We show that a multicolor modulation of the depth of an optical lattice allows for a flexible independent control of correlated hopping, occupation-dependent gauge fields, effective on-site interactions without Feshbach resonances, and nearest-neighbor interactions. As a result, the lattice-depth modulation opens the possibility of engineering with minimal experimental complexity a broad class of lattice models in current experiments with ultracold atoms, including Hubbard models with correlated hopping, peculiar extended models, and twocomponent anyon-Hubbard models.

We show that whereas spin-1/2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladder-like lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry protected topological (SPT) phase that may be readily revealed by analyzing long-range string spin correlations along the ladder legs. We propose a simple scheme for the realization of spin-1/2 U(1) QLMs based on single-component fermions loaded in an optical lattice with s-and p-bands, showing that the SPT phase may be experimentally realized by adiabatic preparation.The realization of lattice gauge models using ultra cold gases has attracted a major theoretical attention in recent years [1][2][3][4]. Various ideas for creating dynamical gauge fields have been proposed [5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently the Schwinger model has been simulated in ion chains [18]. Particular interest has been devoted to quantum-link models (QLMs) [19], which generalize lattice gauge theory [20] by realizing continuous gauge symmetries with discrete gauge variables (quantum links). QLMs are relevant in particle physics, and in particular QCD [21], and in condensed matter physics [22,23]. In U(1) QLMs, links are represented by quantum spins and fermions provide the matter field, making these QLMs particularly suitable for simulation with cold lattice gases.In this Letter we study the topological properties of spin-1/2 U(1) QLMs. Topological quantum systems have become one of the most active research areas during the past decades [24,25]. In particular the understanding of topological phases in strongly correlated quantum systems remains challenging. The study of symmetry protected topological (SPT) states has triggered a large progress in this field [26]. SPT phases have been classified by means of entanglement properties and group theoretical considerations [27][28][29][30][31][32]. Indeed in onedimensional (1D) systems, SPT phases are the only realizable class of topological quantum states, a prominent example being the so-called Haldane phase of odd-integer spin chains [33,34]. Generalizations of the Haldane phase have been theoretically studied in the context of ultracold gases [35][36][37][38][39][40].Real or synthetic ladder-like lattices have recently constituted the focus of major efforts [41][42][43] in the context of the realization of static gauge fields in ultra-cold atomic systems. We show below that although in 1D spin-1/2 U(1) QLMs are topologically trivial, when implemented in ladder-like lattices these models present an intriguing ground-state phase diagram, which interestingly includes an SPT phase that we characterize using a generalized topological order parameter and the entanglement spectrum. We show that the SPT phase may be revealed by analyzing string spin correlations along the ladder legs. Moreover, we propose a simple scheme for the realization of the QLM based on s-p lattices [44], showing that the SPT phase may be experimentally realized by adiab...

We explore the ground-state physics of two-dimensional spin-1/2 U (1) quantum link models, one of the simplest non-trivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the large mass limit we observe Neél-like vortex-antivortex and striped crystalline phases, for small masses there is a transition from the striped phases into a disordered phase whose properties resemble those at the Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized on ladders by boundary Haldane-like properties, such as vanishing parity and finite string ordering. Moreover, from studies of the string tension between gauge charges, we find that whereas the stripe phases are confined, the novel disordered phase present clear indications of being deconfined. Our results open exciting perspectives of studying highly nontrivial physics in quantum simulators, such as spin-liquid behavior and confinement-deconfinement transitions, without the need of explicitly engineering plaquette terms. arXiv:1910.12829v1 [cond-mat.quant-gas]

We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [Phys. Rev. A 94, 023615 (2016)]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semi-synthetic ring set-up allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.

Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we demonstrate how quantum neural networks, in the form of quantum autoencoders, can be trained to learn optimal strategies for active detection and correction of errors, including spatially correlated computational errors as well as qubit losses. We highlight that the denoising capabilities of quantum autoencoders are not limited to the protection of specific states but extend to the entire logical codespace. We also show that quantum neural networks can be used to discover new logical encodings that are optimally adapted to the underlying noise. Moreover, we find that, even in the presence of moderate noise in the quantum autoencoders themselves, they may still be successfully used to perform beneficial quantum error correction and thereby extend the lifetime of a logical qubit.