Visualizing edge states in atomic systems: Visualizing edge states in atomic systems Simulating the solid state using ultracold atoms is an appealing research approach. In solids, however, the charged electrons are susceptible to an external magnetic field, which curves their trajectories and makes them skip along the edge of the sample. To observe this phenomenon with cold atoms requires an artificial magnetic field to have a similar effect on the neutral atoms (see the Perspective by Celi and Tarruell). Stuhl et al. obtained skipping orbits with bosonic atoms using a lattice that consisted of an array of atoms in one direction and three internal atomic spin states in the other. In a complementary experiment, Mancini et al. observed similar physics with fermionic atoms. Science , this issue pp. 1514 and 1510 ; see also p. 1450

In this review recent investigations are summarized of many-body quantum systems with long-range interactions, which are currently realized in Rydberg atom arrays, dipolar systems, trapped-ion setups, and cold atoms in cavities. In these experimental platforms parameters can be easily changed, and control of the range of the interaction has been achieved. The main aim of the review is to present and identify the common and mostly universal features induced by long-range interactions in the behavior of quantum many-body systems. Discussed are the case of strong nonlocal couplings, i.e., the nonadditive regime, and the one in which energy is extensive, but low-energy, long-wavelength properties are altered with respect to the short-range case. When possible, comparisons with the corresponding results for classical systems are presented. Finally, cases of competition with local effects are also reviewed.

Significance: Variational quantum algorithms combine quantum resources with classical optimization methods, providing a promising approach to solve both quantum many-body and classical optimization problems. A crucial question is how variational algorithms perform as a function of qubit number. Here, we address this question by applying a variational quantum algorithm (QAOA) to approximate the ground-state energy of a long-range Ising model, both quantum and classical, and investigating the algorithm performance on a trapped-ion quantum simulator with up to 40 qubits. A negligible performance degradation and almost constant runtime scaling is observed as a function of the number of qubits. By modeling the error sources, we explain the experimental performance, marking a stepping stone toward more general realizations of hybrid quantum–classical algorithms.