Quantum simulation of the transverse Ising model with trapped ions

Crystals of trapped atomic ions are among the most promising platforms for the quantum simulation of many-body quantum physics. Here, we describe recent developments in the simulation of quantummagnetic spin models with trapped 171Yb ions, and discuss the possibility of scaling the system to a level of complexity where classical computation becomes intractable. 5 Author to whom any correspondence should be addressed. 6 Current address: Institute for Interdisciplinary Information Science and Center for Quantum Information, Tsinghua University, Beijing 100084, China. 7 Current address: Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan. 8 Current address: Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore. 9 Current address: University of Connecticut, ITAMP Harvard-Smithsonian Center for Astrophysics, Cambridge,