Phase transitions in random circuit sampling

Morvan, A.; Villalonga, B.; Mi, X.; Mandrà, S.; Bengtsson, A.; Klimov, P. V.; Chen, Z.; Hong, S.; Erickson, C.; Drozdov, I. K.; Chau, J.; Laun, G.; Movassagh, R.; Asfaw, A.; Brandão, L. T. A. N.; Peralta, R.; Abanin, D.; Acharya, R.; Allen, R.; Andersen, T. I.; Anderson, K.; Ansmann, M.; Arute, F.; Arya, K.; Atalaya, J.; Bardin, J. C.; Bilmes, A.; Bortoli, G.; Bourassa, A.; Bovaird, J.; Brill, L.; Broughton, M.; Buckley, B. B.; Buell, D. A.; Burger, T.; Burkett, B.; Bushnell, N.; Campero, J.; Chang, H.-S.; Chiaro, B.; Chik, D.; Chou, C.; Cogan, J.; Collins, R.; Conner, P.; Courtney, W.; Crook, A. L.; Curtin, B.; Debroy, D. M.; Barba, A. Del Toro; Demura, S.; Paolo, A. Di; Dunsworth, A.; Faoro, L.; Farhi, E.; Fatemi, R.; Ferreira, V. S.; Burgos, L. Flores; Forati, E.; Fowler, A. G.; Foxen, B.; Garcia, G.; Genois, É.; Giang, W.; Gidney, C.; Gilboa, D.; Giustina, M.; Gosula, R.; Dau, A. Grajales; Gross, J. A.; Habegger, S.; Hamilton, M. C.; Hansen, M.; Harrigan, M. P.; Harrington, S. D.; Heu, P.; Hoffmann, M. R.; Huang, T.; Huff, A.; Huggins, W. J.; Ioffe, L. B.; Isakov, S. V.; Iveland, J.; Jeffrey, E.; Jiang, Z.; Jones, C.; Juhas, P.; Kafri, D.; Khattar, T.; Khezri, M.; Kieferová, M.; Kim, S.; Kitaev, A.; Klots, A. R.; Korotkov, A. N.; Kostritsa, F.; Kreikebaum, J. M.; Landhuis, D.; Laptev, P.; Lau, K.-M.; Laws, L.; Lee, J.; Lee, K. W.; Lensky, Y. D.; Lester, B. J.; Lill, A. T.; Liu, W.; Livingston, W. P.; Locharla, A.; Malone, F. D.; Martin, O.; Martin, S.; McClean, J. R.; McEwen, M.; Miao, K. C.; Mieszala, A.; Montazeri, S.; Mruczkiewicz, W.; Naaman, O.; Neeley, M.; Neill, C.; Nersisyan, A.; Newman, M.; Ng, J. H.; Nguyen, A.; Nguyen, M.; Niu, M. Yuezhen; O’Brien, T. E.; Omonije, S.; Opremcak, A.; Petukhov, A.; Potter, R.; Pryadko, L. P.; Quintana, C.; Rhodes, D. M.; Rocque, C.; Rosenberg, E.; Rubin, N. C.; Saei, N.; Sank, D.; Sankaragomathi, K.; Satzinger, K. J.; Schurkus, H. F.; Schuster, C.; Shearn, M. J.; Shorter, A.; Shutty, N.; Shvarts, V.; Sivak, V.; Skruzny, J.; Smith, W. C.; Somma, R. D.; Sterling, G.; Strain, D.; Szalay, M.; Thor, D.; Torres, A.; Vidal, G.; Heidweiller, C. Vollgraff; White, T.; Woo, B. W. K.; Xing, C.; Yao, Z. J.; Yeh, P.; Yoo, J.; Young, G.; Zalcman, A.; Zhang, Y.; Zhu, N.; Zobrist, N.; Rieffel, E. G.; Biswas, R.; Babbush, R.; Bacon, D.; Hilton, J.; Lucero, E.; Neven, H.; Megrant, A.; Kelly, J.; Roushan, P.; Aleiner, I.; Smelyanskiy, V.; Kechedzhi, K.; Chen, Y.; Boixo, S.

Phase transitions in random circuit sampling

A. Morvan, B. Villalonga, X. Mi, S. Mandrà, A. Bengtsson, P. V. Klimov, Z. Chen, S. Hong, C. Erickson, I. K. Drozdov, J. Chau, G. Laun, R. Movassagh, A. Asfaw, L. T. A. N. Brandão, R. Peralta, D. Abanin, R. Acharya, R. Allen, T. I. Andersen, K. Anderson, M. Ansmann, F. Arute, K. Arya, J. Atalaya, J. C. Bardin, A. Bilmes, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, B. B. Buckley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, J. Campero, H.-S. Chang, B. Chiaro, D. Chik, C. Chou, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, D. M. Debroy, A. Del Toro Barba, S. Demura, A. Di Paolo, A. Dunsworth, L. Faoro, E. Farhi, R. Fatemi, V. S. Ferreira, L. Flores Burgos, E. Forati, A. G. Fowler, B. Foxen, G. Garcia, É. Genois, W. Giang, C. Gidney, D. Gilboa, M. Giustina, R. Gosula, A. Grajales Dau, J. A. Gross, S. Habegger, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harrington, P. Heu, M. R. Hoffmann, T. Huang, A. Huff, W. J. Huggins, L. B. Ioffe, S. V. Isakov, J. Iveland, E. Jeffrey, Z. Jiang, C. Jones, P. Juhas, D. Kafri, T. Khattar, M. Khezri, M. Kieferová, S. Kim, A. Kitaev, A. R. Klots, A. N. Korotkov, F. Kostritsa, J. M. Kreikebaum, D. Landhuis, P. Laptev, K.-M. Lau, L. Laws, J. Lee, K. W. Lee, Y. D. Lensky, B. J. Lester, A. T. Lill, W. Liu, W. P. Livingston, A. Locharla, F. D. Malone, O. Martin, S. Martin, J. R. McClean, M. McEwen, K. C. Miao, A. Mieszala, S. Montazeri, W. Mruczkiewicz, O. Naaman, M. Neeley, C. Neill, A. Nersisyan, M. Newman, J. H. Ng, A. Nguyen, M. Nguyen, M. Yuezhen Niu, T. E. O’Brien, S. Omonije, A. Opremcak, A. Petukhov, R. Potter, L. P. Pryadko, C. Quintana, D. M. Rhodes, C. Rocque, E. Rosenberg, N. C. Rubin, N. Saei, D. Sank, K. Sankaragomathi, K. J. Satzinger, H. F. Schurkus, C. Schuster, M. J. Shearn, A. Shorter, N. Shutty, V. Shvarts, V. Sivak, J. Skruzny, W. C. Smith, R. D. Somma, G. Sterling, D. Strain, M. Szalay, D. Thor, A. Torres, G. Vidal, C. Vollgraff Heidweiller, T. White, B. W. K. Woo, C. Xing, Z. J. Yao, P. Yeh, J. Yoo, G. Young, A. Zalcman, Y. Zhang, N. Zhu, N. Zobrist, E. G. Rieffel, R. Biswas, R. Babbush, D. Bacon, J. Hilton, E. Lucero, H. Neven, A. Megrant, J. Kelly, P. Roushan, I. Aleiner, V. Smelyanskiy, K. Kechedzhi (), Y. Chen and S. Boixo
Additional contact information
A. Morvan: Google Research
B. Villalonga: Google Research
X. Mi: Google Research
S. Mandrà: Google Research
A. Bengtsson: Google Research
P. V. Klimov: Google Research
Z. Chen: Google Research
S. Hong: Google Research
C. Erickson: Google Research
I. K. Drozdov: Google Research
J. Chau: Google Research
G. Laun: Google Research
R. Movassagh: Google Research
A. Asfaw: Google Research
L. T. A. N. Brandão: Strativia, Foreign Guest Researcher (Contractor) at National Institute of Standards and Technology (NIST)
R. Peralta: National Institute of Standards and Technology (NIST)
D. Abanin: Google Research
R. Acharya: Google Research
R. Allen: Google Research
T. I. Andersen: Google Research
K. Anderson: Google Research
M. Ansmann: Google Research
F. Arute: Google Research
K. Arya: Google Research
J. Atalaya: Google Research
J. C. Bardin: Google Research
A. Bilmes: Google Research
G. Bortoli: Google Research
A. Bourassa: Google Research
J. Bovaird: Google Research
L. Brill: Google Research
M. Broughton: Google Research
B. B. Buckley: Google Research
D. A. Buell: Google Research
T. Burger: Google Research
B. Burkett: Google Research
N. Bushnell: Google Research
J. Campero: Google Research
H.-S. Chang: Google Research
B. Chiaro: Google Research
D. Chik: Google Research
C. Chou: 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
D. M. Debroy: Google Research
A. Del Toro Barba: Google Research
S. Demura: Google Research
A. Di Paolo: Google Research
A. Dunsworth: Google Research
L. Faoro: Google Research
E. Farhi: Google Research
R. Fatemi: 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
G. Garcia: Google Research
É. Genois: Google Research
W. Giang: Google Research
C. Gidney: Google Research
D. Gilboa: Google Research
M. Giustina: Google Research
R. Gosula: Google Research
A. Grajales Dau: Google Research
J. A. Gross: Google Research
S. Habegger: Google Research
M. C. Hamilton: Google Research
M. Hansen: Google Research
M. P. Harrigan: Google Research
S. D. Harrington: Google Research
P. Heu: Google Research
M. R. Hoffmann: Google Research
T. Huang: Google Research
A. Huff: Google Research
W. J. Huggins: Google Research
L. B. Ioffe: Google Research
S. V. Isakov: Google Research
J. Iveland: Google Research
E. Jeffrey: Google Research
Z. Jiang: Google Research
C. Jones: Google Research
P. Juhas: Google Research
D. Kafri: Google Research
T. Khattar: Google Research
M. Khezri: Google Research
M. Kieferová: Google Research
S. Kim: Google Research
A. Kitaev: Google Research
A. R. Klots: Google Research
A. N. Korotkov: Google Research
F. Kostritsa: Google Research
J. M. Kreikebaum: Google Research
D. Landhuis: Google Research
P. Laptev: Google Research
K.-M. Lau: Google Research
L. Laws: Google Research
J. Lee: Google Research
K. W. Lee: Google Research
Y. D. Lensky: Google Research
B. J. Lester: Google Research
A. T. Lill: Google Research
W. Liu: Google Research
W. P. Livingston: Google Research
A. Locharla: Google Research
F. D. Malone: Google Research
O. Martin: Google Research
S. Martin: Google Research
J. R. McClean: Google Research
M. McEwen: Google Research
K. C. Miao: Google Research
A. Mieszala: Google Research
S. Montazeri: Google Research
W. Mruczkiewicz: Google Research
O. Naaman: Google Research
M. Neeley: Google Research
C. Neill: Google Research
A. Nersisyan: Google Research
M. Newman: Google Research
J. H. Ng: Google Research
A. Nguyen: Google Research
M. Nguyen: Google Research
M. Yuezhen Niu: Google Research
T. E. O’Brien: Google Research
S. Omonije: Google Research
A. Opremcak: Google Research
A. Petukhov: Google Research
R. Potter: Google Research
L. P. Pryadko: University of California
C. Quintana: Google Research
D. M. Rhodes: Google Research
C. Rocque: Google Research
E. Rosenberg: Google Research
N. C. Rubin: Google Research
N. Saei: Google Research
D. Sank: Google Research
K. Sankaragomathi: Google Research
K. J. Satzinger: Google Research
H. F. Schurkus: Google Research
C. Schuster: Google Research
M. J. Shearn: Google Research
A. Shorter: Google Research
N. Shutty: Google Research
V. Shvarts: Google Research
V. Sivak: Google Research
J. Skruzny: Google Research
W. C. Smith: Google Research
R. D. Somma: Google Research
G. Sterling: Google Research
D. Strain: Google Research
M. Szalay: Google Research
D. Thor: Google Research
A. Torres: Google Research
G. Vidal: Google Research
C. Vollgraff Heidweiller: Google Research
T. White: Google Research
B. W. K. Woo: Google Research
C. Xing: Google Research
Z. J. Yao: Google Research
P. Yeh: Google Research
J. Yoo: Google Research
G. Young: Google Research
A. Zalcman: Google Research
Y. Zhang: Google Research
N. Zhu: Google Research
N. Zobrist: Google Research
E. G. Rieffel: NASA Ames Research Center
R. Biswas: NASA Ames Research Center
R. Babbush: Google Research
D. Bacon: Google Research
J. Hilton: Google Research
E. Lucero: Google Research
H. Neven: Google Research
A. Megrant: Google Research
J. Kelly: Google Research
P. Roushan: Google Research
I. Aleiner: Google Research
V. Smelyanskiy: Google Research
K. Kechedzhi: Google Research
Y. Chen: Google Research
S. Boixo: Google Research

Nature, 2024, vol. 634, issue 8033, 328-333

Abstract: Abstract Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors1. It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available2–8. Nevertheless, quantum algorithms’ outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.

Date: 2024
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DOI: 10.1038/s41586-024-07998-6

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