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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. A quantum processer is realized using arrays of neutral atoms that are transported in a parallel manner by optical tweezers during computations, and used for quantum error correction and simulations.

Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing 1 , a broad effort is currently underway to build large-scale programmable quantum systems. Such systems provide insights into strongly correlated quantum matter 2 – 6 , while at the same time enabling new methods for computation 7 – 10 and metrology 11 . Here we demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms, featuring strong interactions controlled by coherent atomic excitation into Rydberg states 12 . Using this approach, we realize a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. We benchmark the system by characterizing high-fidelity antiferromagnetically ordered states and demonstrating quantum critical dynamics consistent with an Ising quantum phase transition in (2 + 1) dimensions 13 . We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation 14 , experimentally map the phase diagram and investigate the role of quantum fluctuations. Offering a new lens into the study of complex quantum matter, these observations pave the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics and hardware-efficient realization of quantum algorithms. A programmable quantum simulator with 256 qubits is created using neutral atoms in two-dimensional optical tweezer arrays, demonstrating a quantum phase transition and revealing new quantum phases of matter.

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations 1 . These fluctuations play a dominant part in the quantum critical region surrounding the transition point, where the dynamics is governed by the universal properties associated with the QPT. Although time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early Universe to Bose–Einstein condensates 2 – 5 , understanding critical real-time dynamics in isolated, non-equilibrium quantum systems remains a challenge 6 . Here we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations when crossing the QPT, we experimentally verify the quantum Kibble–Zurek mechanism (QKZM) 7 – 9 for an Ising-type QPT, explore scaling universality and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models 10 , 11 , providing new insights into exotic systems that were not previously understood and opening the door to precision studies of critical phenomena, simulations of lattice gauge theories 12 , 13 and applications to quantum optimization 14 , 15 . A Rydberg atom quantum simulator with programmable interactions is used to experimentally verify the quantum Kibble–Zurek mechanism through the growth of spatial correlations during quantum phase transitions.

An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system’s entanglement, which is experimentally challenging to measure. We realize such a many-body–localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.

Exotic phases of matter can emerge from strong correlations in quantum many-body systems. Quantum gas microscopy affords the opportunity to study these correlations with unprecedented detail. Here, we report site-resolved observations of antiferromagnetic correlations in a two-dimensional, Hubbard-regime optical lattice and demonstrate the ability to measure the spin-correlation function over any distance. We measure the in situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, and observe statistically significant correlations over three lattice sites. The temperatures that we reach approach the limits of available numerical simulations. The direct access to many-body physics at the single-particle level demonstrated by our results will further our understanding of how the interplay of motion and magnetism gives rise to new states of matter.

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing 1 . Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits 2 , 3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture 4 . The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions 5 . 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 control 8 , atomic dark states to reduce scattering 9 and 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 algorithms 14 , error-corrected circuits 7 and digital simulations 15 . The realization of two-qubit entangling gates with 99.5% fidelity on up to 60 rubidium atoms in parallel is reported, surpassing the surface-code threshold for error correction and laying the groundwork for neutral-atom quantum computers.

Suppressing errors is the central challenge for useful quantum computing 1 , requiring quantum error correction (QEC) 2 – 6 for 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 arrays 7 , our system combines high two-qubit gate fidelities 8 , 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-code 6 distance from d  = 3 to d  = 7, preparation of colour-code qubits with break-even fidelities 5 , 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 circuits 18 with up to 48 logical qubits entangled with hypercube connectivity 19 with 228 logical two-qubit gates and 48 logical CCZ gates 20 . 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. A programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits is described, in which improvement of algorithmic performance using a variety of error-correction codes is enabled.

An antiferromagnet with a correlation length that encompasses the whole system is created with the aid of quantum gas microscopy of cold atoms in an optical lattice. Seeking out the secrets of hot superconductivity Although high-temperature superconductivity seems like a complicated phenomenon, its basic features are captured by the very simple Fermi–Hubbard model. Researchers have been able to emulate this model using ultracold quantum gases, but to see exciting phenomena based on long-range correlation, such as superconductivity, the system needs to reach extremely low temperatures. Here, Anton Mazurenko et al . demonstrate a milestone towards these interesting low-temperature phases. They create an antiferromagnet with a correlation length that encompasses the whole system. The foundation for this achievement is a quantum gas microscope developed by the authors. Ultracold quantum gases might soon be able to simulate a Fermi–Hubbard system close to its ground state and help to clarify the mechanism for high-temperature superconductivity. Exotic phenomena in systems with strongly correlated electrons emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet is expected to give rise to pseudogap states and high-temperature superconductors 1 . Quantum simulation 2 , 3 , 4 , 5 , 6 , 7 , 8 using ultracold fermions in optical lattices could help to answer open questions about the doped Hubbard Hamiltonian 9 , 10 , 11 , 12 , 13 , 14 , and has recently been advanced by quantum gas microscopy 15 , 16 , 17 , 18 , 19 , 20 . Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a two-dimensional square lattice of about 80 sites at a temperature of 0.25 times the tunnelling energy. The antiferromagnetic long-range order manifests through the divergence of the correlation length, which reaches the size of the system, the development of a peak in the spin structure factor and a staggered magnetization that is close to the ground-state value. We hole-dope the system away from half-filling, towards a regime in which complex many-body states are expected, and find that strong magnetic correlations persist at the antiferromagnetic ordering vector up to dopings of about 15 per cent. In this regime, numerical simulations are challenging 21 and so experiments provide a valuable benchmark. Our results demonstrate that microscopy of cold atoms in optical lattices can help us to understand the low-temperature Fermi–Hubbard model.

Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.

Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids 1 – 3 . Promising candidate materials for such phases 4 – 6 can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration 7 – 11 . However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model 12 . Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U / t  ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices 8 , 13 and realizing t – t ′ square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials 14 . The magnetic phases of the geometrically frustrated triangular lattice Hubbard model are directly investigated using ultracold fermionic atoms, indicating a possible transition to ferromagnetism at a filling of 1.2.