Abstract
Realizing universal fault-tolerant quantum computation is a key goal in quantum information science1,2,3,4. By encoding quantum information into logical qubits using quantum error correcting codes, physical errors can be detected and corrected, enabling a substantial reduction in logical error rates5,6,7,8,9,10,11. However, the set of logical operations that can be easily implemented on these encoded qubits is often constrained1,12, necessitating the use of special resource states known as ‘magic states’13 to implement universal, classically hard circuits14. A key method to prepare high-fidelity magic states is to perform ‘distillation’, creating them from multiple lower-fidelity inputs13,15. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach uses a dynamically reconfigurable architecture8,16 to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d = 3 and d = 5 colour codes, observing improvements in the logical fidelity of the output magic states compared with the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation and represent an important step towards large-scale logical quantum processors.
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Data availability
Peer reviewer reports are available. All data supporting the findings of this study are available from Zenodo at https://doi.org/10.1038/s41586-025-09367-3 (ref. 75).
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Acknowledgements
We acknowledge the discussions with L. Jiang, M. Kang, G. Masella, C. Pattison, A. Piñeiro Orioli, Q. Xu and M. Yuan and technical contributions from I. Paus, C. Skinker and Q. Yu. This work, including the design, assembly and operation of the Gemini-class neutral-atom quantum computer, was supported by QuEra Computing. Pathfinding work at Harvard and MIT was supported by IARPA and the Army Research Office, under the Entangled Logical Qubits program (cooperative agreement no. W911NF-23-2-0219), the DARPA ONISQ program (W911NF2010021), the DARPA MeasQuIT program (HR0011-24-9-0359), the Center for Ultracold Atoms (an NSF Physics Frontiers Center, PHY-1734011), the National Science Foundation (grant no. PHY-2012023 and grant no. CCF-2313084), the Army Research Office MURI (grant no. W911NF-20-1-0082) and QuEra Computing. Z.H. acknowledges support from the NSF Graduate Research Fellowship Program (grant no. 2141064). D.B. acknowledges support from the NSF Graduate Research Fellowship Program (grant no. DGE1745303) and The Fannie and John Hertz Foundation. S.J.E. acknowledges support from the National Defense Science and Engineering Graduate (NDSEG) fellowship. T. Manovitz acknowledges support from the Harvard Quantum Initiative Postdoctoral Fellowship in Science and Engineering. M.C. acknowledges support from the Department of Energy Computational Science Graduate Fellowship (award no. DE-SC0020347).
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The QuEra Computing staff designed, built and ran the experiment and performed data analysis. P.S.R., J.M.R., P.N.J., Z.H., C.D., C.Z., K.-H.W., J.C., K.B., M. Kwon, T. Karolyshyn, P.W., M.C., S.J.E., A.A.G., M. Kalinowski, S.H.L., T. Manovitz, J.A.-G., J.I.B., L.B., B.B., A.B., A.C., R.J.D., F.F., C.F., P.F., D.H., M. Hamdan, J.H., N.H., M.-G.H., F.H., N.J., D.K., M. Kornjač, F.L., J. Long, J. Lopatin, P.L.S.L., X.-Z.L., T. Macrì, O.M., L.A.M.-M., X.M., S.O., E.O., D.P., Z.Q., V.S., A.S., M.S., N.S., H.T., N.W., Y.W., D.W.-L., T.W., J.W., A.Z., L.Z., M.G., A.K., N.G., V.V., T. Kitagawa, S.-T.W., D.B., M.D.L., A.L., H.Z. and S.H.C. discussed the results, revised and contributed to the writing of this paper.
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M.G., V.V. and M.D.L. are co-founders and shareholders of QuEra Computing. Authors affiliated with QuEra Computing are employees or interns at QuEra Computing at the time of their contributions.
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Extended data figures and tables
Extended Data Fig. 1 Experimental layout of magic state distillation factory.
a, We arrange 7 to 17 87Rb atoms, each corresponding to a physical qubit, into a row. This horizontal register represents a logical qubit, tiled into 5 rows for a total of five logical qubits (LQ1 to LQ5). b, Encoding. Once the register of physical qubits is prepared, we coherently rearrange atoms to perform two-qubit entangling gates using the Rydberg blockade mechanism. We break up the circuit into “layers” each containing one set of local rotations, transport, and CZ gates. c, Coherent movement of logical qubits to perform transversal CZ gates. In the case of 5-to-1 distillation, this is achieved in three layers. The circuit as drawn here corresponds 1 to 1 to the atom layout, whereas in Fig. 3 logical qubits LQ1 and LQ2 are swapped for clarity. d, Global measurement of qubits after circuit execution.
Extended Data Fig. 2 Experimental layout of d = 5 encoding.
The arbitrary-state encoding circuit for the d = 5 color code (left) is comprised of five entangling gate layers, illustrated by averaged images of the corresponding atom configurations (right), and local gates between the layers. We execute encoding with 5x parallelism, one instance per row (LQ1 to LQ5). The horizontal AOD trap array is tiled vertically by the second AOD. For each layer, atoms start in SLM sites, we apply local rotations, pick up and move atoms to their gate location, execute parallel CZ gates, echo (omitted for clarity), and finally move back to SLM sites.
Extended Data Fig. 3 Encoded magic state fidelity and stabilizers.
a, Spatial dependence of distance-3 magic state encoding fidelity, for the experimental run with no added coherent error. Logical qubits numbered 1-5 and 6-10 are the input qubits to two parallel distillation circuits. We observe some spatial dependence on both the fidelity and perfect stabilizer rate, which we attribute to local single-qubit gate inhomogeneity and two-qubit gate inhomogeneity. b, Time dependence of distance-3 color code stabilizers, for the experimental run with no added coherent error. Time traces are averaged with window size of 100. c,d, Same as a and b for distance-5.
Extended Data Fig. 4 Additional decoding results.
a, Simulated injected and distilled magic state fidelities as a function of global rescaling of physical error rates, when no stabilizer postselection is applied. Relative to our error model for decoding, the physical error rates have been further increased by 1.25 × to match the experimental injected and distilled fidelities. b, Simulation and experimental data in table format for d = 3, sorted into bins corresponding to 3 × 5 = 15 stabilizers and 5 logical observables, for a total of 220 bins. We see good agreement between simulation and experiment. c, Sliding-scale postselection of experimental distillation fidelity with added input errors. Fidelity of the output magic state (blue line) as a function of the total accepted fraction. The accepted fraction range decreases with added errors due to the factory acceptance rate decreasing. Horizontal line segments indicate the error corrected fidelity of the factory input states (green). Shaded regions indicate 68% confidence intervals.
Extended Data Fig. 5 Comparison of different fidelity estimation methods for d = 5 distillation.
For low accepted fractions, the small number of samples causes the maximum likelihood estimate (red, allowed to exceed 1 here) and Bayesian estimates (blue) to differ noticeably, since the latter will be influenced by the prior. In our figures in the main text, we therefore focus on the region in which the two methods give consistent estimates. Horizontal line indicates the error corrected fidelity of the factory input states (green). Shaded regions indicate 68% confidence intervals.
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Sales Rodriguez, P., Robinson, J.M., Jepsen, P.N. et al. Experimental demonstration of logical magic state distillation. Nature 645, 620–625 (2025). https://doi.org/10.1038/s41586-025-09367-3
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DOI: https://doi.org/10.1038/s41586-025-09367-3
