Ultrafast variational simulation of nontrivial quantum states with long-range interactions

State preparation protocols ideally require as minimal operations as possible in order to be implemented in near-term, potentially noisy quantum devices. Motivated by long-range interactions (LRIs) intrinsic to many present-day experimental platforms (trapped ions, Rydberg atom arrays, etc.), we investigate the efficacy of variationally simulating nontrivial quantum states using the variational quantum-classical simulation (VQCS) protocol explored recently [W. W. Ho and T. H. Hsieh, SciPost Phys. 6, 29) (2019)], in the presence of LRIs. We show that this approach leads to extremely efficient state preparation: for example, Greenberger-Horne-Zeilinger (GHZ) states can be prepared with O(1) iterations of the protocol, and a quantum critical point of the long-range transverse-field Ising model (TFIM) can be prepared with >99% fidelity on a 100-qubit system with only one iteration. Furthermore, we show that VQCS with LRIs is a promising route for exploring generic points in the phase diagram of the long-range TFIM. Our approach thus provides concrete, ultrafast protocols for quantum simulators equipped with long-range interactions.