Abstract
We propose an exact mathematical mapping that can be useful for making an analog quantum simulator that uses ion-based systems to realize the many-body electron–electron Coulomb interaction of an electron gas. This exact mathematical mapping allows us to deal with a system that is difficult to solve and control using a potentially more experimentally feasible setup. We show that ions can efficiently simulate electronic Coulomb interactions by using a unitary dilatation transform. The transformation does not need to be physically implemented if only the energy spectrum is desired, eliminating the complexity overhead. This proposal works in any number of dimensions and could be used to simulate different topological phases of electrons in graphene-like structures, by using ions confined in honeycomb lattices.
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Acknowledgements
This work is supported by the Basque Government (Grant No. IT472-10), the Spanish MICINN (Project No. FIS2012-36673-C03-03), and the Basque Country University UFI (Project No. 11/55-01-2013). Partial support was provided by LightCone Interactive LLC.
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Luo, DW., Pyshkin, P.V., Modugno, M. et al. Ion-based quantum simulation of many-body electron–electron Coulomb interaction. Quantum Inf Process 17, 238 (2018). https://doi.org/10.1007/s11128-018-2008-5
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DOI: https://doi.org/10.1007/s11128-018-2008-5