Thermalization and criticality on an analogue–digital quantum simulator

T. I. Andersen; N. Astrakhantsev; A. H. Karamlou; J. Berndtsson; J. Motruk; A. Szasz; J. A. Gross; A. Schuckert; T. Westerhout; Y. Zhang; E. Forati; D. Rossi; B. Kobrin; A. Di Paolo; A. R. Klots; I. Drozdov; V. Kurilovich; A. Petukhov; L. B. Ioffe; A. Elben; A. Rath; V. Vitale; B. Vermersch; R. Acharya; L. A. Beni; K. Anderson; M. Ansmann; F. Arute; K. Arya; A. Asfaw; J. Atalaya; B. Ballard; J. C. Bardin; A. Bengtsson; A. Bilmes; 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; Z. Chen; B. Chiaro; J. Claes; A. Y. Cleland; J. Cogan; R. Collins; P. Conner; W. Courtney; A. L. Crook; S. Das; D. M. Debroy; L. De Lorenzo; A. Del Toro Barba; S. Demura; P. Donohoe; A. Dunsworth; C. Earle; A. Eickbusch; A. M. Elbag; M. Elzouka; C. Erickson; L. Faoro; R. Fatemi; V. S. Ferreira; L. Flores Burgos; A. G. Fowler; B. Foxen; S. Ganjam; R. Gasca; W. Giang; C. Gidney; D. Gilboa; M. Giustina; R. Gosula; A. Grajales Dau; D. Graumann; A. Greene; S. Habegger; M. C. Hamilton; M. Hansen; M. P. Harrigan; S. D. Harrington; S. Heslin; P. Heu; G. Hill; M. R. Hoffmann; H. Y. Huang; T. Huang; A. Huff; W. J. Huggins; S. V. Isakov; E. Jeffrey; Z. Jiang; C. Jones; S. Jordan; C. Joshi; P. Juhas; D. Kafri; H. Kang; K. Kechedzhi; T. Khaire; T. Khattar; M. Khezri; M. Kieferová; S. Kim; A. Kitaev; P. Klimov; A. N. Korotkov; F. Kostritsa; J. M. Kreikebaum; D. Landhuis; B. W. Langley; P. Laptev; K. M. Lau; L. Le Guevel; J. Ledford; J. Lee; K. W. Lee; Y. D. Lensky; B. J. Lester; W. Y. Li; A. T. Lill; W. Liu; W. P. Livingston; A. Locharla; D. Lundahl; A. Lunt; S. Madhuk; A. Maloney; S. Mandrà; L. S. Martin; O. Martin; S. Martin; C. Maxfield; J. R. McClean; M. McEwen; S. Meeks; K. C. Miao; A. Mieszala; S. Molina; S. Montazeri; A. Morvan; R. Movassagh; C. Neill; A. Nersisyan; M. Newman; A. Nguyen; M. Nguyen; C. H. Ni; M. Y. Niu; W. D. Oliver; K. Ottosson; A. Pizzuto; R. Potter; O. Pritchard; L. P. Pryadko; C. Quintana; M. J. Reagor; D. M. Rhodes; G. Roberts; C. Rocque; E. Rosenberg; N. C. Rubin; N. Saei; K. Sankaragomathi; K. J. Satzinger; H. F. Schurkus; C. Schuster; M. J. Shearn; A. Shorter; N. Shutty; V. Shvarts; V. Sivak; J. Skruzny; S. Small; W. Clarke Smith; S. Springer; G. Sterling; J. Suchard; M. Szalay; A. Sztein; D. Thor; A. Torres; M. M. Torunbalci; A. Vaishnav; S. Vdovichev; B. Villalonga; C. Vollgraff Heidweiller; S. Waltman; S. X. Wang; T. White; K. Wong; B. W.K. Woo; C. Xing; Z. Jamie Yao; P. Yeh; B. Ying; J. Yoo; N. Yosri; G. Young; A. Zalcman; N. Zhu; N. Zobrist; H. Neven; R. Babbush; S. Boixo; J. Hilton; E. Lucero; A. Megrant; J. Kelly; Y. Chen; V. Smelyanskiy; G. Vidal; P. Roushan; A. M. Läuchli; D. A. Abanin; X. Mi

doi:10.1038/s41586-024-08460-3

Thermalization and criticality on an analogue–digital quantum simulator

T. I. Andersen, N. Astrakhantsev, A. H. Karamlou, J. Berndtsson, J. Motruk, A. Szasz, J. A. Gross, A. Schuckert, T. Westerhout, Y. Zhang, E. Forati, D. Rossi, B. Kobrin, A. Di Paolo, A. R. Klots, I. Drozdov, V. Kurilovich, A. Petukhov, L. B. Ioffe, A. ElbenA. Rath, V. Vitale, B. Vermersch, R. Acharya, L. A. Beni, K. Anderson, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, B. Ballard, J. C. Bardin, A. Bengtsson, A. Bilmes, 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, Z. Chen, B. Chiaro, J. Claes, A. Y. Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, S. Das, D. M. Debroy, L. De Lorenzo, A. Del Toro Barba, S. Demura, P. Donohoe, A. Dunsworth, C. Earle, A. Eickbusch, A. M. Elbag, M. Elzouka, C. Erickson, L. Faoro, R. Fatemi, V. S. Ferreira, L. Flores Burgos, A. G. Fowler, B. Foxen, S. Ganjam, R. Gasca, W. Giang, C. Gidney, D. Gilboa, M. Giustina, R. Gosula, A. Grajales Dau, D. Graumann, A. Greene, S. Habegger, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harrington, S. Heslin, P. Heu, G. Hill, M. R. Hoffmann, H. Y. Huang, T. Huang, A. Huff, W. J. Huggins, S. V. Isakov, E. Jeffrey, Z. Jiang, C. Jones, S. Jordan, C. Joshi, P. Juhas, D. Kafri, H. Kang, K. Kechedzhi, T. Khaire, T. Khattar, M. Khezri, M. Kieferová, S. Kim, A. Kitaev, P. Klimov, A. N. Korotkov, F. Kostritsa, J. M. Kreikebaum, D. Landhuis, B. W. Langley, P. Laptev, K. M. Lau, L. Le Guevel, J. Ledford, J. Lee, K. W. Lee, Y. D. Lensky, B. J. Lester, W. Y. Li, A. T. Lill, W. Liu, W. P. Livingston, A. Locharla, D. Lundahl, A. Lunt, S. Madhuk, A. Maloney, S. Mandrà, L. S. Martin, O. Martin, S. Martin, C. Maxfield, J. R. McClean, M. McEwen, S. Meeks, K. C. Miao, A. Mieszala, S. Molina, S. Montazeri, A. Morvan, R. Movassagh, C. Neill, A. Nersisyan, M. Newman, A. Nguyen, M. Nguyen, C. H. Ni, M. Y. Niu, W. D. Oliver, K. Ottosson, A. Pizzuto, R. Potter, O. Pritchard, L. P. Pryadko, C. Quintana, M. J. Reagor, D. M. Rhodes, G. Roberts, C. Rocque, E. Rosenberg, N. C. Rubin, N. Saei, K. Sankaragomathi, K. J. Satzinger, H. F. Schurkus, C. Schuster, M. J. Shearn, A. Shorter, N. Shutty, V. Shvarts, V. Sivak, J. Skruzny, S. Small, W. Clarke Smith, S. Springer, G. Sterling, J. Suchard, M. Szalay, A. Sztein, D. Thor, A. Torres, M. M. Torunbalci, A. Vaishnav, S. Vdovichev, B. Villalonga, C. Vollgraff Heidweiller, S. Waltman, S. X. Wang, T. White, K. Wong, B. W.K. Woo, C. Xing, Z. Jamie Yao, P. Yeh, B. Ying, J. Yoo, N. Yosri, G. Young, A. Zalcman, N. Zhu, N. Zobrist, H. Neven, R. Babbush, S. Boixo, J. Hilton, E. Lucero, A. Megrant, J. Kelly, Y. Chen, V. Smelyanskiy, G. Vidal, P. Roushan, A. M. Läuchli, D. A. Abanin, X. Mi

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators^1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions³ in the XY model, as well as signatures of the classical Kosterlitz–Thouless phase transition⁴. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis^{5, 6–7} in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Original language	English (US)
Pages (from-to)	79-85
Number of pages	7
Journal	Nature
Volume	638
Issue number	8049
DOIs	https://doi.org/10.1038/s41586-024-08460-3
State	Published - Feb 6 2025

All Science Journal Classification (ASJC) codes

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10.1038/s41586-024-08460-3

Cite this

Andersen, T. I., Astrakhantsev, N., Karamlou, A. H., Berndtsson, J., Motruk, J., Szasz, A., Gross, J. A., Schuckert, A., Westerhout, T., Zhang, Y., Forati, E., Rossi, D., Kobrin, B., Paolo, A. D., Klots, A. R., Drozdov, I., Kurilovich, V., Petukhov, A., Ioffe, L. B., ... Mi, X. (2025). Thermalization and criticality on an analogue–digital quantum simulator. Nature, 638(8049), 79-85. https://doi.org/10.1038/s41586-024-08460-3

@article{4a6fec99626e4d01bd9b31eb8aaa8c63,

title = "Thermalization and criticality on an analogue–digital quantum simulator",

abstract = "Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions3 in the XY model, as well as signatures of the classical Kosterlitz–Thouless phase transition4. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis5, 6–7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.",

author = "Andersen, {T. I.} and N. Astrakhantsev and Karamlou, {A. H.} and J. Berndtsson and J. Motruk and A. Szasz and Gross, {J. A.} and A. Schuckert and T. Westerhout and Y. Zhang and E. Forati and D. Rossi and B. Kobrin and Paolo, {A. Di} and Klots, {A. R.} and I. Drozdov and V. Kurilovich and A. Petukhov and Ioffe, {L. B.} and A. Elben and A. Rath and V. Vitale and B. Vermersch and R. Acharya and Beni, {L. A.} and K. Anderson and M. Ansmann and F. Arute and K. Arya and A. Asfaw and J. Atalaya and B. Ballard and Bardin, {J. C.} and A. Bengtsson and A. Bilmes and G. Bortoli and A. Bourassa and J. Bovaird and L. Brill and M. Broughton and Browne, {D. A.} and B. Buchea and Buckley, {B. B.} and Buell, {D. A.} and T. Burger and B. Burkett and N. Bushnell and A. Cabrera and J. Campero and Chang, {H. S.} and Z. Chen and B. Chiaro and J. Claes and Cleland, {A. Y.} and J. Cogan and R. Collins and P. Conner and W. Courtney and Crook, {A. L.} and S. Das and Debroy, {D. M.} and Lorenzo, {L. De} and Barba, {A. Del Toro} and S. Demura and P. Donohoe and A. Dunsworth and C. Earle and A. Eickbusch and Elbag, {A. M.} and M. Elzouka and C. Erickson and L. Faoro and R. Fatemi and Ferreira, {V. S.} and Burgos, {L. Flores} and Fowler, {A. G.} and B. Foxen and S. Ganjam and R. Gasca and W. Giang and C. Gidney and D. Gilboa and M. Giustina and R. Gosula and Dau, {A. Grajales} and D. Graumann and A. Greene and S. Habegger and Hamilton, {M. C.} and M. Hansen and Harrigan, {M. P.} and Harrington, {S. D.} and S. Heslin and P. Heu and G. Hill and Hoffmann, {M. R.} and Huang, {H. Y.} and T. Huang and A. Huff and Huggins, {W. J.} and Isakov, {S. V.} and E. Jeffrey and Z. Jiang and C. Jones and S. Jordan and C. Joshi and P. Juhas and D. Kafri and H. Kang and K. Kechedzhi and T. Khaire and T. Khattar and M. Khezri and M. Kieferov{\'a} and S. Kim and A. Kitaev and P. Klimov and Korotkov, {A. N.} and F. Kostritsa and Kreikebaum, {J. M.} and D. Landhuis and Langley, {B. W.} and P. Laptev and Lau, {K. M.} and Guevel, {L. Le} and J. Ledford and J. Lee and Lee, {K. W.} and Lensky, {Y. D.} and Lester, {B. J.} and Li, {W. Y.} and Lill, {A. T.} and W. Liu and Livingston, {W. P.} and A. Locharla and D. Lundahl and A. Lunt and S. Madhuk and A. Maloney and S. Mandr{\`a} and Martin, {L. S.} and O. Martin and S. Martin and C. Maxfield and McClean, {J. R.} and M. McEwen and S. Meeks and Miao, {K. C.} and A. Mieszala and S. Molina and S. Montazeri and A. Morvan and R. Movassagh and C. Neill and A. Nersisyan and M. Newman and A. Nguyen and M. Nguyen and Ni, {C. H.} and Niu, {M. Y.} and Oliver, {W. D.} and K. Ottosson and A. Pizzuto and R. Potter and O. Pritchard and Pryadko, {L. P.} and C. Quintana and Reagor, {M. J.} and Rhodes, {D. M.} and G. Roberts and C. Rocque and E. Rosenberg and Rubin, {N. C.} and N. Saei and K. Sankaragomathi and Satzinger, {K. J.} and Schurkus, {H. F.} and C. Schuster and Shearn, {M. J.} and A. Shorter and N. Shutty and V. Shvarts and V. Sivak and J. Skruzny and S. Small and Smith, {W. Clarke} and S. Springer and G. Sterling and J. Suchard and M. Szalay and A. Sztein and D. Thor and A. Torres and Torunbalci, {M. M.} and A. Vaishnav and S. Vdovichev and B. Villalonga and Heidweiller, {C. Vollgraff} and S. Waltman and Wang, {S. X.} and T. White and K. Wong and Woo, {B. W.K.} and C. Xing and Yao, {Z. Jamie} and P. Yeh and B. Ying and J. Yoo and N. Yosri and G. Young and A. Zalcman and N. Zhu and N. Zobrist and H. Neven and R. Babbush and S. Boixo and J. Hilton and E. Lucero and A. Megrant and J. Kelly and Y. Chen and V. Smelyanskiy and G. Vidal and P. Roushan and L{\"a}uchli, {A. M.} and Abanin, {D. A.} and X. Mi",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

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doi = "10.1038/s41586-024-08460-3",

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Andersen, TI, Astrakhantsev, N, Karamlou, AH, Berndtsson, J, Motruk, J, Szasz, A, Gross, JA, Schuckert, A, Westerhout, T, Zhang, Y, Forati, E, Rossi, D, Kobrin, B, Paolo, AD, Klots, AR, Drozdov, I, Kurilovich, V, Petukhov, A, Ioffe, LB, Elben, A, Rath, A, Vitale, V, Vermersch, B, Acharya, R, Beni, LA, Anderson, K, Ansmann, M, Arute, F, Arya, K, Asfaw, A, Atalaya, J, Ballard, B, Bardin, JC, Bengtsson, A, Bilmes, A, Bortoli, G, Bourassa, A, Bovaird, J, Brill, L, Broughton, M, Browne, DA, Buchea, B, Buckley, BB, Buell, DA, Burger, T, Burkett, B, Bushnell, N, Cabrera, A, Campero, J, Chang, HS, Chen, Z, Chiaro, B, Claes, J, Cleland, AY, Cogan, J, Collins, R, Conner, P, Courtney, W, Crook, AL, Das, S, Debroy, DM, Lorenzo, LD, Barba, ADT, Demura, S, Donohoe, P, Dunsworth, A, Earle, C, Eickbusch, A, Elbag, AM, Elzouka, M, Erickson, C, Faoro, L, Fatemi, R, Ferreira, VS, Burgos, LF, Fowler, AG, Foxen, B, Ganjam, S, Gasca, R, Giang, W, Gidney, C, Gilboa, D, Giustina, M, Gosula, R, Dau, AG, Graumann, D, Greene, A, Habegger, S, Hamilton, MC, Hansen, M, Harrigan, MP, Harrington, SD, Heslin, S, Heu, P, Hill, G, Hoffmann, MR, Huang, HY, Huang, T, Huff, A, Huggins, WJ, Isakov, SV, Jeffrey, E, Jiang, Z, Jones, C, Jordan, S, Joshi, C, Juhas, P, Kafri, D, Kang, H, Kechedzhi, K, Khaire, T, Khattar, T, Khezri, M, Kieferová, M, Kim, S, Kitaev, A, Klimov, P, Korotkov, AN, Kostritsa, F, Kreikebaum, JM, Landhuis, D, Langley, BW, Laptev, P, Lau, KM, Guevel, LL, Ledford, J, Lee, J, Lee, KW, Lensky, YD, Lester, BJ, Li, WY, Lill, AT, Liu, W, Livingston, WP, Locharla, A, Lundahl, D, Lunt, A, Madhuk, S, Maloney, A, Mandrà, S, Martin, LS, Martin, O, Martin, S, Maxfield, C, McClean, JR, McEwen, M, Meeks, S, Miao, KC, Mieszala, A, Molina, S, Montazeri, S, Morvan, A, Movassagh, R, Neill, C, Nersisyan, A, Newman, M, Nguyen, A, Nguyen, M, Ni, CH, Niu, MY, Oliver, WD, Ottosson, K, Pizzuto, A, Potter, R, Pritchard, O, Pryadko, LP, Quintana, C, Reagor, MJ, Rhodes, DM, Roberts, G, Rocque, C, Rosenberg, E, Rubin, NC, Saei, N, Sankaragomathi, K, Satzinger, KJ, Schurkus, HF, Schuster, C, Shearn, MJ, Shorter, A, Shutty, N, Shvarts, V, Sivak, V, Skruzny, J, Small, S, Smith, WC, Springer, S, Sterling, G, Suchard, J, Szalay, M, Sztein, A, Thor, D, Torres, A, Torunbalci, MM, Vaishnav, A, Vdovichev, S, Villalonga, B, Heidweiller, CV, Waltman, S, Wang, SX, White, T, Wong, K, Woo, BWK, Xing, C, Yao, ZJ, Yeh, P, Ying, B, Yoo, J, Yosri, N, Young, G, Zalcman, A, Zhu, N, Zobrist, N, Neven, H, Babbush, R, Boixo, S, Hilton, J, Lucero, E, Megrant, A, Kelly, J, Chen, Y, Smelyanskiy, V, Vidal, G, Roushan, P, Läuchli, AM, Abanin, DA & Mi, X 2025, 'Thermalization and criticality on an analogue–digital quantum simulator', Nature, vol. 638, no. 8049, pp. 79-85. https://doi.org/10.1038/s41586-024-08460-3

TY - JOUR

T1 - Thermalization and criticality on an analogue–digital quantum simulator

AU - Andersen, T. I.

AU - Astrakhantsev, N.

AU - Karamlou, A. H.

AU - Berndtsson, J.

AU - Motruk, J.

AU - Szasz, A.

AU - Gross, J. A.

AU - Schuckert, A.

AU - Westerhout, T.

AU - Zhang, Y.

AU - Forati, E.

AU - Rossi, D.

AU - Kobrin, B.

AU - Paolo, A. Di

AU - Klots, A. R.

AU - Drozdov, I.

AU - Kurilovich, V.

AU - Petukhov, A.

AU - Ioffe, L. B.

AU - Elben, A.

AU - Rath, A.

AU - Vitale, V.

AU - Vermersch, B.

AU - Acharya, R.

AU - Beni, L. A.

AU - Anderson, K.

AU - Ansmann, M.

AU - Arute, F.

AU - Arya, K.

AU - Asfaw, A.

AU - Atalaya, J.

AU - Ballard, B.

AU - Bardin, J. C.

AU - Bengtsson, A.

AU - Bilmes, A.

AU - Bortoli, G.

AU - Bourassa, A.

AU - Bovaird, J.

AU - Brill, L.

AU - Broughton, M.

AU - Browne, D. A.

AU - Buchea, B.

AU - Buckley, B. B.

AU - Buell, D. A.

AU - Burger, T.

AU - Burkett, B.

AU - Bushnell, N.

AU - Cabrera, A.

AU - Campero, J.

AU - Chang, H. S.

AU - Chen, Z.

AU - Chiaro, B.

AU - Claes, J.

AU - Cleland, A. Y.

AU - Cogan, J.

AU - Collins, R.

AU - Conner, P.

AU - Courtney, W.

AU - Crook, A. L.

AU - Das, S.

AU - Debroy, D. M.

AU - Lorenzo, L. De

AU - Barba, A. Del Toro

AU - Demura, S.

AU - Donohoe, P.

AU - Dunsworth, A.

AU - Earle, C.

AU - Eickbusch, A.

AU - Elbag, A. M.

AU - Elzouka, M.

AU - Erickson, C.

AU - Faoro, L.

AU - Fatemi, R.

AU - Ferreira, V. S.

AU - Burgos, L. Flores

AU - Fowler, A. G.

AU - Foxen, B.

AU - Ganjam, S.

AU - Gasca, R.

AU - Giang, W.

AU - Gidney, C.

AU - Gilboa, D.

AU - Giustina, M.

AU - Gosula, R.

AU - Dau, A. Grajales

AU - Graumann, D.

AU - Greene, A.

AU - Habegger, S.

AU - Hamilton, M. C.

AU - Hansen, M.

AU - Harrigan, M. P.

AU - Harrington, S. D.

AU - Heslin, S.

AU - Heu, P.

AU - Hill, G.

AU - Hoffmann, M. R.

AU - Huang, H. Y.

AU - Huang, T.

AU - Huff, A.

AU - Huggins, W. J.

AU - Isakov, S. V.

AU - Jeffrey, E.

AU - Jiang, Z.

AU - Jones, C.

AU - Jordan, S.

AU - Joshi, C.

AU - Juhas, P.

AU - Kafri, D.

AU - Kang, H.

AU - Kechedzhi, K.

AU - Khaire, T.

AU - Khattar, T.

AU - Khezri, M.

AU - Kieferová, M.

AU - Kim, S.

AU - Kitaev, A.

AU - Klimov, P.

AU - Korotkov, A. N.

AU - Kostritsa, F.

AU - Kreikebaum, J. M.

AU - Landhuis, D.

AU - Langley, B. W.

AU - Laptev, P.

AU - Lau, K. M.

AU - Guevel, L. Le

AU - Ledford, J.

AU - Lee, J.

AU - Lee, K. W.

AU - Lensky, Y. D.

AU - Lester, B. J.

AU - Li, W. Y.

AU - Lill, A. T.

AU - Liu, W.

AU - Livingston, W. P.

AU - Locharla, A.

AU - Lundahl, D.

AU - Lunt, A.

AU - Madhuk, S.

AU - Maloney, A.

AU - Mandrà, S.

AU - Martin, L. S.

AU - Martin, O.

AU - Martin, S.

AU - Maxfield, C.

AU - McClean, J. R.

AU - McEwen, M.

AU - Meeks, S.

AU - Miao, K. C.

AU - Mieszala, A.

AU - Molina, S.

AU - Montazeri, S.

AU - Morvan, A.

AU - Movassagh, R.

AU - Neill, C.

AU - Nersisyan, A.

AU - Newman, M.

AU - Nguyen, A.

AU - Nguyen, M.

AU - Ni, C. H.

AU - Niu, M. Y.

AU - Oliver, W. D.

AU - Ottosson, K.

AU - Pizzuto, A.

AU - Potter, R.

AU - Pritchard, O.

AU - Pryadko, L. P.

AU - Quintana, C.

AU - Reagor, M. J.

AU - Rhodes, D. M.

AU - Roberts, G.

AU - Rocque, C.

AU - Rosenberg, E.

AU - Rubin, N. C.

AU - Saei, N.

AU - Sankaragomathi, K.

AU - Satzinger, K. J.

AU - Schurkus, H. F.

AU - Schuster, C.

AU - Shearn, M. J.

AU - Shorter, A.

AU - Shutty, N.

AU - Shvarts, V.

AU - Sivak, V.

AU - Skruzny, J.

AU - Small, S.

AU - Smith, W. Clarke

AU - Springer, S.

AU - Sterling, G.

AU - Suchard, J.

AU - Szalay, M.

AU - Sztein, A.

AU - Thor, D.

AU - Torres, A.

AU - Torunbalci, M. M.

AU - Vaishnav, A.

AU - Vdovichev, S.

AU - Villalonga, B.

AU - Heidweiller, C. Vollgraff

AU - Waltman, S.

AU - Wang, S. X.

AU - White, T.

AU - Wong, K.

AU - Woo, B. W.K.

AU - Xing, C.

AU - Yao, Z. Jamie

AU - Yeh, P.

AU - Ying, B.

AU - Yoo, J.

AU - Yosri, N.

AU - Young, G.

AU - Zalcman, A.

AU - Zhu, N.

AU - Zobrist, N.

AU - Neven, H.

AU - Babbush, R.

AU - Boixo, S.

AU - Hilton, J.

AU - Lucero, E.

AU - Megrant, A.

AU - Kelly, J.

AU - Chen, Y.

AU - Smelyanskiy, V.

AU - Vidal, G.

AU - Roushan, P.

AU - Läuchli, A. M.

AU - Abanin, D. A.

AU - Mi, X.

PY - 2025/2/6

Y1 - 2025/2/6

N2 - Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions3 in the XY model, as well as signatures of the classical Kosterlitz–Thouless phase transition4. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis5, 6–7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

AB - Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions3 in the XY model, as well as signatures of the classical Kosterlitz–Thouless phase transition4. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis5, 6–7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

UR - http://www.scopus.com/inward/record.url?scp=85218271445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85218271445&partnerID=8YFLogxK

U2 - 10.1038/s41586-024-08460-3

DO - 10.1038/s41586-024-08460-3

M3 - Article

C2 - 39910386

AN - SCOPUS:85218271445

SN - 0028-0836

VL - 638

SP - 79

EP - 85

JO - Nature

JF - Nature

IS - 8049

ER -

Thermalization and criticality on an analogue–digital quantum simulator

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