Scaling and logic in the colour code on a superconducting quantum processor

Lacroix, N.; Bourassa, A.; Heras, F. J. H.; Zhang, L. M.; Bausch, J.; Senior, A. W.; Edlich, T.; Shutty, N.; Sivak, V.; Bengtsson, A.; McEwen, M.; Higgott, O.; Kafri, D.; Claes, J.; Morvan, A.; Chen, Z.; Zalcman, A.; Madhuk, S.; Acharya, R.; Beni, L. Aghababaie; Aigeldinger, G.; Alcaraz, R.; Andersen, T. I.; Ansmann, M.; Arute, F.; Arya, K.; Asfaw, A.; Atalaya, J.; Babbush, R.; Ballard, B.; Bardin, J. C.; Bilmes, A.; Blackwell, S.; Bovaird, J.; Bowers, D.; Brill, L.; Broughton, M.; Browne, D. A.; Buchea, B.; Buckley, B. B.; Burger, T.; Burkett, B.; Bushnell, N.; Cabrera, A.; Campero, J.; Chang, H.-S.; Chiaro, B.; Chih, L.-Y.; Cleland, A. Y.; Cogan, J.; Collins, R.; Conner, P.; Courtney, W.; Crook, A. L.; Curtin, B.; Das, S.; Demura, S.; De Lorenzo, L.; Paolo, A. Di; 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.; Garcia, G.; Gasca, R.; Genois, É.; Giang, W.; Gilboa, D.; Gosula, R.; Dau, A. Grajales; Graumann, D.; Greene, A.; Gross, J. A.; Ha, T.; Habegger, S.; Hansen, M.; Harrigan, M. P.; Harrington, S. D.; Heslin, S.; Heu, P.; Hiltermann, R.; Hilton, J.; Hong, S.; Huang, H.-Y.; Huff, A.; Huggins, W. J.; Jeffrey, E.; Jiang, Z.; Jin, X.; Joshi, C.; Juhas, P.; Kabel, A.; Kang, H.; Karamlou, A. H.; Kechedzhi, K.; Khaire, T.; Khattar, T.; Khezri, M.; Kim, S.; Klimov, P. V.; Kobrin, B.; Korotkov, A. N.; Kostritsa, F.; Kreikebaum, J. Mark; Kurilovich, V. D.; Landhuis, D.; Lange-Dei, T.; Langley, B. W.; Laptev, P.; Lau, K.-M.; Ledford, J.; Lee, K.; Lester, B. J.; Guevel, L. Le; Li, W. Yan; Li, Y.; Lill, A. T.; Livingston, W. P.; Locharla, A.; Lucero, E.; Lundahl, D.; Lunt, A.; Maloney, A.; Mandrà, S.; Martin, L. S.; Martin, O.; Maxfield, C.; McClean, J. R.; Meeks, S.; Megrant, A.; Miao, K. C.; Molavi, R.; Molina, S.; Montazeri, S.; Movassagh, R.; Neill, C.; Newman, M.; Nguyen, A.; Nguyen, M.; Ni, C.-H.; Niu, M. Y.; Oas, L.; Oliver, W. D.; Orosco, R.; Ottosson, K.; Pizzuto, A.; Potter, R.; Pritchard, O.; Quintana, C.; Ramachandran, G.; Reagor, M. J.; Resnick, R.; Rhodes, D. M.; Roberts, G.; Rosenberg, E.; Rosenfeld, E.; Rossi, E.; Roushan, P.; Sankaragomathi, K.; Schurkus, H. F.; Shearn, M. J.; Shorter, A.; Shvarts, V.; Small, S.; Smith, W. Clarke; Springer, S.; Sterling, G.; Suchard, J.; Szasz, A.; Sztein, A.; Thor, D.; Tomita, E.; Torres, A.; Torunbalci, M. Mert; Vaishnav, A.; Vargas, J.; Vdovichev, S.; Vidal, G.; Heidweiller, C. Vollgraff; Waltman, S.; Waltz, J.; Wang, S. X.; Ware, B.; Weidel, T.; White, T.; Wong, K.; Woo, B. W. K.; Woodson, M.; Xing, C.; Yao, Z. Jamie; Yeh, P.; Ying, B.; Yoo, J.; Yosri, N.; Young, G.; Zhang, Y.; Zhu, N.; Zobrist, N.; Neven, H.; Kohli, P.; Davies, A.; Boixo, S.; Kelly, J.; Jones, C.; Gidney, C.; Satzinger, K. J.

Scaling and logic in the colour code on a superconducting quantum processor

N. Lacroix (), A. Bourassa (), F. J. H. Heras, L. M. Zhang, J. Bausch, A. W. Senior, T. Edlich, N. Shutty, V. Sivak, A. Bengtsson, M. McEwen, O. Higgott, D. Kafri, J. Claes, A. Morvan, Z. Chen, A. Zalcman, S. Madhuk, R. Acharya, L. Aghababaie Beni, G. Aigeldinger, R. Alcaraz, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush, B. Ballard, J. C. Bardin, A. Bilmes, S. Blackwell, J. Bovaird, D. Bowers, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, B. Chiaro, L.-Y. Chih, A. Y. Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, S. Demura, L. De Lorenzo, A. Di 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, G. Garcia, R. Gasca, É. Genois, W. Giang, D. Gilboa, R. Gosula, A. Grajales Dau, D. Graumann, A. Greene, J. A. Gross, T. Ha, S. Habegger, M. Hansen, M. P. Harrigan, S. D. Harrington, S. Heslin, P. Heu, R. Hiltermann, J. Hilton, S. Hong, H.-Y. Huang, A. Huff, W. J. Huggins, E. Jeffrey, Z. Jiang, X. Jin, C. Joshi, P. Juhas, A. Kabel, H. Kang, A. H. Karamlou, K. Kechedzhi, T. Khaire, T. Khattar, M. Khezri, S. Kim, P. V. Klimov, B. Kobrin, A. N. Korotkov, F. Kostritsa, J. Mark Kreikebaum, V. D. Kurilovich, D. Landhuis, T. Lange-Dei, B. W. Langley, P. Laptev, K.-M. Lau, J. Ledford, K. Lee, B. J. Lester, L. Le Guevel, W. Yan Li, Y. Li, A. T. Lill, W. P. Livingston, A. Locharla, E. Lucero, D. Lundahl, A. Lunt, A. Maloney, S. Mandrà, L. S. Martin, O. Martin, C. Maxfield, J. R. McClean, S. Meeks, A. Megrant, K. C. Miao, R. Molavi, S. Molina, S. Montazeri, R. Movassagh, C. Neill, M. Newman, A. Nguyen, M. Nguyen, C.-H. Ni, M. Y. Niu, L. Oas, W. D. Oliver, R. Orosco, K. Ottosson, A. Pizzuto, R. Potter, O. Pritchard, C. Quintana, G. Ramachandran, M. J. Reagor, R. Resnick, D. M. Rhodes, G. Roberts, E. Rosenberg, E. Rosenfeld, E. Rossi, P. Roushan, K. Sankaragomathi, H. F. Schurkus, M. J. Shearn, A. Shorter, V. Shvarts, S. Small, W. Clarke Smith, S. Springer, G. Sterling, J. Suchard, A. Szasz, A. Sztein, D. Thor, E. Tomita, A. Torres, M. Mert Torunbalci, A. Vaishnav, J. Vargas, S. Vdovichev, G. Vidal, C. Vollgraff Heidweiller, S. Waltman, J. Waltz, S. X. Wang, B. Ware, T. Weidel, T. White, K. Wong, B. W. K. Woo, M. Woodson, C. Xing, Z. Jamie Yao, P. Yeh, B. Ying, J. Yoo, N. Yosri, G. Young, Y. Zhang, N. Zhu, N. Zobrist, H. Neven, P. Kohli, A. Davies, S. Boixo, J. Kelly, C. Jones, C. Gidney and K. J. Satzinger ()
Additional contact information
N. Lacroix: Google Research
A. Bourassa: Google Research
F. J. H. Heras: Google DeepMind
L. M. Zhang: Google DeepMind
J. Bausch: Google DeepMind
A. W. Senior: Google DeepMind
T. Edlich: Google DeepMind
N. Shutty: Google Research
V. Sivak: Google Research
A. Bengtsson: Google Research
M. McEwen: Google Research
O. Higgott: Google Research
D. Kafri: Google Research
J. Claes: Google Research
A. Morvan: Google Research
Z. Chen: Google Research
A. Zalcman: Google Research
S. Madhuk: Google Research
R. Acharya: Google Research
L. Aghababaie Beni: Google Research
G. Aigeldinger: Google Research
R. Alcaraz: 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. Bilmes: Google Research
S. Blackwell: Google DeepMind
J. Bovaird: Google Research
D. Bowers: Google Research
L. Brill: 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
B. Chiaro: Google Research
L.-Y. Chih: 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. De Lorenzo: Google Research
A. Di 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
G. Garcia: 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
T. Ha: Google Research
S. Habegger: Google Research
M. Hansen: Google Research
M. P. Harrigan: Google Research
S. D. Harrington: Google Research
S. Heslin: Google Research
P. Heu: Google Research
R. Hiltermann: Google Research
J. Hilton: Google Research
S. Hong: Google Research
H.-Y. Huang: Google Research
A. Huff: Google Research
W. J. Huggins: Google Research
E. Jeffrey: Google Research
Z. Jiang: Google Research
X. Jin: Google Research
C. Joshi: Google Research
P. Juhas: Google Research
A. Kabel: 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. V. Klimov: Google Research
B. Kobrin: Google Research
A. N. Korotkov: Google Research
F. Kostritsa: Google Research
J. Mark Kreikebaum: Google Research
V. D. Kurilovich: Google Research
D. Landhuis: Google Research
T. Lange-Dei: Google Research
B. W. Langley: Google Research
P. Laptev: Google Research
K.-M. Lau: Google Research
J. Ledford: Google Research
K. Lee: Google Research
B. J. Lester: Google Research
L. Le Guevel: Google Research
W. Yan Li: Google Research
Y. Li: Google DeepMind
A. T. Lill: Google Research
W. P. Livingston: Google Research
A. Locharla: Google Research
E. Lucero: Google Research
D. Lundahl: Google Research
A. Lunt: Google Research
A. Maloney: Google Research
S. Mandrà: Google Research
L. S. Martin: Google Research
O. Martin: Google Research
C. Maxfield: Google Research
J. R. McClean: Google Research
S. Meeks: Google Research
A. Megrant: Google Research
K. C. 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
M. Y. Niu: Google Research
L. Oas: Google Research
W. D. Oliver: Google Research
R. Orosco: 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. J. Reagor: Google Research
R. Resnick: Google Research
D. M. Rhodes: Google Research
G. Roberts: Google Research
E. Rosenberg: Google Research
E. Rosenfeld: Google Research
E. Rossi: Google Research
P. Roushan: Google Research
K. Sankaragomathi: Google Research
H. F. Schurkus: Google Research
M. J. Shearn: Google Research
A. Shorter: Google Research
V. Shvarts: Google Research
S. Small: Google Research
W. Clarke Smith: Google Research
S. Springer: Google Research
G. Sterling: Google Research
J. Suchard: Google Research
A. Szasz: Google Research
A. Sztein: Google Research
D. Thor: Google Research
E. Tomita: Google Research
A. Torres: Google Research
M. Mert 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
J. Waltz: Google Research
S. X. Wang: Google Research
B. Ware: Google Research
T. Weidel: Google Research
T. White: Google Research
K. Wong: Google Research
B. W. K. Woo: Google Research
M. Woodson: 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
Y. Zhang: Google Research
N. Zhu: Google Research
N. Zobrist: Google Research
H. Neven: Google Research
P. Kohli: Google DeepMind
A. Davies: Google DeepMind
S. Boixo: Google Research
J. Kelly: Google Research
C. Jones: Google Research
C. Gidney: Google Research
K. J. Satzinger: Google Research

Nature, 2025, vol. 645, issue 8081, 614-619

Abstract: Abstract Quantum error correction1–4 is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors5–8 have focused primarily on the surface code9, which offers a high error threshold but poses limitations for logical operations. The colour code10 enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and realizations of colour codes11–19 have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor8. Scaling the code distance from three to five suppresses logical errors by a factor of Λ3/5 = 1.56(4). Simulations indicate this performance is below the threshold of the colour code, and the colour code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking20 and inject magic states21, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery22. This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

Date: 2025
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