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Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology1,2. 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 strategies3,4,5,6,7. Neutral-atom optical clocks8, which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation9,10,11 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 platform9,12,13,14,15,16 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 interactions15,17,18 and dynamical connectivity19 for optical clock qubits, which we combine with local addressing16 to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state1,4, a cascade of Greenberger–Horne–Zeilinger states of different sizes, and perform a dual-quadrature5 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 spectroscopy20 for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell-state preparation21,22,23,24. 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 sensors25. 

Abstract 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 experiments⁶. 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 entanglement⁶, 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. 

Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2,3,4,5, and it remains unsolved how to estimate the actual entanglement content of experiments6. 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 entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2,3,4,5. 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. 

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. 

Abstract 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. 

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices1 and for the quest towards fault-tolerant quantum computation2,3. Rydberg arrays have emerged as a prominent platform in this context4 with impressive system sizes5,6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution7,8, a form of erasure error conversion9,10,11,12. However, two-qubit entanglement fidelities in Rydberg atom arrays13,14 have lagged behind competitors15,16 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 simulator5,6,17,18. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms19,20,21,22, we achieve a Bell state fidelity of ≥0.9971−13+10, which improves to ≥0.9985−12+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 qubits7,22,23,24. 

Abstract Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices¹and for the quest towards fault-tolerant quantum computation^2,3. Rydberg arrays have emerged as a prominent platform in this context⁴with impressive system sizes^5,6and 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^13,14have lagged behind competitors^15,16and 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$$\ge 0.997{1}_{-13}^{+10}$$ $\ge 0.9971_{-13}^{+10}$, which improves to$$\ge 0.998{5}_{-12}^{+7}$$ $\ge 0.9985_{-12}^{+7}$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.