state, the resultant quantum circuit guarantees an output state within the specified tolerance, and the resource requirement is optimal in space and nearly optimal in time. In many cases the actual resource cost is much less than the resource bound, making the circuit even more feasible. Wider implications. Our efficient circuit-design algorithm will enable realizations of experimental quantum simulators for physically relevant Hamiltonians with guaranteed upper bounds on output-state errors. Such quantum simulators will be valuable in many areas, including condensed-matter physics and linear-equation solvers.