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Realizing topologically ordered states on a quantum processor

Satzinger, K. J. and Liu, Y.-J and Smith, A. and Knapp, C. and Newman, M. and Jones, C. and Chen, Z. and Quintana, C. and Mi, X. and Dunsworth, A. and Gidney, C. and Aleiner, I. and Arute, F. and Arya, K. and Atalaya, J. and Babbush, R. and Bardin, J. C. and Barends, R. and Basso, J. and Bengtsson, A. and Bilmes, A. and Broughton, M. and Buckley, B. B. and Buell, D. A. and Burkett, B. and Bushnell, N. and Chiaro, B. and Collins, R. and Courtney, W. and Demura, S. and Derk, A. R. and Eppens, D. and Erickson, C. and Faoro, L. and Farhi, E. and Fowler, A. G. and Foxen, B. and Giustina, M. and Greene, A. and Gross, J. A. and Harrigan, M. P. and Harrington, S. D. and Hilton, J. and Hong, S. and Huang, T. and Huggins, W. J. and Ioffe, L. B. and Isakov, S. V. and Jeffrey, E. and Jiang, Z. and Kafri, D. and Kechedzhi, K. and Khattar, T. and Kim, S. and Klimov, P. V. and Korotkov, A. N. and Kostritsa, F. and Landhuis, D. and Laptev, P. and Locharla, A. and Lucero, E. and Martin, O. and McClean, J. R. and McEwen, M. and Miao, K. C. and Mohseni, M. and Montazeri, S. and Mruczkiewicz, W. and Mutus, J. and Naaman, O. and Neeley, M. and Neill, C. and Niu, M. Y. and O’Brien, T. E. and Opremcak, A. and Pató, B. and Petukhov, A. and Rubin, N. C. and Sank, D. and Shvarts, V. and Strain, D. and Szalay, M. and Villalonga, B. and White, T. C. and Yao, Z. and Yeh, P. and Yoo, J. and Zalcman, A. and Neven, H. and Boixo, S. and Megrant, A. and Chen, Y. and Kelly, J. and Smelyanskiy, V. and Kitaev, A. and Knap, M. and Pollmann, F. and Roushan, P. (2021) Realizing topologically ordered states on a quantum processor. Science, 374 (6572). pp. 1237-1241. ISSN 0036-8075. doi:10.1126/science.abi8378.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Satzinger, K. J.0000-0001-5865-0813
Liu, Y.-J0000-0002-7657-9464
Smith, A.0000-0002-6744-4592
Knapp, C.0000-0002-5982-8107
Mi, X.0000-0003-0507-0211
Arya, K.0000-0002-6486-7100
Babbush, R.0000-0001-6979-9533
Bardin, J. C.0000-0002-6523-6730
Basso, J.0000-0001-5547-691X
Bengtsson, A.0000-0001-5264-4025
Buckley, B. B.0000-0001-5139-7931
Burkett, B.0000-0001-8474-6317
Bushnell, N.0000-0001-7445-1654
Collins, R.0000-0002-6164-0007
Demura, S.0000-0003-3727-7380
Eppens, D.0000-0001-7134-5733
Fowler, A. G.0000-0002-9048-2896
Foxen, B.0000-0002-3732-168X
Greene, A.0000-0002-4034-8744
Gross, J. A.0000-0001-7049-6206
Harrigan, M. P.0000-0001-9412-0553
Harrington, S. D.0000-0003-0521-8378
Ioffe, L. B.0000-0002-8777-6789
Jiang, Z.0000-0003-0435-655X
Kafri, D.0000-0001-9160-5176
Kechedzhi, K.0000-0002-0136-1428
Kim, S.0000-0003-3397-0444
Landhuis, D.0000-0001-9804-2185
Lucero, E.0000-0002-6449-2273
Martin, O.0000-0002-9576-573X
McClean, J. R.0000-0002-2809-0509
McEwen, M.0000-0002-9544-141X
Mruczkiewicz, W.0000-0002-8497-6363
Naaman, O.0000-0002-7760-9186
Neeley, M.0000-0002-5548-0051
Neill, C.0000-0002-6563-3568
O’Brien, T. E.0000-0002-8406-6626
Rubin, N. C.0000-0003-3963-1830
Sank, D.0000-0001-8188-364X
Szalay, M.0000-0002-1310-9174
White, T. C.0000-0002-9803-7471
Yao, Z.0000-0003-1806-5454
Yeh, P.0000-0003-0837-1028
Zalcman, A.0000-0002-2585-2424
Neven, H.0000-0002-9681-6746
Boixo, S.0000-0002-1090-7584
Megrant, A.0000-0002-6371-6140
Chen, Y.0000-0002-7473-6745
Smelyanskiy, V.0000-0002-3000-6732
Kitaev, A.0000-0002-5777-642X
Knap, M.0000-0002-7093-9502
Pollmann, F.0000-0003-0320-9304
Roushan, P.0000-0003-1917-3879
Additional Information:© 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. This is an article distributed under the terms of the Science Journals Default License. 2 April 2021; accepted 28 October 2021. We thank B. Bauer, A. Elben, B. Vermersch, and G. Vidal for useful discussions. F.P., Y.-J.L., A.S., and M.K. acknowledge support from the Technical University of Munich–Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763; the Max Planck Gesellschaft (MPG) through the International Max Planck Research School for Quantum Science and Technology (IMPRS-QST); the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) under Germany’s Excellence Strategy–EXC–2111–390814868, TRR80, and DFG grant KN1254/2-1; and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreements 771537 and 851161). A.S. was supported by a Research Fellowship from the Royal Commission for the Exhibition of 1851. C.K. was supported by the Walter Burke Institute for Theoretical Physics at Caltech, and by the IQIM, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, the Packard Foundation, and the Simons Foundation. Author contributions: A.S., M.K., F.P., K.J.S., Y.-J.L., C.K., and P.R. designed the experiment. K.J.S. and P.R. performed the experiment. K.J.S. and Y.-J.L. analyzed the data and wrote the supplement. Y.-J.L., A.S., C.K., M.K., F.P., and K.J.S. provided theoretical support and analysis. C.K., K.JS., Y.-J.L., A.S., M.K., F.P., and P.R. wrote the manuscript. All authors contributed to revising the manuscript and supplement. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. The authors declare no competing interests. Data and materials availability: Data and code used for analysis and simulation are available at (44).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Technical University of MunichUNSPECIFIED
European Research Council (ERC)291763
International Max Planck Research School for Quantum Science and TechnologyUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Deutsche Forschungsgemeinschaft (DFG)TRR80
Deutsche Forschungsgemeinschaft (DFG)KN1254/2-1
European Research Council (ERC)771537
European Research Council (ERC)851161
Royal Commission for the Exhibition of 1851UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:6572
Record Number:CaltechAUTHORS:20211203-174950058
Persistent URL:
Official Citation:Realizing topologically ordered states on a quantum processor. K. J. Satzinger, et. al., Science, 374 (6572); DOI: 10.1126/science.abi8378
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112190
Deposited By: George Porter
Deposited On:03 Dec 2021 20:41
Last Modified:03 Dec 2021 20:48

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