Visualizing dynamics of charges and strings in (2 + 1)D lattice gauge theories

Cochran, T. A.; Jobst, B.; Rosenberg, E.; Lensky, Y. D.; Gyawali, G.; Eassa, N.; Will, M.; Szasz, A.; Abanin, D.; Acharya, R.; Beni, L. Aghababaie; Andersen, T. I.; Ansmann, M.; Arute, F.; Arya, K.; Asfaw, A.; Atalaya, J.; Babbush, R.; Ballard, B.; Bardin, J. C.; Bengtsson, A.; Bilmes, A.; Bourassa, A.; Bovaird, J.; Broughton, M.; Browne, D. A.; Buchea, B.; Buckley, B. B.; Burger, T.; Burkett, B.; Bushnell, N.; Cabrera, A.; Campero, J.; Chang, H.-S.; Chen, Z.; Chiaro, B.; Claes, J.; Cleland, A. Y.; Cogan, J.; Collins, R.; Conner, P.; Courtney, W.; Crook, A. L.; Curtin, B.; Das, S.; Demura, S.; Lorenzo, L.; Paolo, A.; Donohoe, P.; Drozdov, I.; Dunsworth, A.; Eickbusch, A.; Elbag, A. Moshe; Elzouka, M.; Erickson, C.; Ferreira, V. S.; Burgos, L. Flores; Forati, E.; Fowler, A. G.; Foxen, B.; Ganjam, S.; Gasca, R.; Genois, É.; Giang, W.; Gilboa, D.; Gosula, R.; Dau, A. Grajales; Graumann, D.; Greene, A.; Gross, J. A.; Habegger, S.; Hansen, M.; Harrigan, M. P.; Harrington, S. D.; Heu, P.; Higgott, O.; Hilton, J.; Huang, H.-Y.; Huff, A.; Huggins, W.; Jeffrey, E.; Jiang, Z.; Jones, C.; Joshi, C.; Juhas, P.; Kafri, D.; Kang, H.; Karamlou, A. H.; Kechedzhi, K.; Khaire, T.; Khattar, T.; Khezri, M.; Kim, S.; Klimov, P.; Kobrin, B.; Korotkov, A.; Kostritsa, F.; Kreikebaum, J.; Kurilovich, V.; Landhuis, D.; Lange-Dei, T.; Langley, B.; Lau, K.-M.; Ledford, J.; Lee, K.; Lester, B.; Guevel, L.; Li, W.; Lill, A. T.; Livingston, W.; Locharla, A.; Lundahl, D.; Lunt, A.; Madhuk, S.; Maloney, A.; Mandrà, S.; Martin, L.; Martin, O.; Maxfield, C.; McClean, J.; McEwen, M.; Meeks, S.; Megrant, A.; Miao, K.; Molavi, R.; Molina, S.; Montazeri, S.; Movassagh, R.; Neill, C.; Newman, M.; Nguyen, A.; Nguyen, M.; Ni, C.-H.; Ottosson, K.; Pizzuto, A.; Potter, R.; Pritchard, O.; Quintana, C.; Ramachandran, G.; Reagor, M.; Rhodes, D.; Roberts, G.; Sankaragomathi, K.; Satzinger, K.; Schurkus, H.; Shearn, M.; Shorter, A.; Shutty, N.; Shvarts, V.; Sivak, V.; Small, S.; Smith, W. C.; Springer, S.; Sterling, G.; Suchard, J.; Sztein, A.; Thor, D.; Torunbalci, M.; Vaishnav, A.; Vargas, J.; Vdovichev, S.; Vidal, G.; Heidweiller, C. Vollgraff; Waltman, S.; Wang, S. X.; Ware, B.; White, T.; Wong, K.; Woo, B. W. K.; Xing, C.; Yao, Z. Jamie; Yeh, P.; Ying, B.; Yoo, J.; Yosri, N.; Young, G.; Zalcman, A.; Zhang, Y.; Zhu, N.; Zobrist, N.; Boixo, S.; Kelly, J.; Lucero, E.; Chen, Y.; Smelyanskiy, V.; Neven, H.; Gammon-Smith, A.; Pollmann, F.; Knap, M.; Roushan, P.

Visualizing dynamics of charges and strings in (2 + 1)D lattice gauge theories

T. A. Cochran, B. Jobst, E. Rosenberg, Y. D. Lensky, G. Gyawali, N. Eassa, M. Will, A. Szasz, D. Abanin, R. Acharya, L. Aghababaie Beni, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush, B. Ballard, J. C. Bardin, A. Bengtsson, A. Bilmes, A. Bourassa, J. Bovaird, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, 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, B. Curtin, S. Das, S. Demura, L. Lorenzo, A. Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, A. Eickbusch, A. Moshe Elbag, M. Elzouka, C. Erickson, V. S. Ferreira, L. Flores Burgos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, R. Gasca, É. Genois, W. Giang, D. Gilboa, R. Gosula, A. Grajales Dau, D. Graumann, A. Greene, J. A. Gross, S. Habegger, M. Hansen, M. P. Harrigan, S. D. Harrington, P. Heu, O. Higgott, J. Hilton, H.-Y. Huang, A. Huff, W. Huggins, E. Jeffrey, Z. Jiang, C. Jones, C. Joshi, P. Juhas, D. Kafri, H. Kang, A. H. Karamlou, K. Kechedzhi, T. Khaire, T. Khattar, M. Khezri, S. Kim, P. Klimov, B. Kobrin, A. Korotkov, F. Kostritsa, J. Kreikebaum, V. Kurilovich, D. Landhuis, T. Lange-Dei, B. Langley, K.-M. Lau, J. Ledford, K. Lee, B. Lester, L. Guevel, W. Li, A. T. Lill, W. Livingston, A. Locharla, D. Lundahl, A. Lunt, S. Madhuk, A. Maloney, S. Mandrà, L. Martin, O. Martin, C. Maxfield, J. McClean, M. McEwen, S. Meeks, A. Megrant, K. Miao, R. Molavi, S. Molina, S. Montazeri, R. Movassagh, C. Neill, M. Newman, A. Nguyen, M. Nguyen, C.-H. Ni, K. Ottosson, A. Pizzuto, R. Potter, O. Pritchard, C. Quintana, G. Ramachandran, M. Reagor, D. Rhodes, G. Roberts, K. Sankaragomathi, K. Satzinger, H. Schurkus, M. Shearn, A. Shorter, N. Shutty, V. Shvarts, V. Sivak, S. Small, W. C. Smith, S. Springer, G. Sterling, J. Suchard, A. Sztein, D. Thor, M. Torunbalci, A. Vaishnav, J. Vargas, S. Vdovichev, G. Vidal, C. Vollgraff Heidweiller, S. Waltman, S. X. Wang, B. Ware, 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, Y. Zhang, N. Zhu, N. Zobrist, S. Boixo, J. Kelly, E. Lucero, Y. Chen, V. Smelyanskiy, H. Neven, A. Gammon-Smith, F. Pollmann (), M. Knap () and P. Roushan ()
Additional contact information
T. A. Cochran: Google Research
B. Jobst: Technical University of Munich
E. Rosenberg: Google Research
Y. D. Lensky: Google Research
G. Gyawali: Google Research
N. Eassa: Google Research
M. Will: Technical University of Munich
A. Szasz: Google Research
D. Abanin: Google Research
R. Acharya: Google Research
L. Aghababaie Beni: Google Research
T. I. Andersen: Google Research
M. Ansmann: Google Research
F. Arute: Google Research
K. Arya: Google Research
A. Asfaw: Google Research
J. Atalaya: Google Research
R. Babbush: Google Research
B. Ballard: Google Research
J. C. Bardin: Google Research
A. Bengtsson: Google Research
A. Bilmes: Google Research
A. Bourassa: Google Research
J. Bovaird: Google Research
M. Broughton: Google Research
D. A. Browne: Google Research
B. Buchea: Google Research
B. B. Buckley: Google Research
T. Burger: Google Research
B. Burkett: Google Research
N. Bushnell: Google Research
A. Cabrera: Google Research
J. Campero: Google Research
H.-S. Chang: Google Research
Z. Chen: Google Research
B. Chiaro: Google Research
J. Claes: Google Research
A. Y. Cleland: Google Research
J. Cogan: Google Research
R. Collins: Google Research
P. Conner: Google Research
W. Courtney: Google Research
A. L. Crook: Google Research
B. Curtin: Google Research
S. Das: Google Research
S. Demura: Google Research
L. Lorenzo: Google Research
A. Paolo: Google Research
P. Donohoe: Google Research
I. Drozdov: Google Research
A. Dunsworth: Google Research
A. Eickbusch: Google Research
A. Moshe Elbag: Google Research
M. Elzouka: Google Research
C. Erickson: Google Research
V. S. Ferreira: Google Research
L. Flores Burgos: Google Research
E. Forati: Google Research
A. G. Fowler: Google Research
B. Foxen: Google Research
S. Ganjam: Google Research
R. Gasca: Google Research
É. Genois: Google Research
W. Giang: Google Research
D. Gilboa: Google Research
R. Gosula: Google Research
A. Grajales Dau: Google Research
D. Graumann: Google Research
A. Greene: Google Research
J. A. Gross: Google Research
S. Habegger: Google Research
M. Hansen: Google Research
M. P. Harrigan: Google Research
S. D. Harrington: Google Research
P. Heu: Google Research
O. Higgott: Google Research
J. Hilton: Google Research
H.-Y. Huang: Google Research
A. Huff: Google Research
W. Huggins: Google Research
E. Jeffrey: Google Research
Z. Jiang: Google Research
C. Jones: Google Research
C. Joshi: Google Research
P. Juhas: Google Research
D. Kafri: Google Research
H. Kang: Google Research
A. H. Karamlou: Google Research
K. Kechedzhi: Google Research
T. Khaire: Google Research
T. Khattar: Google Research
M. Khezri: Google Research
S. Kim: Google Research
P. Klimov: Google Research
B. Kobrin: Google Research
A. Korotkov: Google Research
F. Kostritsa: Google Research
J. Kreikebaum: Google Research
V. Kurilovich: Google Research
D. Landhuis: Google Research
T. Lange-Dei: Google Research
B. Langley: Google Research
K.-M. Lau: Google Research
J. Ledford: Google Research
K. Lee: Google Research
B. Lester: Google Research
L. Guevel: Google Research
W. Li: Google Research
A. T. Lill: Google Research
W. Livingston: Google Research
A. Locharla: Google Research
D. Lundahl: Google Research
A. Lunt: Google Research
S. Madhuk: Google Research
A. Maloney: Google Research
S. Mandrà: Google Research
L. Martin: Google Research
O. Martin: Google Research
C. Maxfield: Google Research
J. McClean: Google Research
M. McEwen: Google Research
S. Meeks: Google Research
A. Megrant: Google Research
K. Miao: Google Research
R. Molavi: Google Research
S. Molina: Google Research
S. Montazeri: Google Research
R. Movassagh: Google Research
C. Neill: Google Research
M. Newman: Google Research
A. Nguyen: Google Research
M. Nguyen: Google Research
C.-H. Ni: Google Research
K. Ottosson: Google Research
A. Pizzuto: Google Research
R. Potter: Google Research
O. Pritchard: Google Research
C. Quintana: Google Research
G. Ramachandran: Google Research
M. Reagor: Google Research
D. Rhodes: Google Research
G. Roberts: Google Research
K. Sankaragomathi: Google Research
K. Satzinger: Google Research
H. Schurkus: Google Research
M. Shearn: Google Research
A. Shorter: Google Research
N. Shutty: Google Research
V. Shvarts: Google Research
V. Sivak: Google Research
S. Small: Google Research
W. C. Smith: Google Research
S. Springer: Google Research
G. Sterling: Google Research
J. Suchard: Google Research
A. Sztein: Google Research
D. Thor: Google Research
M. Torunbalci: Google Research
A. Vaishnav: Google Research
J. Vargas: Google Research
S. Vdovichev: Google Research
G. Vidal: Google Research
C. Vollgraff Heidweiller: Google Research
S. Waltman: Google Research
S. X. Wang: Google Research
B. Ware: Google Research
T. White: Google Research
K. Wong: Google Research
B. W. K. Woo: Google Research
C. Xing: Google Research
Z. Jamie Yao: Google Research
P. Yeh: Google Research
B. Ying: Google Research
J. Yoo: Google Research
N. Yosri: Google Research
G. Young: Google Research
A. Zalcman: Google Research
Y. Zhang: Google Research
N. Zhu: Google Research
N. Zobrist: Google Research
S. Boixo: Google Research
J. Kelly: Google Research
E. Lucero: Google Research
Y. Chen: Google Research
V. Smelyanskiy: Google Research
H. Neven: Google Research
A. Gammon-Smith: University of Nottingham
F. Pollmann: Technical University of Munich
M. Knap: Technical University of Munich
P. Roushan: Google Research

Nature, 2025, vol. 642, issue 8067, 315-320

Abstract: Abstract Lattice gauge theories (LGTs)1–4 can be used to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials5–7. Studying dynamical properties of emergent phases can be challenging, as it requires solving many-body problems that are generally beyond perturbative limits8–10. Here we investigate the dynamics of local excitations in a $${{\mathbb{Z}}}_{2}$$ Z 2 LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit that prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics by means of a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT, from which we uncover two distinct regimes inside the confining phase: for weak confinement, the string fluctuates strongly in the transverse direction, whereas for strong confinement, transverse fluctuations are effectively frozen11,12. We also demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a new set of techniques for investigating emergent excitations and string dynamics.

Date: 2025
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DOI: 10.1038/s41586-025-08999-9

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