Realizing topologically ordered states on a quantum processor

Creators: 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.

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.

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. https://www.sciencemag.org/about/science-licenses-journal-article-reuse 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).

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