Universal quantum simulator
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.
Quantum simulations of interacting spin systems have been realized with in a variety of experiments using a platform of trapped atomic ions:
Friedenauer et al., adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states .
Kim et al., extended the trapped ion quantum simulator to 3 spins, with global antiferromagnetic Ising interactions featuring frustration and showing the link between frustration and entanglement  and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a phase transition between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9 .
Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir  and Lanyon et al. demonstrated digital quantum simulation with up to 6 ions.
Islam, et al., demonstrated adiabatic quantum simulation of the transverse Ising model with variable (long) range interactions with up to 18 trapped ion spins, showing control of the level of spin frustration by adjusting the antiferromagnetic interaction range .
Britton, et al. have benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism.
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- Islam, R. et al (2011). "Onset of a quantum phase transition with a trapped ion quantum simulator". Nature Communications 2 (7): 377. arXiv:1103.2400. Bibcode:2011NatCo...2E.377I. doi:10.1038/ncomms1374.
- Barreiro, J. T. et al (2011). "An Open-System Quantum Simulator with Trapped Ions". Nature 470 (7335): 486–91. arXiv:1104.1146. Bibcode:2011Natur.470..486B. doi:10.1038/nature09801.
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- Islam, R. et al (2013). "Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator". Science 340 (6132): 583–587. arXiv:1210.0142. Bibcode:2013Sci...340..583I. doi:10.1126/science.1232296.
- Britton, J.W., et al. (2012). "Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins". Nature 484: 489–492. arXiv:1204.5789. Bibcode:2012Natur.484..489B. doi:10.1038/nature10981. PMID 22538611. Retrieved 2012-04-28.
- Deutsch's 1985 paper
- Online Web-based Quantum Computer Simulator (University Of Patras, Wire Communications Laboratory)
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