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Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices 1 and for the quest towards fault-tolerant quantum computation 2 , 3 . Rydberg arrays have emerged as a prominent platform in this context 4 with impressive system sizes 5 , 6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution 7 , 8 , a form of erasure error conversion 9 – 12 . However, two-qubit entanglement fidelities in Rydberg atom arrays 13 , 14 have lagged behind competitors 15 , 16 and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator 5 , 6 , 17 , 18 . When excising data with erasure errors observed via fast imaging of alkaline-earth atoms 19 – 22 , we achieve a Bell state fidelity of ≥ 0.997 1 − 13 + 10 , which improves to ≥ 0.998 5 − 12 + 7 when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits 7 , 22 – 24 . Erasure conversion and detection are used in a Rydberg quantum simulator to create Bell states with high fidelity, competitive with other state-of-the-art platforms.

We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated with a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a nontrivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology 1 , 2 . Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and read-out strategies 3 – 7 . Neutral-atom optical clocks 8 , which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation 9 – 11 but at present lack the control capabilities for realizing such schemes. Here we show universal quantum operations and ancilla-based read-out for ultranarrow optical transitions of neutral atoms. Our demonstration in a tweezer clock platform 9 , 12 – 16 enables a circuit-based approach to quantum metrology with neutral-atom optical clocks. To this end, we demonstrate two-qubit entangling gates with 99.62(3)% fidelity—averaged over symmetric input states—through Rydberg interactions 15 , 17 , 18 and dynamical connectivity 19 for optical clock qubits, which we combine with local addressing 16 to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state 1 , 4 , a cascade of Greenberger–Horne–Zeilinger states of different sizes, and perform a dual-quadrature 5 Greenberger–Horne–Zeilinger read-out. We also show repeated fast phase detection with non-destructive conditional reset of clock qubits and minimal dead time between repetitions by implementing ancilla-based quantum logic spectroscopy 20 for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell-state preparation 21 – 24 . Our work lays the foundation for hybrid processor–clock devices with neutral atoms and more generally points to a future of practical applications for quantum processors linked with quantum sensors 25 . We demonstrate high-fidelity entangling gates, universal quantum operations, and ancilla-based read-out for ultranarrow optical transitions of neutral atoms in a tweezer clock platform.

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail 1 . Many platforms are being developed towards this goal, in particular based on trapped ions 2 – 4 , superconducting circuits 5 – 7 , neutral atoms 8 – 11 or molecules 12 , 13 . All of these platforms face two key challenges: scaling up the ensemble size while retaining high-quality control over the parameters, and validating the outputs for these large systems. Here we use programmable arrays of individual atoms trapped in optical tweezers, with interactions controlled by laser excitation to Rydberg states 11 , to implement an iconic many-body problem—the antiferromagnetic two-dimensional transverse-field Ising model. We push this platform to a regime with up to 196 atoms manipulated with high fidelity and probe the antiferromagnetic order by dynamically tuning the parameters of the Hamiltonian. We illustrate the versatility of our platform by exploring various system sizes on two qualitatively different geometries—square and triangular arrays. We obtain good agreement with numerical calculations up to a computationally feasible size (approximately 100 particles). This work demonstrates that our platform can be readily used to address open questions in many-body physics. Programmable quantum simulation of two-dimensional antiferromagnets is achieved with up to 196 neutral atoms, and the capability of the platform is demonstrated on square and triangular arrays.

Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states 1 , 2 . However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices 2 – 5 , and it remains unsolved how to estimate the actual entanglement content of experiments 6 . Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement 6 , finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution 2 – 5 . Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems. Fidelity benchmarking of an analogue quantum simulator reaches a high-entanglement regime where exact classical simulation of quantum systems becomes impractical, and enables a new method for evaluating the mixed-state entanglement of quantum devices.

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions 1 – 3 . The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase 4 , 5 . Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry 6 – 9 . A two-dimensional dipolar XY model with a continuous spin-rotational symmetry is realized using a programmable Rydberg quantum simulator, complementing recent studies using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry.

Current optical atomic clocks do not utilize their resources optimally. In particular, an exponential gain in sensitivity could be achieved if multiple atomic ensembles were to be controlled or read out individually, even without entanglement. However, controlling optical transitions locally remains an outstanding challenge for neutral-atom-based clocks and quantum computing platforms. Here we show arbitrary, single-site addressing for an optical transition via sub-wavelength controlled moves of atoms trapped in tweezers. The scheme is highly robust as it relies only on the relative position changes of tweezers and requires no additional addressing beams. Using this technique, we implement single-shot, dual-quadrature readout of Ramsey interferometry using two atomic ensembles simultaneously, and show an enhancement of the usable interrogation time at a given phase-slip error probability. Finally, we program a sequence that performs local dynamical decoupling during Ramsey evolution to evolve three ensembles with variable phase sensitivities, a key ingredient of optimal clock interrogation. Our results demonstrate the potential of fully programmable quantum optical clocks even without entanglement and could be combined with metrologically useful entangled states in the future. Addressing optical transitions at the level of a single site is crucial to unlock the potential of quantum computers and atomic clocks. A scheme based on atom rearrangement now demonstrates such control with demonstrable metrological benefits.

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices and for the quest towards fault-tolerant quantum computation. Rydberg arrays have emerged as a prominent platform in this context with impressive system sizes and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution, a form of erasure error conversion. However, two-qubit entanglement fidelities in Rydberg atom arrays have lagged behind competitors and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator. We implement erasure conversion via fast imaging of alkaline-earth atoms, which leaves atoms in a metastable state unperturbed and yields additional information independent of the final qubit readout. When excising data with observed erasure errors, we achieve a lower-bound for the Bell state generation fidelity of \\({\\geq} 0.9971^{+10}_{-13}\\), which improves to \\({\\geq}0.9985^{+7}_{-12}\\) when correcting for remaining state preparation errors. We further demonstrate erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, where we explicitly differentiate erasure conversion of preparation and Rydberg decay errors. We unveil the otherwise hidden impact of these errors on the simulation outcome by evaluating correlations between erasures and the final readout as well as between erasures themselves. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the \\({\\sim} 0.999\\) regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices.

Neutral atoms and molecules trapped in optical tweezers have become a prevalent resource for quantum simulation, computation, and metrology. However, the maximum achievable system sizes of such arrays are often limited by the stochastic nature of loading into optical tweezers, with a typical loading probability of only 50%. Here we present a species-agnostic method for dark-state enhanced loading (DSEL) based on real-time feedback, long-lived shelving states, and iterated array reloading. We demonstrate this technique with a 95-tweezer array of \\(^{88}\\)Sr atoms, achieving a maximum loading probability of 84.02(4)% and a maximum array size of 91 atoms in one dimension. Our protocol is complementary to, and compatible with, existing schemes for enhanced loading based on direct control over light-assisted collisions, and we predict it can enable close-to-unity filling for arrays of atoms or molecules.