Error correction of a logical qubit encoded in a single atomic ion

Nature Physics (2026) Cite this article Quantum error correction is essential for quantum computers to run useful algorithms, but large-scale fault-tolerant computation remains limited by requirements for operation fidelity and the number of controllable qubits. Traditional schemes encode each logical qubit into multiple physical qubits, increasing resource demands and complexity. Recent theoretical work has proposed a complementary approach that performs error correction at the level of single qubits by using additional internal quantum states, which could reduce overhead. This approach has not yet been demonstrated experimentally, partly due to the difficulty of performing error measurements and subsequent error correction with high fidelity. Here we demonstrate a quantum error-correction protocol in a single atomic ion that reduces errors by up to a factor of 2.2 and extends the qubit lifetime by a factor of up to 1.5 compared with an unencoded qubit. We encode the qubit in spin-cat logical states and implement an autonomous correction scheme that operates without mid-circuit measurements of an ancilla. The approach is applicable to a range of finite-dimensional quantum platforms and could serve either as a component of larger error-correction codes or as a standalone strategy in few-qubit devices such as quantum network nodes.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 data generated in this study are available via Zenodo at https://doi.org/10.5281/zenodo.19323592 (ref. 97). Owing to the size of the full set of raw experimental data, the raw data are available from the corresponding author upon reasonable request.Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2010).Gottesman, D. An introduction to quantum error correction and fault-tolerant quantum computation.

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I.L.C. acknowledges support, in part, from the NSF Center for Ultracold Atoms. This material is based on work supported by the Department of Defense under Air Force contract number FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Department of Defense.John ChiaveriniPresent address: IonQ, Inc., Boston, MA, USAMassachusetts Institute of Technology, Cambridge, MA, USAKyle DeBry, Agustin Valdes Martinez, Xiaoyang Shi, Isaac L. Chuang & John ChiaveriniLincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA, USAKyle DeBry, Agustin Valdes Martinez, Colin D. Bruzewicz, David Reens, Robert McConnell & John ChiaveriniCalifornia Institute of Technology, Pasadena, CA, USANadine MeisterSearch 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 ScholarK.D., I.L.C. and J.C. conceived of the work. K.D., N.M. and A.V.M. performed the experiments. D.R. and R.M. assisted with and provided advice on performing the experiments. All work was supervised by C.D.B., J.C. and I.L.C. All authors discussed the results and contributed to the manuscript.Correspondence to Kyle DeBry.The authors declare no competing interests.Nature Physics thanks Wesley Campbell and the other, anonymous, reviewer(s) 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 logical \(\left|{\mathbb{1}}\right\rangle\) codeword in the \({\widehat{J}}_{x}\) and \({\widehat{J}}_{z}\) bases. a, Spin-cat \(\left|{\mathbb{1}}\right\rangle\) codeword in eigenbasis of \({\widehat{J}}_{x}\), showing the action of error operators \({\widehat{{\mathcal{E}}}}_{1}={\widehat{J}}_{z}\) and \({\widehat{{\mathcal{E}}}}_{2}={\widehat{J}}_{z}^{2}\) in this basis. Support of the \(\left|{\mathbb{1}}\right\rangle\) codeword is highlighted in orange. b, The \(\left|{\mathbb{1}}\right\rangle\) codeword in the \({\widehat{J}}_{z}\) basis, with the coefficients of the \(\left|{m}_{J}\right\rangle\) basis states written above each state. Support of \(\left|{\mathbb{1}}\right\rangle\) in this basis is highlighted in orange.A simplified view of the experimental pulse sequence, highlighting which laser or radio-frequency source is used to perform each operation, with time proceeding from left to right. The approximate duration of each operation is listed along the top of the figure. Sideband cooling, S1/2 to D5/2 π-pulses, the \({\widehat{U}}_{{\rm{c}}}\) error-correction operation, and tomography operations contain multiple individual pulses, which are described in detail in the text. ‘Quadrupole correction’ and ‘Motion selection’ operations are also described in the text below.Energy level diagrams demonstrating the action of pulses in \({\widehat{U}}_{{\rm{c}}}\). Energy level spacing is not drawn to scale. a, Error correction operation \({\widehat{U}}_{{\rm{c}}}\) acting on an error state \(\left|{{\mathcal{E}}}_{1}\right\rangle =\alpha \left|-\frac{3}{2}\right\rangle +\beta \left|+\frac{3}{2}\right\rangle\) (following the application of \({\widehat{U}}_{{\rm{enc}}}^{\dagger }\), see Fig. 1), with the effect of moving the population from \(\left|\pm \frac{3}{2}\right\rangle {\left|0\right\rangle }_{{\rm{M}}}\) to \(\left|\pm \frac{5}{2}\right\rangle {\left|1\right\rangle }_{{\rm{M}}}\) via blue sideband (motion-adding) pulses. b,\({\widehat{U}}_{{\rm{c}}}\) acting on an error-free state \(\left|\psi \right\rangle =\alpha \left|-\frac{5}{2}\right\rangle +\beta \left|+\frac{5}{2}\right\rangle\), with no effect on the state. Because the ion starts in the \({\left|0\right\rangle }_{{\rm{M}}}\) motional state, there is no \({\left|-1\right\rangle }_{{\rm{M}}}\) motional state for the sideband pulse to couple \(\left|\psi \right\rangle\) to, so there is no change to the ion’s state.Surface electrode trap and laser beam geometry, including labels of the five beams, and RF antennas, used in the experiment. Ion not drawn to scale. a, Close-up of trapping region with laser beams labeled. b, Rendering of 5 K stage of the cryostat (windows not shown) showing the trap (center) held in a ceramic pin grid array and the locations of the RF antennas that apply all RF pulses during the experiment. The trap (light gray square) is 1 cm on a side.Each point is derived from 1,000 individual trials. Mean values are plotted along with error bars and shaded fit uncertainty regions each representing 68% confidence intervals.A linear fit to the data gives a slope of 8.3(2) s−1. Each point is the mean of 108,000 individual trials, and error bars/shaded regions represent 68% confidence intervals.Upper left: encoding the logical qubits but not performing the error correction operations. Upper right: performing error correction, without removing flagged erasure errors due to motional heating. Lower left: ground state physical qubit. Lower right: performing error correction, with erasure errors removed. The number of individual trials for each data point are 108,000 for the error corrected logical qubit (with and without erasure conversion), 10,800 for the uncorrected logical qubit, and 2,000 for the physical qubit. Mean values are plotted along with error bars and shaded fit uncertainty regions each representing 68% confidence intervals.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 permissionsDeBry, K., Meister, N., Valdes Martinez, A. et al. Error correction of a logical qubit encoded in a single atomic ion. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03315-2Download citationReceived: 17 April 2025Accepted: 24 April 2026Published: 13 July 2026Version of record: 13 July 2026DOI: https://doi.org/10.1038/s41567-026-03315-2Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. 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