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State preparation protocols ideally require as minimal operations aspossible, in order to be implemented in near-term, potentially noisy quantumdevices. Motivated by long range interactions (LRIs) intrinsic to manypresent-day experimental platforms (trapped ions, Rydberg atom arrays, etc.),we investigate the efficacy of variationally simulating non-trivial quantumstates using the Variational Quantum-Classical Simulation (VQCS) protocolexplored recently in [SciPost Phys. 6, 029 (2019)], in the presence of LRIs. Weshow that this approach leads to extremely efficient state preparation: forexample, Greene-Horne-Zeilinger (GHZ) states can be prepared with O(1)iterations of the protocol, and a quantum critical point of the long rangetransverse field Ising model (TFIM) can be prepared with > 99% fidelity on a100 qubit system with only one iteration. Furthermore, we show that VQCS withLRIs is a promising route for exploring generic points in the phase diagram ofthe long-range TFIM. Our approach thus provides concrete, ultrafast protocolsfor quantum simulators equipped with long range interactions.

Ultrafast Variational Simulation of Non-trivial Quantum States with Long Range Interactions