Realizing topologically ordered states on a quantum processor

Satzinger, K. J.; Liu, Y.-J; Smith, A.; Knapp, C.; Newman, M.; Jones, C.; Chen, Z.; Quintana, C.; Mi, X.; Dunsworth, A.; Gidney, C.; Aleiner, I.; Arute, F.; Arya, K.; Atalaya, J.; Babbush, R.; Bardin, J. C.; Barends, R.; Basso, J.; Bengtsson, A.; Bilmes, A.; Broughton, M.; Buckley, B. B.; Buell, D. A.; Burkett, B.; Bushnell, N.; Chiaro, B.; Collins, R.; Courtney, W.; Demura, S.; Derk, A. R.; Eppens, D.; Erickson, C.; Faoro, L.; Farhi, E.; Fowler, A. G.; Foxen, B.; Giustina, M.; Greene, A.; Gross, J. A.; Harrigan, M. P.; Harrington, S. D.; Hilton, J.; Hong, S.; Huang, T.; Huggins, W. J.; Ioffe, L. B.; Isakov, S. V.; Jeffrey, E.; Jiang, Z.; Kafri, D.; Kechedzhi, K.; Khattar, T.; Kim, S.; Klimov, P. V.; Korotkov, A. N.; Kostritsa, F.; Landhuis, D.; Laptev, P.; Locharla, A.; Lucero, E.; Martin, O.; McClean, J. R.; McEwen, M.; Miao, K. C.; Mohseni, M.; Montazeri, S.; Mruczkiewicz, W.; Mutus, J.; Naaman, O.; Neeley, M.; Neill, C.; Niu, M. Y.; O’Brien, T. E.; Opremcak, A.; Pató, B.; Petukhov, A.; Rubin, N. C.; Sank, D.; Shvarts, V.; Strain, D.; Szalay, M.; Villalonga, B.; White, T. C.; Yao, Z.; Yeh, P.; Yoo, J.; Zalcman, A.; Neven, H.; Boixo, S.; Megrant, A.; Chen, Y.; Kelly, J.; Smelyanskiy, V.; Kitaev, A.; Knap, M.; Pollmann, F.; Roushan, P.

doi:10.1126/science.abi8378

Realizing topologically ordered states on a quantum processor

Satzinger, K. J.; Liu, Y.-J; Smith, A.; Knapp, C.; Newman, M.; Jones, C.; Chen, Z.; Quintana, C.; Mi, X.; Dunsworth, A.; Gidney, C.; Aleiner, I.; Arute, F.; Arya, K.; Atalaya, J.; Babbush, R.; Bardin, J. C.; Barends, R.; Basso, J.; Bengtsson, A.; Bilmes, A.; Broughton, M.; Buckley, B. B.; Buell, D. A.; Burkett, B.; Bushnell, N.; Chiaro, B.; Collins, R.; Courtney, W.; Demura, S.; Derk, A. R.; Eppens, D.; Erickson, C.; Faoro, L.; Farhi, E.; Fowler, A. G.; Foxen, B.; Giustina, M.; Greene, A.; Gross, J. A.; Harrigan, M. P.; Harrington, S. D.; Hilton, J.; Hong, S.; Huang, T.; Huggins, W. J.; Ioffe, L. B.; Isakov, S. V.; Jeffrey, E.; Jiang, Z.; Kafri, D.; Kechedzhi, K.; Khattar, T.; Kim, S.; Klimov, P. V.; Korotkov, A. N.; Kostritsa, F.; Landhuis, D.; Laptev, P.; Locharla, A.; Lucero, E.; Martin, O.; McClean, J. R.; McEwen, M.; Miao, K. C.; Mohseni, M.; Montazeri, S.; Mruczkiewicz, W.; Mutus, J.; Naaman, O.; Neeley, M.; Neill, C.; Niu, M. Y.; O’Brien, T. E.; Opremcak, A.; Pató, B.; Petukhov,...

Authors

K. J. Satzinger

Y.-J Liu

Dr ADAM GAMMON-SMITH Adam.Gammon-Smith@nottingham.ac.uk
Associate Professor

C. Knapp

M. Newman

C. Jones

Z. Chen

C. Quintana

X. Mi

A. Dunsworth

C. Gidney

I. Aleiner

F. Arute

K. Arya

J. Atalaya

R. Babbush

J. C. Bardin

R. Barends

J. Basso

A. Bengtsson

A. Bilmes

M. Broughton

B. B. Buckley

D. A. Buell

B. Burkett

N. Bushnell

B. Chiaro

R. Collins

W. Courtney

S. Demura

A. R. Derk

D. Eppens

C. Erickson

L. Faoro

E. Farhi

A. G. Fowler

B. Foxen

M. Giustina

A. Greene

J. A. Gross

M. P. Harrigan

S. D. Harrington

J. Hilton

S. Hong

T. Huang

W. J. Huggins

L. B. Ioffe

S. V. Isakov

E. Jeffrey

Z. Jiang

D. Kafri

K. Kechedzhi

T. Khattar

S. Kim

P. V. Klimov

A. N. Korotkov

F. Kostritsa

D. Landhuis

P. Laptev

A. Locharla

E. Lucero

O. Martin

J. R. McClean

M. McEwen

K. C. Miao

M. Mohseni

S. Montazeri

W. Mruczkiewicz

J. Mutus

O. Naaman

M. Neeley

C. Neill

M. Y. Niu

T. E. O’Brien

A. Opremcak

B. Pató

A. Petukhov

N. C. Rubin

D. Sank

V. Shvarts

D. Strain

M. Szalay

B. Villalonga

T. C. White

Z. Yao

P. Yeh

J. Yoo

A. Zalcman

H. Neven

S. Boixo

A. Megrant

Y. Chen

J. Kelly

V. Smelyanskiy

A. Kitaev

M. Knap

F. Pollmann

P. Roushan

Abstract

The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error-correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of -ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.

Citation

Satzinger, K. J., Liu, Y.-J., Smith, A., Knapp, C., Newman, M., Jones, C., Chen, Z., Quintana, C., Mi, X., Dunsworth, A., Gidney, C., Aleiner, I., Arute, F., Arya, K., Atalaya, J., Babbush, R., Bardin, J. C., Barends, R., Basso, J., Bengtsson, A., …Roushan, P. (2021). Realizing topologically ordered states on a quantum processor. Science, 374(6572), 1237-1241. https://doi.org/10.1126/science.abi8378

Journal Article Type	Article
Acceptance Date	Oct 28, 2021
Online Publication Date	Dec 2, 2021
Publication Date	Dec 3, 2021
Deposit Date	Jan 26, 2022
Publicly Available Date	Jan 26, 2022
Journal	Science
Print ISSN	0036-8075
Electronic ISSN	1095-9203
Publisher	American Association for the Advancement of Science
Peer Reviewed	Peer Reviewed
Volume	374
Issue	6572
Pages	1237-1241
DOI	https://doi.org/10.1126/science.abi8378
Keywords	Multidisciplinary
Public URL	https://nottingham-repository.worktribe.com/output/7340738
Publisher URL	https://www.science.org/doi/10.1126/science.abi8378
Additional Information	This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science Vol. 374 on 02/12/2021, DOI: 10.1126/science.abi8378