A universal quantum simulator is a quantum computer proposed by Richard Feynman in 1982. Feynman showed that a classical Turing machine would presumably experience an exponential slowdown when simulating quantum phenomena, while his hypothetical universal quantum simulator would not. David Deutsch in 1985, took the ideas further and described a universal quantum computer. In 1996, Seth Lloyd showed that a standard quantum computer can be programmed to simulate any local quantum system efficiently.
A quantum system of many particles is described by a Hilbert space whose dimension is exponentially large in the number of particles. Therefore, the obvious approach to simulate such a system requires exponential time on a classical computer. However, it is conceivable that a quantum system of many particles could be simulated by a quantum computer using a number of quantum bits similar to the number of particles in the original system. As shown by Lloyd, this is true for a class of quantum systems known as local quantum systems. This has been extended to much larger classes of quantum systems.
Barreiro et al. have created a Universal Open-System Digital Quantum Simulator with trapped ions.
Lanyon et al. have created a Universal Digital Quantum Simulation with Trapped Ions.
J.W. Britton, et al. have benchmarked a quantum simulator with hundreds of qubits for studies of quantum magnetism
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