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Quantum simulation of frustrated Ising spins with trapped ions

Abstract

A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. This compromise is central to the behaviour of many complex systems, from social1 and neural2 networks to protein folding3 and magnetism4,5. Frustrated networks have highly degenerate ground states, with excess entropy and disorder even at zero temperature. In the case of quantum networks, frustration can lead to massively entangled ground states, underpinning exotic materials such as quantum spin liquids and spin glasses6,7,8,9. Here we realize a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions10,11,12, whose interactions are precisely controlled using optical forces13. We study the ground state of this system as it adiabatically evolves from a transverse polarized state, and observe that frustration induces extra degeneracy. We also measure the entanglement in the system, finding a link between frustration and ground-state entanglement. This experimental system can be scaled to simulate larger numbers of spins, the ground states of which (for frustrated interactions) cannot be simulated on a classical computer.

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Figure 1: Frustrated Ising spins.
Figure 2: Quantum simulation of the three-spin Ising model with a transverse field.
Figure 3: Entanglement generation through the quantum simulation.
Figure 4: Entanglement and frustration.

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Acknowledgements

We acknowledge discussions with J. Moore, M. Newman, J. Wang and S. Das Sarma. This work is supported by US Army Research Office (ARO) award W911NF0710576 with funds from the Defense Advanced Research Projects Agency Optical Lattice Emulator programme, the Intelligence Advanced Research Projects Agency under ARO award W911NF0410234, the US National Science Foundation (NSF) Physics at the Information Frontier programme and the NSF Physics Frontier Center at the Joint Quantum Institute.

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All of the authors contributed equally to this work: experimental work was performed by K.K., M.-S.C., S.K., R.I., E.E.E. and C.M.; and theoretical work was performed by J.K.F., G.-D.L. and L.-M.D.

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Correspondence to K. Kim.

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The authors declare no competing financial interests.

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Kim, K., Chang, MS., Korenblit, S. et al. Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590–593 (2010). https://doi.org/10.1038/nature09071

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