Logical qubits with erasure conversion using metastable neutral atoms

Nature Physics (2026) Cite this article Implementing large-scale quantum algorithms with practical advantage will require fault tolerance achieved through quantum error correction, but the associated overhead is prohibitive. This overhead can be reduced by engineering physical qubits with fewer errors, and by shaping the residual errors to be more easily correctable. In this work, we demonstrate quantum error-correcting codes and logical qubit circuits in a metastable ytterbium-171 nuclear spin qubit with a noise bias towards erasure errors. These errors can be located separately from any syndrome information diagnosing the error, and we demonstrate adaptive circuit execution based on erasure information. We show that dephasing errors on the qubit during coherent transport can be strongly suppressed, and implement entangling gates that maintain a high fidelity in the presence of gate-beam inhomogeneity or pointing errors. Furthermore, we demonstrate logical qubit encoding in the [[4, 2, 2]] code, with error correction during decoding based on mid-circuit erasure measurements despite the fact that the code is too small to correct any Pauli errors. Finally, we demonstrate logical qubit teleportation between multiple code blocks with conditionally selected ancillas based on mid-circuit erasure checks, a key part of leakage-robust error correction schemes using neutral atoms.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe source data underlying the figures in this study are available via Zenodo at https://doi.org/10.5281/zenodo.19491381 (ref. 80).Ryan-Anderson, C. et al. Realization of real-time fault-tolerant quantum error correction. Phys. Rev. X 11, 041058 (2021).

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Ludlow, K. Beloy and A. Kaufman for helpful conversations. This work was supported by the Army Research Office (W911NF-18-10215 and W911NF-24-10358), DARPA MeasQuIT (HR00112490363) and ONISQ (W911NF-20-10021), the Office of Naval Research (N00014-23-1-2621), and the National Science Foundation through the CAREER program (PHY-2047620) and the Center for Robust Quantum Simulation (OMA-2120757).Pai PengPresent address: School of Physics, Peking University, Beijing, ChinaShuo MaPresent address: Department of Physics, University of California, Berkeley, CA, USAShilin HuangPresent address: Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, ChinaThese authors contributed equally: Bichen Zhang, Genyue Liu.Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USABichen Zhang, Genyue Liu, Guillaume Bornet, Sebastian P. Horvath, Pai Peng & Jeff D. ThompsonDepartment of Physics, Princeton University, Princeton, NJ, USAShuo MaDepartment of Applied Physics, Yale University, New Haven, CT, USAShilin Huang & Shruti PuriSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarB.Z., G.L., G.B., S.P.H., P.P. and S.M. built the experimental setup, performed the measurements and analysed the data. S.H. and S.P. contributed to the circuit constructions, data analysis and stabilizer circuit simulations. All authors discussed the results. B.Z., G.L., G.B. and J.D.T. wrote the manuscript with input from all authors. The work was supervised by S.P. and J.D.T.Correspondence to Jeff D. Thompson.S.P.H. and J.D.T. are co-founders and shareholders of Logiqal, Inc. J.D.T., B.Z., G.L., G.B., P.P., S.P.H. and S.M. have filed a provisional patent application (US 63/817,558) directly arising from the results detailed in this manuscript. The remaining authors declare no competing interests.Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.The AOD waveforms are generated on a Xilinx RFSoC ZCU216 evaluation board. The trajectories are expressed as piecewise polynomial coefficients in frequency and amplitude. The coefficients are transmitted to the FPGA over ethernet, and the execution of each segment is triggered by a TTL line. Two output channels drive orthogonally oriented AODs, each supporting up to 32 DDS tones.(a) Due to the finite shear mode acoustic speed in the AOD crystal and a large optical aperture, a non-negligible lensing effect occurs when chirping the AOD driving frequency, causing defocus and astigmatism. (b) Experimentally measured survival probability (circles) after a one-way trip between the storage and gate zones while changing moving time T, with the zero-jerk trajectory (blue) and minimum-jerk trajectory (green). Numerical simulations with (solid line) and without (dashed line) considering the lensing effect are also shown. The simulation matches with experiment only if the lensing effect is included. (c) Acceleration and jerk profiles of the zero-jerk trajectory (blue) and minimum-jerk trajectory (green).(a) Schematic and trajectory of a one-way transport sequence: two hand-off phases between the static and moving optical tweezers (grey shading) bracket a moving phase (white). (b) Measured metastable state scattering rate versus trap depth, together with a quadratic fit29. (c) Time trace of the total trap power experienced by the atom during the full trajectory (red); using the model in (b) we infer the cumulative probability of photo-ionization (grey dashed) and the total number of scattered photons (grey solid).(a) Schematic of the suboptimal configuration for the SLM and AOD traps, with the two traps orthogonally polarized. The atom sees a summed trap potential of the two traps. When two traps are displaced in the y direction, the atom is pulled away from the center of the SLM trap, experiencing an unsuppressed vector light shift. (b) Larmor frequency shift with various displacement d shown in (a). The purple data is experimentally measured via Ramsey experiments, while the orange curve is the theoretical prediction with a single fitting parameter ηvls. Based on this measurement, we estimate the ηvls = 3 × 10−4 at a wavelength of 487 nm. (c) The Ramsey fringes after a round-trip between the storage and gate zones under d = − 240 nm (red), d = 0 (gray) and d = 240 nm (blue). (d) Measurement of the Ramsey fringes with various number of one-way trips that the atoms undergo during the Ramsey experiment (same dataset as the blue curve in Fig. 1e). (e) Fitted contrast A/C as a function of the number of one-way-trip. A linear fit gives a spin flip rate of 1(6) × 10−4 per one-way trip.(a) Measured lifetime τ of the 3Po qubit in an optical trap under different trap modulation frequencies fm (blue dots). Green dots show the corresponding number of modulation cycles n = τ fm, which exceeds 106 for experimentally realistic fm values. (b) Schematics of synchronizing trap modulation with entangling gates and optical pumping. To switch on (off) trap modulation, we adiabatically ramp down (up) the duty cycle while keeping the averaged trap power unchanged.(a) In our experiment, the Rydberg laser is linearly polarized perpendicular to the quantization axis, resulting in equal σ+ and σ− components. The laser is tuned to the \(| 1\rangle\) to \(| r\rangle =| \nu =54.3,F=1/2,{{\rm{m}}}_{F}=-1/2\rangle\) resonance, but also couples \(| 0\rangle\) to \(| {r}^{{\prime} }\rangle =| \nu =54.3,F=1/2,{{\rm{m}}}_{F}=1/2\rangle\) with a detuning Δr from the Zeeman splitting of the Rydberg state. (b) For the local single-qubit phase gate, we tune the Rydberg beam to the midpoint between the two Zeeman-split Rydberg transitions, so that the σ+ (σ−) component off-resonantly couples \(| 0\rangle \to | {r}^{{\prime} }\rangle (| 1\rangle \to | r\rangle )\) with equal detuning magnitude Δr/2 ≈ 8 MHz. The off-resonant coupling produces a differential AC Stark shift that implements RZ rotations. (c) Simulated gate infidelity (including spontaneous decay) versus relative laser-intensity error for the AR and TO gates, using Rydberg lifetime τRyd = 88μs and the two-photon differential light-shift coefficient χ2−photon ≈ 0.945 MHz/MHz2 from ref. 52. Curves are shown for nominal Rabi frequencies Ω/2π = 2, 4, 8, 12 and 16 MHz (light to dark). The AR gate is driven via a single-photon Rydberg transition and therefore has negligible intensity-dependent light shift. The TO gate is simulated for both single-photon and two-photon Rydberg implementations; the two-photon case includes the additional differential light shift on top of the spontaneous-decay contribution. (d) Simulated gate infidelity (including spontaneous decay), averaged over the targeted gate-zone, is plotted against the waist of an elliptical laser beam along the gate-zone direction. The curves correspond to targeted gate-zone sizes of 30 μm, 50 μm, and 70 μm, shown in colors ranging from light to dark, respectively. The total laser power is held constant at 3.75 W, and the waist perpendicular to the gate-zone direction is fixed at 12 μm (1/e2 radius). Solid curves represent AR gates, and dashed curves represent TO gates without the light shift. The star and circle markers denote the respective optimal fidelities achieved for each gate type and target zone size. (e) Randomized circuit characterization of the CZ gate as a function of circuit depth d. The protocol follows that introduced in ref. 40.(a) Encoding circuit for preparing logical qubit states \({| 00\rangle }_{{\rm{L}}}\) with the [[4,2,2]] code. A flag qubit is used to herald certain Pauli errors and leakage errors during the preparation circuit. (b) \({| ++\rangle }_{{\rm{L}}}\) can be prepared by adding extra Ry(π/2) gates on all data qubits after preparing \({| 00\rangle }_{{\rm{L}}}\). (c) Circuit for the ‘encode-hold-decode’ experiment. Logical qubits are measured directly in the Z basis, or in the X basis by inserting an additional π/2-pulse. During the wait, we implement a Hahn echo sequence to extend the coherence time. Before the final measurement, we apply an extra π rotation on the first and second physical qubits to prevent the misidentification mentioned in the text. (d) The native entangling gates are a CZ gate up to a single qubit phase rotation θ ≈ − 3.4 rad. Moreover, throughout this figure, we use purple (grey) shade to represent operations applied in the gate (storage) zones. (e) Teleportation circuit on distinct logical blocks encoded by the [[4,2,2]] code.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsZhang, B., Liu, G., Bornet, G. et al. Logical qubits with erasure conversion using metastable neutral atoms. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03309-0Download citationReceived: 05 August 2025Accepted: 20 April 2026Published: 12 June 2026Version of record: 12 June 2026DOI: https://doi.org/10.1038/s41567-026-03309-0Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative