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1. Erasure conversion in a high-fidelity Rydberg quantum simulator

   Scholl, Pascal; Shaw, Adam; Tsai, Richard; Finkelstein, Ran; Choi, Joonhee; Endres, Manuel (October 2023, Nature)

   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. 

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2. Erasure conversion in a high-fidelity Rydberg quantum simulator

   https://doi.org/10.1038/s41586-023-06516-4  

   Scholl, Pascal; Shaw, Adam L.; Tsai, Richard Bing-Shiun; Finkelstein, Ran; Choi, Joonhee; Endres, Manuel (October 2023, Nature)

   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. 

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3. Theory of long range interactions for Rydberg states attached to hyperfine split cores

   Robicheaux, F.; Booth, D.; Saffman, M. (January 2018, 49th annual meeting of the APS division of atomic, molecular and optical physics)

   Theory for one and two atom interactions is developed for the case when the atoms have a Rydberg electron attached to a hyper- fi ne split core state, a situation relevant for some rare earth and some alkaline earth atoms proposed for experiments on Rydberg-Rydberg in- teractions. For the rare earth atoms, the core electrons can have a very substantial total angular momentum, J, and a non-zero nuclear spin, I. For alkaline earth atoms there is a single, s, core electron whose spin can couple to a non-zero nuclear spin for odd isotopes. The hyper fine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the un- perturbed Rydberg series of the alkali atoms, series perturbations and near degeneracies from the different parity states could lead to quali- tatively different behavior for single atom Rydberg properties (polariz- ability, Zeeman mixing and splitting, etc) as well as Rydberg-Rydberg interactions (C5 and C6 matrices). 

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4. High-fidelity gates and mid-circuit erasure conversion in an atomic qubit

   https://doi.org/10.1038/s41586-023-06438-1  

   Ma, Shuo; Liu, Genyue; Peng, Pai; Zhang, Bichen; Jandura, Sven; Claes, Jahan; Burgers, Alex P.; Pupillo, Guido; Puri, Shruti; Thompson, Jeff D. (October 2023, Nature)

   The development of scalable, high-fidelity qubits is a key challenge in quantum information science. Neutral atom qubits have progressed rapidly in recent years, demonstrating programmable processors1,2 and quantum simulators with scaling to hundreds of atoms3,4. Exploring new atomic species, such as alkaline earth atoms5,6,7, or combining multiple species8 can provide new paths to improving coherence, control and scalability. For example, for eventual application in quantum error correction, it is advantageous to realize qubits with structured error models, such as biased Pauli errors9 or conversion of errors into detectable erasures10. Here we demonstrate a new neutral atom qubit using the nuclear spin of a long-lived metastable state in 171Yb. The long coherence time and fast excitation to the Rydberg state allow one- and two-qubit gates with fidelities of 0.9990(1) and 0.980(1), respectively. Importantly, a large fraction of all gate errors result in decays out of the qubit subspace to the ground state. By performing fast, mid-circuit detection of these errors, we convert them into erasure errors; during detection, the induced error probability on qubits remaining in the computational space is less than 10−5. This work establishes metastable 171Yb as a promising platform for realizing fault-tolerant quantum computing. 

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5. Spectroscopy and Modeling of ${}^{171}\mathrm{Yb}$ Rydberg States for High-Fidelity Two-Qubit Gates

   https://doi.org/10.1103/PhysRevX.15.011009  

   Peper, Michael; Li, Yiyi; Knapp, Daniel Y; Bileska, Mila; Ma, Shuo; Liu, Genyue; Peng, Pai; Zhang, Bichen; Horvath, Sebastian P; Burgers, Alex P; et al (January 2025, Physical Review X)

   Highly excited Rydberg states and their interactions play an important role in quantum computing and simulation. These properties can be predicted accurately for alkali atoms with simple Rydberg level structures. However, an extension of these methods to more complex atoms such as alkaline-earth atoms has not been demonstrated or experimentally validated. Here, we present multichannel quantum defect models for highly excited ${}^{174}\mathrm{Yb}$and ${}^{171}\mathrm{Yb}$Rydberg states with $L\le 2$. The models are developed using a combination of existing literature data and new, high-precision laser and microwave spectroscopy in an atomic beam, and validated by detailed comparison with experimentally measured Stark shifts and magnetic moments. We then use these models to compute interaction potentials between two Yb atoms, and find excellent agreement with direct measurements in an optical tweezer array. From the computed interaction potential, we identify an anomalous Förster resonance that likely degraded the fidelity of previous entangling gates in ${}^{171}\mathrm{Yb}$using $F=3/2$Rydberg states. We then identify a more suitable $F=1/2$state, and achieve a state-of-the-art controlled- gate fidelity of $\mathcal{F}=0.994\left(1\right)$, with the remaining error fully explained by known sources. This work establishes a solid foundation for the continued development of quantum computing, simulation, and entanglement-enhanced metrology with Yb neutral atom arrays. Published by the American Physical Society2025 

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