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In quantum mechanical many-body systems, long-range and anisotropic interactions promote rich spatial structure and can lead to quantum frustration, giving rise to a wealth of complex, strongly correlated quantum phases1. Long-range interactions play an important role in nature; however, quantum simulations of lattice systems have largely not been able to realize such interactions. A wide range of efforts are underway to explore long-range interacting lattice systems using polar molecules2–5, Rydberg atoms2,6–8, optical cavities9–11 or magnetic atoms12–15. Here we realize novel quantum phases in a strongly correlated lattice system with long-range dipolar interactions using ultracold magnetic erbium atoms. As we tune the dipolar interaction to be the dominant energy scale in our system, we observe quantum phase transitions from a superfluid into dipolar quantum solids, which we directly detect using quantum gas microscopy with accordion lattices. Controlling the interaction anisotropy by orienting the dipoles enables us to realize a variety of stripe-ordered states. Furthermore, by transitioning non-adiabatically through the strongly correlated regime, we observe the emergence of a range of metastable stripe-ordered states. This work demonstrates that novel strongly correlated quantum phases can be realized using long-range dipolar interactions in optical lattices, opening the door to quantum simulations of a wide range of lattice models with long-range and anisotropic interactions. 

Abstract The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing¹. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits^2,3and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture⁴. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions⁵. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction^6,7. Our method uses fast, single-pulse gates based on optimal control⁸, atomic dark states to reduce scattering⁹and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications^10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates^12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms¹⁴, error-corrected circuits⁷and digital simulations¹⁵. 

Abstract Suppressing errors is the central challenge for useful quantum computing¹, requiring quantum error correction (QEC)^2–6for large-scale processing. However, the overhead in the realization of error-corrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy^2–4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays⁷, our system combines high two-qubit gate fidelities⁸, arbitrary connectivity^7,9, as well as fully programmable single-qubit rotations and mid-circuit readout^10–15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code⁶distance fromd = 3 tod = 7, preparation of colour-code qubits with break-even fidelities⁵, fault-tolerant creation of logical Greenberger–Horne–Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks^16,17, we realize computationally complex sampling circuits¹⁸with up to 48 logical qubits entangled with hypercube connectivity¹⁹with 228 logical two-qubit gates and 48 logical CCZ gates²⁰. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling^21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors. 

Abstract The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems 1,2 . In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation 3–5 . We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state 6,7 . Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits 8 and a toric code state on a torus with sixteen data and eight ancillary qubits 9 . Finally, we use this architecture to realize a hybrid analogue–digital evolution 2 and use it for measuring entanglement entropy in quantum simulations 10–12 , experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars 13,14 . Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.