The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity1,2. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles3. Feynman predicted that a quantum simulator—a special-purpose ‘analogue’ processor built using quantum bits (qubits)—would be inherently suited to solving such problems4,5. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach6,7,8,9,10,11,12,13,14, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin–spin interaction, Ji,j , on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction , where 0 ≤ a ≤ 3 and di,j is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb–like (a = 1), monopole–dipole (a = 2) and dipole–dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism.
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This work was supported by the DARPA OLE programme and NIST. A.C.K. was supported by the NSF under grant number DMR-1004268. B.C.S. is supported by an NRC fellowship funded by NIST. J.K.F. was supported by the McDevitt endowment bequest at Georgetown University. M.J.B. and J.J.B. acknowledge partial support from the Australian Research Council Center of Excellence for Engineered Quantum Systems CE110001013. We thank F. Da Silva, R. Jordens, D. Leibfried, A. O’Brien, R. Scalettar and A. M. Rey for discussions.
The authors declare no competing financial interests.
This manuscript is a contribution of the US National Institute of Standards and Technology and is not subject to US copyright.
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Britton, J., Sawyer, B., Keith, A. et al. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012). https://doi.org/10.1038/nature10981
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