Acharyaet al., Quantum error correction below the surface code threshold, Nature638, 10.1038/s41586-024-08449-y (2025), arXiv:2503.16602 [hep-ph]

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Rajeev Acharya, Dmitry A. Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Bab- bush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, Andreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabr- era, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexan- der L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Cather- ine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flo- res Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Élie Genois, William Giang, C

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“Quantum error correction below the surface code threshold,” Nature, vol. 638, no. 8052, pp. 920–926, 2025. [Online]. Available: https://doi.org/10.1038/s41586-024-08449-y

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R. Acharyaet al., “Quantum error correction below the surface code threshold,”Nature, vol. 638, no. 8052, p. 920–926, Dec. 2024. [Online]. Available: http://dx.doi.org/10.1038/s41586-024-08449-y

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Google Quantum AI and Collaborators. 2025. Quantum error correc- tion below the surface code threshold.Nature638, 8052 (Feb. 2025), 920–926. doi:10.1038/s41586-024-08449-y

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R. Acharya,et al., Quantum error correction below the surface code threshold.Nature 638(8052), 920–926 (2025), doi:10.1038/s41586-024-08449-y,https://doi.org/10. 1038/s41586-024-08449-y

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evidence for pre-fault-tolerant utility in many-body dynamics [27]. Google's superconducting processors first showed that logical performance can improve as surface-code distance increases from d = 3to d = 5[ 28], and then reached below-threshold operation with a 101-qubitd = 7surface-code memory with0 .143% ± 0.003%logical error per cycle and real-time decoding [29]. For a buyer, these demonstrations show that superconducting systems already support both ambitious NISQ-scale quantum simulation and early logical-qubit experiments. IBM anchors this platform family because it offers the clearest access ladder. Buyers can start with a free Open Plan, move to paid access, and then negotiate deeper enterprise arrangements.

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evidence for pre-fault-tolerant utility in many-body dynamics [27]. Google's superconducting processors first showed that logical performance can improve as surface-code distance increases from d = 3to d = 5[ 28], and then reached below-threshold operation with a 101-qubitd = 7surface-code memory with0 .143% ± 0.003%logical error per cycle and real-time decoding [29]. For a buyer, these demonstrations show that superconducting systems already support both ambitious NISQ-scale quantum simulation and early logical-qubit experiments. IBM anchors this platform family because it offers the clearest access ladder. Buyers can start with a free Open Plan, move to paid access, and then negotiate deeper enterprise arrangements

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Google Quantum AI and Collaborators, “Quantum error correction below the surface code threshold,”Nature, vol. 638, no. 8052, pp. 920–926, 2025. [Online]. Available: https://doi.org/10.1038/s41586-024-08449-y

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Google Quantum AI and Collaborators, “Quantum error correction below the surface code threshold,”Nature, vol. 638, no. 8052, pp. 920–926, 2025. [Online]. Available: https://doi.org/10.1038/s41586-024-08449-y

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Currently, several technologies have demonstrated the integration of qubits on a small to medium scale. These include superconducting qubit [13], [14], silicon spin qubit [14], [15], photonic qubits [16], trapped ion qubit [17], [18], neutral atom qubit [19], and others. Among them, the superconducting qubit technology is one of the most promising ones. For example, IBM [20] and Google [21] have superconducting quantum computers with o ver 100 physical qubits. One-qubit and two-qubit gate error rates for most isolated systems have also reached ~ 10-3. Combining with long qubit coherence time, they have reach ed the threshold of some error correction codes [22], [23] . A superconducting qubit quantum processing unit (QPU) is usually composed of superconducting microwave circuit s

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Rajeev Acharya, Dmitry A. Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, An- dreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y . Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Fer- reira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Élie Genois, William Giang, Craig

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Google Quantum AI and Collaborators . Quantum error correction below the surface code threshold. http://dx.doi.org/10.1038/s41586-024-08449-y Nature (2024) , arXiv:2408.13687 http://arxiv.org/abs/2408.13687

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Google Quantum AI and Collaborators . Quantum error correction below the surface code threshold. http://dx.doi.org/10.1038/s41586-024-08449-y Nature (2024), arXiv:2408.13687 http://arxiv.org/abs/2408.13687

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ISSN 1476-4687. doi:10.1038/s41586-024-08449-y

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Google Quantum AI and Collaborators . Quantum error correction below the surface code threshold. http://dx.doi.org/10.1038/s41586-024-08449-y Nature 638:920--926 (2025) , arXiv:2408.13687 http://arxiv.org/abs/2408.13687

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Google Quantum AI and Collaborators . Quantum error correction below the surface code threshold. http://dx.doi.org/10.1038/s41586-024-08449-y Nature 638:920--926 (2025), arXiv:2408.13687 http://arxiv.org/abs/2408.13687

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Google Quantum AI and Collaborators, Quantum er- ror correction below the surface code threshold, Nature 10.1038/s41586-024-08449-y (2024)

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Rajeev Acharya, Dmitry A. Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, Andreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y . Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, ´Elie Genois, William Giang, Craig Gid

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Google Quantum AI and Collaborators, “Quantum error correction below the surface code threshold,” Nature (2024), 10.1038/s41586-024-08449-y

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Google Quantum AI and Collaborators. Quantum error correction below the surface code threshold.Nature, 638:920–926, 2025. doi: 10.1038/s41586-024-08449-y

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Google Quantum AI. Quantum error correction below the surface code threshold.Nature, 638:920–926, 2025. doi: 10.1038/s41586-024-08449-y. URLhttps://doi.org/10.1038/ s41586-024-08449-y. 21

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Google Quantum AI. Quantum error correction below the surface code threshold.Nature, 638:920–926, 2025. doi: 10.1038/s41586-024-08449-y. URLhttps://doi.org/10.1038/ s41586-024-08449-y. 22

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R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buck- ley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, Y. Chen, Z. Chen, B. Chiaro, D. Chik, C. Chou, J. Claes, A. Y. Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, A. Davies, L. De Lorenzo, D. M. Debroy, S. Demura, M. Devoret, A. Di Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, C. Earle, T. Edlich, A. Eickbusch, A. M. Elbag, M. Elzouka, C. Er- ickson, L. Faoro, E. Farhi, V. S. Ferreira, L. F. Bur- gos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, G. Garcia, R. Gasca, ´E. Genois, W. Giang, C. Gid- ney, D. Gilboa, R. Gosula, A. G. Dau, D. Graumann, A. Greene, J. A. Gross, S. Habegger, J. Hall, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harring- ton, F. J. H. Heras, S. Heslin, P. Heu, O. Higgott, G. Hill, J. Hilton, G. Holland, S. Hong, H.-Y. Huang, A. Huff,

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R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buck- ley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, Y. Chen, Z. Chen, B. Chiaro, D. Chik, C. Chou, J. Claes, A. Y. Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, A. Davies, L. De Lorenzo, D. M. Debroy, S. Demura, M. Devoret, A. Di Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, C. Earle, T. Edlich, A. Eickbusch, A. M. Elbag, M. Elzouka, C. Er- ickson, L. Faoro, E. Farhi, V. S. Ferreira, L. F. Bur- gos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, G. Garcia, R. Gasca, ´E. Genois, W. Giang, C. Gid- ney, D. Gilboa, R. Gosula, A. G. Dau, D. Graumann, A. Greene, J. A. Gross, S. Habegger, J. Hall, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harring- ton, F. J. H. Heras, S. Heslin, P. Heu, O. Higgott, G. Hill, J. Hilton, G. Holland, S. Hong, H.-Y. Huang, A. Huff

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Acharya, R., Abanin, D. A., et al. Quantum error correction below the surface code threshold. Nature, 2024. doi:10.1038/s41586-024-08449-y

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R. Acharya, D. A. Abanin, L. Aghababaie-Beni,et al., Nature (2024), 10.1038/s41586-024-08449-y

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author author Google Quantum AI and Collaborators ,\ title title Quantum error correction below the surface code threshold ,\ https://doi.org/10.1038/s41586-024-08449-y journal journal Nature \ volume 638 ,\ pages 920 ( year 2025 ) NoStop

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author author Google Quantum AI and Collaborators, title title Quantum error correction below the surface code threshold, https://doi.org/10.1038/s41586-024-08449-y journal journal Nature volume 638, pages 920 ( year 2025 )

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Quantum Error Correction below the Surface Code Threshold , author =. Nature , volume =. doi:10.1038/s41586-024-08449-y , copyright =

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Quantum Error Correction below the Surface Code Threshold, author =. Nature, volume =. doi:10.1038/s41586-024-08449-y, copyright =

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Acharya, R., Abanin, D. A., Aghababaie-Beni, L., Aleiner, I., Andersen, T. I., et al. “Quantum error correction below the surface code threshold.” Nature Vo l . 6 3 8 N o . 8 0 5 2 (2025): pp. 920–926. DOI 10.1038/s41586-024-08449-y

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R. Acharyaet al.(Google Quantum AI), “Quantum er- ror correction below the surface code threshold,” Nature 638, 920–926 (2025), doi:10.1038/s41586-024-08449-y

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Rajeev Acharya et al. “Quantum error correction below the surface code threshold”. en. In: Nature638.8052 (Feb. 2025), pp. 920–926.doi:10.1038/s41586-024-08449-y

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Quantum error correction below the surface code threshold , volume=. Nature , publisher=. 2024 , month=dec, pages=. doi:10.1038/s41586-024-08449-y , number=

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Quantum error correction below the surface code threshold, volume=. Nature, publisher=. 2024, month=dec, pages=. doi:10.1038/s41586-024-08449-y, number=

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R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, Y . Chen, Z. Chen, B. Chiaro, D. Chik, C. Chou, J. Claes, A. Y . Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, A. Davies, L. De Lorenzo, D. M. Debroy, S. Demura, M. Devoret, A. Di Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, C. Earle, T. Edlich, A. Eickbusch, A. M. Elbag, M. Elzouka, C. Erickson, L. Faoro, E. Farhi, V . S. Ferreira, L. F. Burgos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, G. Garcia, R. Gasca, ´E. Genois, W. Giang, C. Gidney, D. Gilboa, R. Gosula, A. G. Dau, D. Graumann, A. Greene, J. A. Gross, S. Habegger, J. Hall, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harrington, F. J. H. Heras, S. Heslin, P. Heu, O. Higgott, G. Hill, J. Hilton, G. Holland, S. Hong, H.-Y . Huang, A. Huff, W. J.

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R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, Y . Chen, Z. Chen, B. Chiaro, D. Chik, C. Chou, J. Claes, A. Y . Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, A. Davies, L. De Lorenzo, D. M. Debroy, S. Demura, M. Devoret, A. Di Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, C. Earle, T. Edlich, A. Eickbusch, A. M. Elbag, M. Elzouka, C. Erickson, L. Faoro, E. Farhi, V . S. Ferreira, L. F. Burgos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, G. Garcia, R. Gasca, ´E. Genois, W. Giang, C. Gidney, D. Gilboa, R. Gosula, A. G. Dau, D. Graumann, A. Greene, J. A. Gross, S. Habegger, J. Hall, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harrington, F. J. H. Heras, S. Heslin, P. Heu, O. Higgott, G. Hill, J. Hilton, G. Holland, S. Hong, H.-Y . Huang, A. Huff, W. J

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Google Quantum AI: Quantum error correction below the surface code threshold. Nature638(8052), 920–926 (2025) https://doi.org/10.1038/s41586-024-08449-y

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Google Quantum AIet al., “Quantum error correction below the surface code threshold,”Nature, vol. 638, pp. 920–926, 2025. [Online]. Available: https://doi.org/10.1038/s41586-024-08449-y

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Quantum error correction below the surface code threshold , volume =. Nature , author =. 2025 , note =. doi:10.1038/s41586-024-08449-y , abstract =

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Quantum error correction below the surface code threshold, volume =. Nature, author =. 2025, note =. doi:10.1038/s41586-024-08449-y, abstract =

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Acharya, Rajeev and Abanin, Dmitry A. and Google Quantum AI and Collaborators , title =. Nature , year =. doi:10.1038/s41586-024-08449-y , url =

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Acharya, Rajeev and Abanin, Dmitry A. and Google Quantum AI and Collaborators, title =. Nature, year =. doi:10.1038/s41586-024-08449-y, url =

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Quantum Error Correction below the Surface Code Threshold , year = 2025, month = feb, journal =. doi:10.1038/s41586-024-08449-y , url =

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Quantum Error Correction below the Surface Code Threshold, year = 2025, month = feb, journal =. doi:10.1038/s41586-024-08449-y, url =

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Quantum error correction below the surface code threshold , volume=. Nature , publisher=. 2024 , month=dec, pages=. doi:10.1038/s41586-024-08449-y , number=

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Quantum error correction below the surface code threshold, volume=. Nature, publisher=. 2024, month=dec, pages=. doi:10.1038/s41586-024-08449-y, number=

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G. Q. AI and Collaborators,Quantum error correction below the surface code threshold, https://doi.org/ 10.1038/s41586-024-08449-y , First below-threshold scalable QEC experiment; Accessed: 2026-04-08, 2025

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G. Q. AI and Collaborators,Quantum error correction below the surface code threshold, https://doi.org/ 10.1038/s41586-024-08449-y, First below-threshold scalable QEC experiment; Accessed: 2026-04-08, 2025

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R. Acharyaet al., Quantum error correction below the surface code threshold, Nature638, 10.1038/s41586-024-08449-y (2025), arXiv:2503.16602 [hep-ph]

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Rajeev Acharya, Laleh Aghababaie-Beni, Igor Aleiner, Trond I Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, et al. 2024. Quantum error correction below the surface code threshold.arXiv preprint arXiv:2408.13687(2024). doi:10.1038/s41586-024-08449-y

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[Online]. Available: http://doi.org/10.1038/s41586-024-08449-y

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Rajeev Acharya, Dmitry A. Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Bab- bush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, Andreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabr- era, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexan- der L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Cather- ine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flo- res Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Élie Genois, William Giang, C

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R.e.a.Acharya,Quantumerrorcorrectionbelowthesur- face code threshold, Nature 10.1038/s41586-024-08449-y (2024)

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author author Rajeev \ Acharya et al ,\ title title Quantum error correction below the surface code threshold , \ 10.1038/s41586-024-08449-y journal journal \ volume 638 ,\ pages 920--926 ( year 2025 ) ,\ http://arxiv.org/abs/2408.13687 arXiv:2408.13687 [quant-ph] NoStop

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author author Rajeev Acharya et al, title title Quantum error correction below the surface code threshold, 10.1038/s41586-024-08449-y journal journal volume 638, pages 920--926 ( year 2025 ), http://arxiv.org/abs/2408.13687 arXiv:2408.13687 [quant-ph]