{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T14:55:04Z","timestamp":1786114504845,"version":"3.56.0"},"reference-count":68,"publisher":"Springer Science and Business Media LLC","issue":"8050","license":[{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nature"],"published-print":{"date-parts":[[2025,2,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Distributed quantum computing (DQC) combines the computing power of multiple networked quantum processing modules, ideally enabling the execution of large quantum circuits without compromising performance or qubit connectivity<jats:sup>1,2<\/jats:sup>. Photonic networks are well suited as a versatile and reconfigurable interconnect layer for DQC; remote entanglement shared between matter qubits across the network enables all-to-all logical connectivity through quantum gate teleportation (QGT)<jats:sup>3,4<\/jats:sup>. For a scalable DQC architecture, the QGT implementation must be deterministic and repeatable; until now, no demonstration has satisfied these requirements. Here we experimentally demonstrate the distribution of quantum computations between two photonically interconnected trapped-ion modules. The modules, separated by about\u00a0two\u2009metres, each contain dedicated network and circuit qubits. By using heralded remote entanglement between the network qubits, we deterministically teleport a controlled-Z (CZ) gate between two circuit qubits in separate modules, achieving 86% fidelity. We then execute Grover\u2019s search algorithm<jats:sup>5<\/jats:sup>\u2014to our knowledge, the first implementation of a distributed quantum algorithm comprising several non-local two-qubit gates\u2014and measure a 71% success rate. Furthermore, we implement distributed iSWAP and SWAP circuits, compiled with two and three instances of QGT, respectively, demonstrating the ability to distribute arbitrary two-qubit operations<jats:sup>6<\/jats:sup>. As photons can be interfaced with a variety of systems, the versatile DQC architecture demonstrated here provides a viable pathway towards large-scale quantum computing for a range of physical platforms.<\/jats:p>","DOI":"10.1038\/s41586-024-08404-x","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T16:04:46Z","timestamp":1738771486000},"page":"383-388","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":174,"title":["Distributed quantum computing across an optical network link"],"prefix":"10.1038","volume":"638","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8455-0859","authenticated-orcid":false,"given":"D.","family":"Main","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2241-885X","authenticated-orcid":false,"given":"P.","family":"Drmota","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0219-274X","authenticated-orcid":false,"given":"D. P.","family":"Nadlinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5999-6314","authenticated-orcid":false,"given":"E. M.","family":"Ainley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6200-9746","authenticated-orcid":false,"given":"A.","family":"Agrawal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4267-6255","authenticated-orcid":false,"given":"B. C.","family":"Nichol","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8462-6072","authenticated-orcid":false,"given":"R.","family":"Srinivas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1128-2571","authenticated-orcid":false,"given":"G.","family":"Araneda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D. M.","family":"Lucas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"8404_CR1","unstructured":"Grover, L. K. Quantum telecomputation. Preprint at https:\/\/arxiv.org\/abs\/quant-ph\/9704012 (1997)."},{"key":"8404_CR2","doi-asserted-by":"crossref","first-page":"4249","DOI":"10.1103\/PhysRevA.59.4249","volume":"59","author":"JI Cirac","year":"1999","unstructured":"Cirac, J. I., Ekert, A. K., Huelga, S. F. & Macchiavello, C. Distributed quantum computation over noisy channels. Phys. Rev. A 59, 4249 (1999).","journal-title":"Phys. Rev. A"},{"key":"8404_CR3","doi-asserted-by":"crossref","first-page":"062323","DOI":"10.1103\/PhysRevA.76.062323","volume":"76","author":"L Jiang","year":"2007","unstructured":"Jiang, L., Taylor, J. M., S\u00f8rensen, A. S. & Lukin, M. D. Distributed quantum computation based on small quantum registers. Phys. Rev. A 76, 062323 (2007).","journal-title":"Phys. Rev. A"},{"key":"8404_CR4","doi-asserted-by":"crossref","first-page":"022317","DOI":"10.1103\/PhysRevA.89.022317","volume":"89","author":"C Monroe","year":"2014","unstructured":"Monroe, C. et al. Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014).","journal-title":"Phys. Rev. A"},{"key":"8404_CR5","doi-asserted-by":"crossref","unstructured":"Grover, L. K. A fast quantum mechanical algorithm for database search. In Proc. Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC \u201996 212\u2013219 (Association for Computing Machinery, 1996).","DOI":"10.1145\/237814.237866"},{"key":"8404_CR6","doi-asserted-by":"crossref","first-page":"010301","DOI":"10.1103\/PhysRevA.69.010301","volume":"69","author":"G Vidal","year":"2004","unstructured":"Vidal, G. & Dawson, C. M. Universal quantum circuit for two-qubit transformations with three controlled-NOT gates. Phys. Rev. A 69, 010301 (2004).","journal-title":"Phys. Rev. A"},{"key":"8404_CR7","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"PW Shor","year":"1997","unstructured":"Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484\u20131509 (1997).","journal-title":"SIAM J. Comput."},{"key":"8404_CR8","doi-asserted-by":"crossref","first-page":"6:1","DOI":"10.1147\/JRD.2018.2888987","volume":"62","author":"Y Cao","year":"2018","unstructured":"Cao, Y., Romero, J. & Aspuru-Guzik, A. Potential of quantum computing for drug discovery. IBM J. Res. Dev. 62, 6:1\u20136:20 (2018).","journal-title":"IBM J. Res. Dev."},{"key":"8404_CR9","doi-asserted-by":"crossref","first-page":"021314","DOI":"10.1063\/1.5088164","volume":"6","author":"CD Bruzewicz","year":"2019","unstructured":"Bruzewicz, C. D., Chiaverini, J., McConnell, R. & Sage, J. M. Trapped-ion quantum computing: progress and challenges. Appl. Phys. Rev. 6, 021314 (2019).","journal-title":"Appl. Phys. Rev."},{"key":"8404_CR10","doi-asserted-by":"crossref","first-page":"160902","DOI":"10.1063\/5.0082975","volume":"132","author":"S Bravyi","year":"2022","unstructured":"Bravyi, S., Dial, O., Gambetta, J. M., Gil, D. & Nazario, Z. The future of quantum computing with superconducting qubits. J. Appl. Phys. 132, 160902 (2022).","journal-title":"J. Appl. Phys."},{"key":"8404_CR11","unstructured":"Gill, S. S. et al. Quantum computing: vision and challenges. Preprint at https:\/\/arxiv.org\/abs\/2403.02240 (2024)."},{"key":"8404_CR12","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","volume":"70","author":"CH Bennett","year":"1993","unstructured":"Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein\u2013Podolsky\u2013Rosen channels. Phys. Rev. Lett. 70, 1895 (1993).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR13","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1038\/46503","volume":"402","author":"D Gottesman","year":"1999","unstructured":"Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390\u2013393 (1999).","journal-title":"Nature"},{"key":"8404_CR14","doi-asserted-by":"crossref","first-page":"052317","DOI":"10.1103\/PhysRevA.62.052317","volume":"62","author":"J Eisert","year":"2000","unstructured":"Eisert, J., Jacobs, K., Papadopoulos, P. & Plenio, M. B. Optimal local implementation of nonlocal quantum gates. Phys. Rev. A 62, 052317 (2000).","journal-title":"Phys. Rev. A"},{"key":"8404_CR15","doi-asserted-by":"crossref","first-page":"032302","DOI":"10.1103\/PhysRevA.64.032302","volume":"64","author":"D Collins","year":"2001","unstructured":"Collins, D., Linden, N. & Popescu, S. Nonlocal content of quantum operations. Phys. Rev. A 64, 032302 (2001).","journal-title":"Phys. Rev. A"},{"key":"8404_CR16","doi-asserted-by":"crossref","first-page":"5932","DOI":"10.1103\/PhysRevLett.81.5932","volume":"81","author":"H-J Briegel","year":"1998","unstructured":"Briegel, H.-J., D\u00fcr, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932 (1998).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR17","doi-asserted-by":"crossref","first-page":"067901","DOI":"10.1103\/PhysRevLett.90.067901","volume":"90","author":"W D\u00fcr","year":"2003","unstructured":"D\u00fcr, W. & Briegel, H.-J. Entanglement purification for quantum computation. Phys. Rev. Lett. 90, 067901 (2003).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR18","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1038\/nature00784","volume":"417","author":"D Kielpinski","year":"2002","unstructured":"Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709\u2013711 (2002).","journal-title":"Nature"},{"key":"8404_CR19","doi-asserted-by":"crossref","DOI":"10.1038\/s41467-022-35285-3","volume":"14","author":"M Akhtar","year":"2023","unstructured":"Akhtar, M. et al. A high-fidelity quantum matter-link between ion-trap microchip modules. Nat. Commun. 14, 531 (2023).","journal-title":"Nat. Commun."},{"key":"8404_CR20","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1126\/science.aaw9415","volume":"364","author":"Y Wan","year":"2019","unstructured":"Wan, Y. et al. Quantum gate teleportation between separated qubits in a trapped-ion processor. Science 364, 875\u2013878 (2019).","journal-title":"Science"},{"key":"8404_CR21","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1038\/s41586-021-03318-4","volume":"592","author":"JM Pino","year":"2021","unstructured":"Pino, J. M. et al. Demonstration of the trapped-ion quantum CCD computer architecture. Nature 592, 209\u2013213 (2021).","journal-title":"Nature"},{"key":"8404_CR22","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1038\/s41586-018-0200-5","volume":"558","author":"PC Humphreys","year":"2018","unstructured":"Humphreys, P. C. et al. Deterministic delivery of remote entanglement on a quantum network. Nature 558, 268\u2013273 (2018).","journal-title":"Nature"},{"key":"8404_CR23","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1038\/s41586-024-07252-z","volume":"629","author":"CM Knaut","year":"2024","unstructured":"Knaut, C. M. et al. Entanglement of nanophotonic quantum memory nodes in a telecom network. Nature 629, 573\u2013578 (2024).","journal-title":"Nature"},{"key":"8404_CR24","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1038\/s41586-023-05885-0","volume":"617","author":"S Storz","year":"2023","unstructured":"Storz, S. et al. Loophole-free Bell inequality violation with superconducting circuits. Nature 617, 265\u2013270 (2023).","journal-title":"Nature"},{"key":"8404_CR25","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nature11023","volume":"484","author":"S Ritter","year":"2012","unstructured":"Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195\u2013200 (2012).","journal-title":"Nature"},{"key":"8404_CR26","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1038\/s41586-022-04764-4","volume":"607","author":"T van Leent","year":"2022","unstructured":"van Leent, T. et al. Entangling single atoms over 33 km telecom fibre. Nature 607, 69\u201373 (2022).","journal-title":"Nature"},{"key":"8404_CR27","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1038\/nature06118","volume":"449","author":"DL Moehring","year":"2007","unstructured":"Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68\u201371 (2007).","journal-title":"Nature"},{"key":"8404_CR28","doi-asserted-by":"crossref","first-page":"110501","DOI":"10.1103\/PhysRevLett.124.110501","volume":"124","author":"LJ Stephenson","year":"2020","unstructured":"Stephenson, L. J. et al. High-rate, high-fidelity entanglement of qubits across an elementary quantum network. Phys. Rev. Lett. 124, 110501 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR29","unstructured":"Saha, S. et al. High-fidelity remote entanglement of trapped atoms mediated by time-bin photons. Preprint at https:\/\/arxiv.org\/abs\/2406.01761 (2024)."},{"key":"8404_CR30","doi-asserted-by":"crossref","first-page":"240501","DOI":"10.1103\/PhysRevLett.93.240501","volume":"93","author":"Y-F Huang","year":"2004","unstructured":"Huang, Y.-F., Ren, X.-F., Zhang, Y.-S., Duan, L.-M. & Guo, G.-C. Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Lett. 93, 240501 (2004).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR31","doi-asserted-by":"crossref","first-page":"20869","DOI":"10.1073\/pnas.1005720107","volume":"107","author":"W-B Gao","year":"2010","unstructured":"Gao, W.-B. et al. Teleportation-based realization of an optical quantum two-qubit entangling gate. Proc. Natl Acad. Sci. USA 107, 20869 (2010).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"8404_CR32","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1038\/s41586-018-0470-y","volume":"561","author":"KS Chou","year":"2018","unstructured":"Chou, K. S. et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 368\u2013373 (2018).","journal-title":"Nature"},{"key":"8404_CR33","doi-asserted-by":"crossref","first-page":"030339","DOI":"10.1103\/PRXQuantum.5.030339","volume":"5","author":"E B\u00e4umer","year":"2024","unstructured":"B\u00e4umer, E. et al. Efficient long-range entanglement using dynamic circuits. PRX Quantum 5, 030339 (2024).","journal-title":"PRX Quantum"},{"key":"8404_CR34","unstructured":"Hashim, A. et al. Efficient generation of multi-partite entanglement between non-local superconducting qubits using classical feedback. Preprint at https:\/\/arxiv.org\/abs\/2403.18768 (2024)."},{"key":"8404_CR35","doi-asserted-by":"crossref","first-page":"250502","DOI":"10.1103\/PhysRevLett.102.250502","volume":"102","author":"P Maunz","year":"2009","unstructured":"Maunz, P. et al. Heralded quantum gate between remote quantum memories. Phys. Rev. Lett. 102, 250502 (2009).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR36","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1126\/science.abe3150","volume":"371","author":"S Daiss","year":"2021","unstructured":"Daiss, S. et al. A quantum-logic gate between distant quantum-network modules. Science 371, 614\u2013617 (2021).","journal-title":"Science"},{"key":"8404_CR37","doi-asserted-by":"crossref","first-page":"090803","DOI":"10.1103\/PhysRevLett.130.090803","volume":"130","author":"P Drmota","year":"2023","unstructured":"Drmota, P. et al. Robust quantum memory in a trapped-ion quantum network node. Phys. Rev. Lett. 130, 090803 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR38","doi-asserted-by":"crossref","first-page":"140501","DOI":"10.1103\/PhysRevLett.117.140501","volume":"117","author":"TP Harty","year":"2016","unstructured":"Harty, T. P. et al. High-fidelity trapped-ion quantum logic using near-field microwaves. Phys. Rev. Lett. 117, 140501 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR39","doi-asserted-by":"crossref","first-page":"060504","DOI":"10.1103\/PhysRevLett.117.060504","volume":"117","author":"CJ Ballance","year":"2016","unstructured":"Ballance, C. J., Harty, T. P., Linke, N. M., Sepiol, M. A. & Lucas, D. M. High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett. 117, 060504 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR40","doi-asserted-by":"crossref","first-page":"080504","DOI":"10.1103\/PhysRevLett.125.080504","volume":"125","author":"AC Hughes","year":"2020","unstructured":"Hughes, A. C. et al. Benchmarking a high-fidelity mixed-species entangling gate. Phys. Rev. Lett. 125, 080504 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR41","doi-asserted-by":"crossref","first-page":"050306","DOI":"10.1103\/PhysRevA.72.050306","volume":"72","author":"K-A Brickman","year":"2005","unstructured":"Brickman, K.-A. et al. Implementation of Grover\u2019s quantum search algorithm in a scalable system. Phys. Rev. A 72, 050306 (2005).","journal-title":"Phys. Rev. A"},{"key":"8404_CR42","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1038\/nature08121","volume":"460","author":"L DiCarlo","year":"2009","unstructured":"DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240\u2013244 (2009).","journal-title":"Nature"},{"key":"8404_CR43","doi-asserted-by":"crossref","first-page":"060505","DOI":"10.1103\/PhysRevLett.117.060505","volume":"117","author":"JP Gaebler","year":"2016","unstructured":"Gaebler, J. P. et al. High-fidelity universal gate set for 9Be+ ion qubits. Phys. Rev. Lett. 117, 060505 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR44","doi-asserted-by":"crossref","DOI":"10.1038\/s41467-019-13068-7","volume":"10","author":"A Erhard","year":"2019","unstructured":"Erhard, A. et al. Characterizing large-scale quantum computers via cycle benchmarking. Nat. Commun. 10, 5347 (2019).","journal-title":"Nat. Commun."},{"key":"8404_CR45","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1038\/s41586-021-03809-4","volume":"597","author":"R Srinivas","year":"2021","unstructured":"Srinivas, R. et al. High-fidelity laser-free universal control of trapped ion qubits. Nature 597, 209\u2013213 (2021).","journal-title":"Nature"},{"key":"8404_CR46","doi-asserted-by":"crossref","first-page":"130505","DOI":"10.1103\/PhysRevLett.127.130505","volume":"127","author":"CR Clark","year":"2021","unstructured":"Clark, C. R. et al. High-fidelity Bell-state preparation with 40Ca+ optical qubits. Phys. Rev. Lett. 127, 130505 (2021).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR47","first-page":"041052","volume":"13","author":"SA Moses","year":"2023","unstructured":"Moses, S. A. et al. A race-track trapped-ion quantum processor. Phys. Rev. X 13, 041052 (2023).","journal-title":"Phys. Rev. X"},{"key":"8404_CR48","doi-asserted-by":"crossref","first-page":"L010601","DOI":"10.1103\/PhysRevA.110.L010601","volume":"110","author":"MA Weber","year":"2024","unstructured":"Weber, M. A. et al. Robust and fast microwave-driven quantum logic for trapped-ion qubits. Phys. Rev. A 110, L010601 (2024).","journal-title":"Phys. Rev. A"},{"key":"8404_CR49","doi-asserted-by":"crossref","first-page":"103028","DOI":"10.1088\/1367-2630\/18\/10\/103028","volume":"18","author":"R Nigmatullin","year":"2016","unstructured":"Nigmatullin, R., Ballance, C. J., de Beaudrap, N. & Benjamin, S. C. Minimally complex ion traps as modules for quantum communication and computing. New J. Phys. 18, 103028 (2016).","journal-title":"New J. Phys."},{"key":"8404_CR50","first-page":"011032","volume":"12","author":"J Hilder","year":"2022","unstructured":"Hilder, J. et al. Fault-tolerant parity readout on a shuttling-based trapped-ion quantum computer. Phys. Rev. X 12, 011032 (2022).","journal-title":"Phys. Rev. X"},{"key":"8404_CR51","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1364\/OPTICAQ.522128","volume":"2","author":"FW Knollmann","year":"2024","unstructured":"Knollmann, F. W. et al. Integrated photonic structures for photon-mediated entanglement of trapped ions. Opt. Quantum 2, 230\u2013244 (2024).","journal-title":"Opt. Quantum"},{"key":"8404_CR52","doi-asserted-by":"crossref","first-page":"070505","DOI":"10.1103\/PhysRevLett.123.070505","volume":"123","author":"Y-H Luo","year":"2019","unstructured":"Luo, Y.-H. et al. Quantum teleportation in high dimensions. Phys. Rev. Lett. 123, 070505 (2019).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR53","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1103\/PhysRevLett.82.1784","volume":"82","author":"S Lloyd","year":"1999","unstructured":"Lloyd, S. & Braunstein, S. L. Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784 (1999).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR54","doi-asserted-by":"crossref","first-page":"062411","DOI":"10.1103\/PhysRevA.102.062411","volume":"102","author":"BW Walshe","year":"2020","unstructured":"Walshe, B. W., Baragiola, B. Q., Alexander, R. N. & Menicucci, N. C. Continuous-variable gate teleportation and bosonic-code error correction. Phys. Rev. A 102, 062411 (2020).","journal-title":"Phys. Rev. A"},{"key":"8404_CR55","doi-asserted-by":"crossref","first-page":"eaam9288","DOI":"10.1126\/science.aam9288","volume":"362","author":"S Wehner","year":"2018","unstructured":"Wehner, S., Elkouss, D. & Hanson, R. Quantum internet: a vision for the road ahead. Science 362, eaam9288 (2018).","journal-title":"Science"},{"key":"8404_CR56","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1103\/PhysRevA.59.1829","volume":"59","author":"M Hillery","year":"1999","unstructured":"Hillery, M., Bu\u017eek, V. & Berthiaume, A. Quantum secret sharing. Phys. Rev. A 59, 1829 (1999).","journal-title":"Phys. Rev. A"},{"key":"8404_CR57","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1038\/nphys3000","volume":"10","author":"P K\u00f3m\u00e1r","year":"2014","unstructured":"K\u00f3m\u00e1r, P. et al. A quantum network of clocks. Nat. Phys. 10, 582\u2013587 (2014).","journal-title":"Nat. Phys."},{"key":"8404_CR58","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1119\/1.16243","volume":"58","author":"DM Greenberger","year":"1990","unstructured":"Greenberger, D. M., Horne, M. A., Shimony, A. & Zeilinger, A. Bell\u2019s theorem without inequalities. Am. J. Phys. 58, 1131\u20131143 (1990).","journal-title":"Am. J. Phys."},{"key":"8404_CR59","doi-asserted-by":"publisher","unstructured":"Maunz, P. L. W. High Optical Access Trap 2.0 (US Department of Energy, Office of Scientific and Technical Information, 2016); https:\/\/doi.org\/10.2172\/1237003.","DOI":"10.2172\/1237003"},{"key":"8404_CR60","unstructured":"Revelle, M. C., Phoenix and Peregrine ion traps. Preprint at https:\/\/arxiv.org\/abs\/2009.02398 (2020)."},{"key":"8404_CR61","doi-asserted-by":"crossref","first-page":"042108","DOI":"10.1103\/PhysRevA.75.042108","volume":"75","author":"J \u0158eh\u00e1\u010dek","year":"2007","unstructured":"\u0158eh\u00e1\u010dek, J., Hradil, Z., Knill, E. & Lvovsky, A. I. Diluted maximum-likelihood algorithm for quantum tomography. Phys. Rev. A 75, 042108 (2007).","journal-title":"Phys. Rev. A"},{"key":"8404_CR62","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0375-9601(02)01272-0","volume":"303","author":"MA Nielsen","year":"2002","unstructured":"Nielsen, M. A. A simple formula for the average gate fidelity of a quantum dynamical operation. Phys. Lett. A 303, 249\u2013252 (2002).","journal-title":"Phys. Lett. A"},{"key":"8404_CR63","unstructured":"Stephenson, L. Entanglement Between Nodes of a Quantum Network. DPhil thesis, Univ. Oxford (2019); https:\/\/ora.ox.ac.uk\/objects\/uuid:5066d87a-55e8-4fd5-b5b8-df1878af97a8."},{"key":"8404_CR64","unstructured":"Nadlinger, D. P. Device-independent Key Distribution Between Trapped-ion Quantum Network Nodes. DPhil thesis, Univ. Oxford (2022)."},{"key":"8404_CR65","volume":"12","author":"P Wang","year":"2021","unstructured":"Wang, P. et al. Single ion qubit with estimated coherence time exceeding one hour. Nat. Commun. 12, 233 (2021).","journal-title":"Nat. Commun."},{"key":"8404_CR66","doi-asserted-by":"crossref","first-page":"240501","DOI":"10.1103\/PhysRevLett.106.240501","volume":"106","author":"AM Souza","year":"2011","unstructured":"Souza, A. M., \u00c1lvarez, G. A. & Suter, D. Robust dynamical decoupling for quantum computing and quantum memory. Phys. Rev. Lett. 106, 240501 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"8404_CR67","doi-asserted-by":"crossref","first-page":"012509","DOI":"10.1103\/PhysRevA.72.012509","volume":"72","author":"V Letchumanan","year":"2005","unstructured":"Letchumanan, V., Wilson, M. A., Gill, P. & Sinclair, A. G. Lifetime measurement of the metastable 4d2D5\/2 state in 88Sr+ using a single trapped ion. Phys. Rev. A 72, 012509 (2005).","journal-title":"Phys. Rev. A"},{"key":"8404_CR68","doi-asserted-by":"publisher","unstructured":"Bourdeauducq, S. et al. m-labs\/artiq: 4.0 (4.0). Zenodo https:\/\/doi.org\/10.5281\/zenodo.1492176 (2021).","DOI":"10.5281\/zenodo.1492176"}],"container-title":["Nature"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41586-024-08404-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-024-08404-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-024-08404-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T15:01:44Z","timestamp":1739372504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41586-024-08404-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,5]]},"references-count":68,"journal-issue":{"issue":"8050","published-print":{"date-parts":[[2025,2,13]]}},"alternative-id":["8404"],"URL":"https:\/\/doi.org\/10.1038\/s41586-024-08404-x","relation":{},"ISSN":["0028-0836","1476-4687"],"issn-type":[{"value":"0028-0836","type":"print"},{"value":"1476-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,5]]},"assertion":[{"value":"30 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"R.S. is partly employed by Oxford Ionics Ltd. The other authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}