Realizing topologically ordered states on a quantum processor
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...
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| Veröffentlicht in: | Science (American Association for the Advancement of Science) 2021-12, Vol.374 (6572), p.1237-1241 |
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| creator | 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 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. Jeffrey, E. Jiang, Z. Kafri, D. Kechedzhi, K. Khattar, T. Kim, S. Klimov, P. 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. Pato, B. Petukhov, A. Rubin, N. C. Sank, D. Shvarts 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 Kitaev, A. Knap, M. Pollmann, F. Roushan, P. |
| description | 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. |
| doi_str_mv | 10.1126/science.abi8378 |
| format | Article |
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J. ; Liu, Y-J ; Smith, A. ; Knapp, C. ; Newman, M. ; Jones, C. ; Chen, Z. ; Quintana, C. ; Mi, X. ; Dunsworth, A. ; Gidney, C. ; Aleiner ; 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. ; Jeffrey, E. ; Jiang, Z. ; Kafri, D. ; Kechedzhi, K. ; Khattar, T. ; Kim, S. ; Klimov, P. ; 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. ; Pato, B. ; Petukhov, A. ; Rubin, N. C. ; Sank, D. ; Shvarts ; 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 ; Kitaev, A. ; Knap, M. ; Pollmann, F. ; Roushan, P.</creator><creatorcontrib>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 ; 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. ; Jeffrey, E. ; Jiang, Z. ; Kafri, D. ; Kechedzhi, K. ; Khattar, T. ; Kim, S. ; Klimov, P. ; 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. ; Pato, B. ; Petukhov, A. ; Rubin, N. C. ; Sank, D. ; Shvarts ; 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 ; Kitaev, A. ; Knap, M. ; Pollmann, F. ; Roushan, P.</creatorcontrib><description>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.</description><identifier>ISSN: 0036-8075</identifier><identifier>EISSN: 1095-9203</identifier><identifier>DOI: 10.1126/science.abi8378</identifier><identifier>PMID: 34855491</identifier><language>eng</language><publisher>WASHINGTON: Amer Assoc Advancement Science</publisher><subject>Braiding ; Circuits ; Entropy ; Error correction ; Excitation ; Ground state ; Interferometry ; Microprocessors ; Multidisciplinary Sciences ; Order parameters ; Quantum entanglement ; Science & Technology ; Science & Technology - Other Topics ; Scientific Concepts ; Spin liquid ; Topology</subject><ispartof>Science (American Association for the Advancement of Science), 2021-12, Vol.374 (6572), p.1237-1241</ispartof><rights>Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>219</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000728578700054</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c432t-d3a74324f197675fff654b6332e51e9932d3daec9e95b8b78a16670ef94da203</citedby><cites>FETCH-LOGICAL-c432t-d3a74324f197675fff654b6332e51e9932d3daec9e95b8b78a16670ef94da203</cites><orcidid>0000-0003-0320-9304 ; 0000-0002-7093-9502 ; 0000-0002-6523-6730 ; 0000-0001-5865-0813 ; 0000-0002-5982-8107 ; 0000-0002-1153-6156 ; 0000-0002-6744-4592 ; 0000-0002-6164-0007 ; 0000-0001-6979-9533 ; 0000-0001-9412-0553 ; 0000-0001-7049-6206 ; 0000-0001-5264-4025 ; 0000-0002-9576-573X ; 0000-0002-9544-141X ; 0000-0003-0837-1028 ; 0000-0002-7760-9186 ; 0000-0002-9048-2896 ; 0000-0002-0136-1428 ; 0000-0001-8474-6317 ; 0000-0002-8777-6789 ; 0000-0003-3397-0444 ; 0000-0003-1806-5454 ; 0000-0001-5547-691X ; 0000-0001-7134-5733 ; 0000-0002-4034-8744 ; 0000-0001-9160-5176 ; 0000-0003-0521-8378 ; 0000-0003-3963-1830 ; 0000-0002-3732-168X ; 0000-0002-6449-2273 ; 0000-0002-6486-7100 ; 0000-0002-6371-6140 ; 0000-0001-7445-1654 ; 0000-0003-0435-655X ; 0000-0002-8406-6626 ; 0000-0002-7657-9464 ; 0000-0001-9804-2185 ; 0000-0003-0507-0211 ; 0000-0002-9681-6746 ; 0000-0003-3727-7380 ; 0000-0002-9803-7471 ; 0000-0003-1917-3879 ; 0000-0002-2585-2424 ; 0000-0002-5548-0051 ; 0000-0001-8188-364X ; 0000-0002-2809-0509 ; 0000-0002-1090-7584 ; 0000-0002-6563-3568 ; 0000-0002-1310-9174 ; 0000-0002-7473-6745 ; 0000-0002-8497-6363 ; 0000-0001-5139-7931 ; 0000-0002-3000-6732</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,782,786,2888,2889,27933,27934,39267</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/34855491$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Satzinger, K. J.</creatorcontrib><creatorcontrib>Liu, Y-J</creatorcontrib><creatorcontrib>Smith, A.</creatorcontrib><creatorcontrib>Knapp, C.</creatorcontrib><creatorcontrib>Newman, M.</creatorcontrib><creatorcontrib>Jones, C.</creatorcontrib><creatorcontrib>Chen, Z.</creatorcontrib><creatorcontrib>Quintana, C.</creatorcontrib><creatorcontrib>Mi, X.</creatorcontrib><creatorcontrib>Dunsworth, A.</creatorcontrib><creatorcontrib>Gidney, C.</creatorcontrib><creatorcontrib>Aleiner</creatorcontrib><creatorcontrib>Arute, F.</creatorcontrib><creatorcontrib>Arya, K.</creatorcontrib><creatorcontrib>Atalaya, J.</creatorcontrib><creatorcontrib>Babbush, R.</creatorcontrib><creatorcontrib>Bardin, J. C.</creatorcontrib><creatorcontrib>Barends, R.</creatorcontrib><creatorcontrib>Basso, J.</creatorcontrib><creatorcontrib>Bengtsson, A.</creatorcontrib><creatorcontrib>Bilmes, A.</creatorcontrib><creatorcontrib>Broughton, M.</creatorcontrib><creatorcontrib>Buckley, B. B.</creatorcontrib><creatorcontrib>Buell, D. 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J.</creatorcontrib><creatorcontrib>Ioffe, L. B.</creatorcontrib><creatorcontrib>Isakov, S.</creatorcontrib><creatorcontrib>Jeffrey, E.</creatorcontrib><creatorcontrib>Jiang, Z.</creatorcontrib><creatorcontrib>Kafri, D.</creatorcontrib><creatorcontrib>Kechedzhi, K.</creatorcontrib><creatorcontrib>Khattar, T.</creatorcontrib><creatorcontrib>Kim, S.</creatorcontrib><creatorcontrib>Klimov, P.</creatorcontrib><creatorcontrib>Korotkov, A. N.</creatorcontrib><creatorcontrib>Kostritsa, F.</creatorcontrib><creatorcontrib>Landhuis, D.</creatorcontrib><creatorcontrib>Laptev, P.</creatorcontrib><creatorcontrib>Locharla, A.</creatorcontrib><creatorcontrib>Lucero, E.</creatorcontrib><creatorcontrib>Martin, O.</creatorcontrib><creatorcontrib>McClean, J. R.</creatorcontrib><creatorcontrib>McEwen, M.</creatorcontrib><creatorcontrib>Miao, K. C.</creatorcontrib><creatorcontrib>Mohseni, M.</creatorcontrib><creatorcontrib>Montazeri, S.</creatorcontrib><creatorcontrib>Mruczkiewicz, W.</creatorcontrib><creatorcontrib>Mutus, J.</creatorcontrib><creatorcontrib>Naaman, O.</creatorcontrib><creatorcontrib>Neeley, M.</creatorcontrib><creatorcontrib>Neill, C.</creatorcontrib><creatorcontrib>Niu, M. Y.</creatorcontrib><creatorcontrib>O'Brien, T. E.</creatorcontrib><creatorcontrib>Opremcak, A.</creatorcontrib><creatorcontrib>Pato, B.</creatorcontrib><creatorcontrib>Petukhov, A.</creatorcontrib><creatorcontrib>Rubin, N. C.</creatorcontrib><creatorcontrib>Sank, D.</creatorcontrib><creatorcontrib>Shvarts</creatorcontrib><creatorcontrib>Strain, D.</creatorcontrib><creatorcontrib>Szalay, M.</creatorcontrib><creatorcontrib>Villalonga, B.</creatorcontrib><creatorcontrib>White, T. C.</creatorcontrib><creatorcontrib>Yao, Z.</creatorcontrib><creatorcontrib>Yeh, P.</creatorcontrib><creatorcontrib>Yoo, J.</creatorcontrib><creatorcontrib>Zalcman, A.</creatorcontrib><creatorcontrib>Neven, H.</creatorcontrib><creatorcontrib>Boixo, S.</creatorcontrib><creatorcontrib>Megrant, A.</creatorcontrib><creatorcontrib>Chen, Y.</creatorcontrib><creatorcontrib>Kelly, J.</creatorcontrib><creatorcontrib>Smelyanskiy</creatorcontrib><creatorcontrib>Kitaev, A.</creatorcontrib><creatorcontrib>Knap, M.</creatorcontrib><creatorcontrib>Pollmann, F.</creatorcontrib><creatorcontrib>Roushan, P.</creatorcontrib><title>Realizing topologically ordered states on a quantum processor</title><title>Science (American Association for the Advancement of Science)</title><addtitle>SCIENCE</addtitle><addtitle>Science</addtitle><description>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.</description><subject>Braiding</subject><subject>Circuits</subject><subject>Entropy</subject><subject>Error correction</subject><subject>Excitation</subject><subject>Ground state</subject><subject>Interferometry</subject><subject>Microprocessors</subject><subject>Multidisciplinary Sciences</subject><subject>Order parameters</subject><subject>Quantum entanglement</subject><subject>Science & Technology</subject><subject>Science & Technology - Other Topics</subject><subject>Scientific Concepts</subject><subject>Spin liquid</subject><subject>Topology</subject><issn>0036-8075</issn><issn>1095-9203</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><recordid>eNqNkM1LwzAYh4Mobk7P3qTgRZBuSdN8HTxI8QsGguxe0vbtyGibmbTI_OvNWOfBk6e8kOf3fjwIXRM8JyThC18a6EqY68JIKuQJmhKsWKwSTE_RFGPKY4kFm6AL7zcYhz9Fz9GEppKxVJEpevgA3Zhv062j3m5tY9em1E2zi6yrwEEV-V734CPbRTr6HHTXD220dbYE7627RGe1bjxcje8MrZ6fVtlrvHx_ecsel3GZ0qSPK6pFKNKaKMEFq-uas7TglCbACChFk4pWGkoFihWyEFITzgWGWqWVDqfM0N2hbRj8OYDv89b4EppGd2AHnyccc0VTIXlAb_-gGzu4LiwXKCqxZDjZU4sDVTrrvYM63zrTarfLCc73YvNRbD6KDYmbse9QtFD98keTAZAH4AsKWx_jRyyoF4lkQopQsTQzwaqxXWaHrg_R-_9H6Q8hKpZZ</recordid><startdate>20211203</startdate><enddate>20211203</enddate><creator>Satzinger, K. 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J. ; Liu, Y-J ; Smith, A. ; Knapp, C. ; Newman, M. ; Jones, C. ; Chen, Z. ; Quintana, C. ; Mi, X. ; Dunsworth, A. ; Gidney, C. ; Aleiner ; 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. ; Jeffrey, E. ; Jiang, Z. ; Kafri, D. ; Kechedzhi, K. ; Khattar, T. ; Kim, S. ; Klimov, P. ; 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. ; Pato, B. ; Petukhov, A. ; Rubin, N. C. ; Sank, D. ; Shvarts ; 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 ; Kitaev, A. ; Knap, M. ; Pollmann, F. ; Roushan, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c432t-d3a74324f197675fff654b6332e51e9932d3daec9e95b8b78a16670ef94da203</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Braiding</topic><topic>Circuits</topic><topic>Entropy</topic><topic>Error correction</topic><topic>Excitation</topic><topic>Ground state</topic><topic>Interferometry</topic><topic>Microprocessors</topic><topic>Multidisciplinary Sciences</topic><topic>Order parameters</topic><topic>Quantum entanglement</topic><topic>Science & Technology</topic><topic>Science & Technology - Other Topics</topic><topic>Scientific Concepts</topic><topic>Spin liquid</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Satzinger, K. 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C.</creatorcontrib><creatorcontrib>Yao, Z.</creatorcontrib><creatorcontrib>Yeh, P.</creatorcontrib><creatorcontrib>Yoo, J.</creatorcontrib><creatorcontrib>Zalcman, A.</creatorcontrib><creatorcontrib>Neven, H.</creatorcontrib><creatorcontrib>Boixo, S.</creatorcontrib><creatorcontrib>Megrant, A.</creatorcontrib><creatorcontrib>Chen, Y.</creatorcontrib><creatorcontrib>Kelly, J.</creatorcontrib><creatorcontrib>Smelyanskiy</creatorcontrib><creatorcontrib>Kitaev, A.</creatorcontrib><creatorcontrib>Knap, M.</creatorcontrib><creatorcontrib>Pollmann, F.</creatorcontrib><creatorcontrib>Roushan, P.</creatorcontrib><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Aluminium Industry Abstracts</collection><collection>Animal Behavior Abstracts</collection><collection>Bacteriology Abstracts (Microbiology B)</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Chemoreception Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Ecology Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Entomology Abstracts (Full archive)</collection><collection>Industrial and Applied Microbiology Abstracts (Microbiology A)</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Copper Technical Reference Library</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Genetics Abstracts</collection><collection>MEDLINE - Academic</collection><jtitle>Science (American Association for the Advancement of Science)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Satzinger, K. J.</au><au>Liu, Y-J</au><au>Smith, A.</au><au>Knapp, C.</au><au>Newman, M.</au><au>Jones, C.</au><au>Chen, Z.</au><au>Quintana, C.</au><au>Mi, X.</au><au>Dunsworth, A.</au><au>Gidney, C.</au><au>Aleiner</au><au>Arute, F.</au><au>Arya, K.</au><au>Atalaya, J.</au><au>Babbush, R.</au><au>Bardin, J. C.</au><au>Barends, R.</au><au>Basso, J.</au><au>Bengtsson, A.</au><au>Bilmes, A.</au><au>Broughton, M.</au><au>Buckley, B. B.</au><au>Buell, D. A.</au><au>Burkett, B.</au><au>Bushnell, N.</au><au>Chiaro, B.</au><au>Collins, R.</au><au>Courtney, W.</au><au>Demura, S.</au><au>Derk, A. R.</au><au>Eppens, D.</au><au>Erickson, C.</au><au>Faoro, L.</au><au>Farhi, E.</au><au>Fowler, A. G.</au><au>Foxen, B.</au><au>Giustina, M.</au><au>Greene, A.</au><au>Gross, J. A.</au><au>Harrigan, M. P.</au><au>Harrington, S. D.</au><au>Hilton, J.</au><au>Hong, S.</au><au>Huang, T.</au><au>Huggins, W. J.</au><au>Ioffe, L. B.</au><au>Isakov, S.</au><au>Jeffrey, E.</au><au>Jiang, Z.</au><au>Kafri, D.</au><au>Kechedzhi, K.</au><au>Khattar, T.</au><au>Kim, S.</au><au>Klimov, P.</au><au>Korotkov, A. N.</au><au>Kostritsa, F.</au><au>Landhuis, D.</au><au>Laptev, P.</au><au>Locharla, A.</au><au>Lucero, E.</au><au>Martin, O.</au><au>McClean, J. R.</au><au>McEwen, M.</au><au>Miao, K. C.</au><au>Mohseni, M.</au><au>Montazeri, S.</au><au>Mruczkiewicz, W.</au><au>Mutus, J.</au><au>Naaman, O.</au><au>Neeley, M.</au><au>Neill, C.</au><au>Niu, M. Y.</au><au>O'Brien, T. E.</au><au>Opremcak, A.</au><au>Pato, B.</au><au>Petukhov, A.</au><au>Rubin, N. C.</au><au>Sank, D.</au><au>Shvarts</au><au>Strain, D.</au><au>Szalay, M.</au><au>Villalonga, B.</au><au>White, T. C.</au><au>Yao, Z.</au><au>Yeh, P.</au><au>Yoo, J.</au><au>Zalcman, A.</au><au>Neven, H.</au><au>Boixo, S.</au><au>Megrant, A.</au><au>Chen, Y.</au><au>Kelly, J.</au><au>Smelyanskiy</au><au>Kitaev, A.</au><au>Knap, M.</au><au>Pollmann, F.</au><au>Roushan, P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Realizing topologically ordered states on a quantum processor</atitle><jtitle>Science (American Association for the Advancement of Science)</jtitle><stitle>SCIENCE</stitle><addtitle>Science</addtitle><date>2021-12-03</date><risdate>2021</risdate><volume>374</volume><issue>6572</issue><spage>1237</spage><epage>1241</epage><pages>1237-1241</pages><issn>0036-8075</issn><eissn>1095-9203</eissn><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.</abstract><cop>WASHINGTON</cop><pub>Amer Assoc Advancement Science</pub><pmid>34855491</pmid><doi>10.1126/science.abi8378</doi><tpages>45</tpages><orcidid>https://orcid.org/0000-0003-0320-9304</orcidid><orcidid>https://orcid.org/0000-0002-7093-9502</orcidid><orcidid>https://orcid.org/0000-0002-6523-6730</orcidid><orcidid>https://orcid.org/0000-0001-5865-0813</orcidid><orcidid>https://orcid.org/0000-0002-5982-8107</orcidid><orcidid>https://orcid.org/0000-0002-1153-6156</orcidid><orcidid>https://orcid.org/0000-0002-6744-4592</orcidid><orcidid>https://orcid.org/0000-0002-6164-0007</orcidid><orcidid>https://orcid.org/0000-0001-6979-9533</orcidid><orcidid>https://orcid.org/0000-0001-9412-0553</orcidid><orcidid>https://orcid.org/0000-0001-7049-6206</orcidid><orcidid>https://orcid.org/0000-0001-5264-4025</orcidid><orcidid>https://orcid.org/0000-0002-9576-573X</orcidid><orcidid>https://orcid.org/0000-0002-9544-141X</orcidid><orcidid>https://orcid.org/0000-0003-0837-1028</orcidid><orcidid>https://orcid.org/0000-0002-7760-9186</orcidid><orcidid>https://orcid.org/0000-0002-9048-2896</orcidid><orcidid>https://orcid.org/0000-0002-0136-1428</orcidid><orcidid>https://orcid.org/0000-0001-8474-6317</orcidid><orcidid>https://orcid.org/0000-0002-8777-6789</orcidid><orcidid>https://orcid.org/0000-0003-3397-0444</orcidid><orcidid>https://orcid.org/0000-0003-1806-5454</orcidid><orcidid>https://orcid.org/0000-0001-5547-691X</orcidid><orcidid>https://orcid.org/0000-0001-7134-5733</orcidid><orcidid>https://orcid.org/0000-0002-4034-8744</orcidid><orcidid>https://orcid.org/0000-0001-9160-5176</orcidid><orcidid>https://orcid.org/0000-0003-0521-8378</orcidid><orcidid>https://orcid.org/0000-0003-3963-1830</orcidid><orcidid>https://orcid.org/0000-0002-3732-168X</orcidid><orcidid>https://orcid.org/0000-0002-6449-2273</orcidid><orcidid>https://orcid.org/0000-0002-6486-7100</orcidid><orcidid>https://orcid.org/0000-0002-6371-6140</orcidid><orcidid>https://orcid.org/0000-0001-7445-1654</orcidid><orcidid>https://orcid.org/0000-0003-0435-655X</orcidid><orcidid>https://orcid.org/0000-0002-8406-6626</orcidid><orcidid>https://orcid.org/0000-0002-7657-9464</orcidid><orcidid>https://orcid.org/0000-0001-9804-2185</orcidid><orcidid>https://orcid.org/0000-0003-0507-0211</orcidid><orcidid>https://orcid.org/0000-0002-9681-6746</orcidid><orcidid>https://orcid.org/0000-0003-3727-7380</orcidid><orcidid>https://orcid.org/0000-0002-9803-7471</orcidid><orcidid>https://orcid.org/0000-0003-1917-3879</orcidid><orcidid>https://orcid.org/0000-0002-2585-2424</orcidid><orcidid>https://orcid.org/0000-0002-5548-0051</orcidid><orcidid>https://orcid.org/0000-0001-8188-364X</orcidid><orcidid>https://orcid.org/0000-0002-2809-0509</orcidid><orcidid>https://orcid.org/0000-0002-1090-7584</orcidid><orcidid>https://orcid.org/0000-0002-6563-3568</orcidid><orcidid>https://orcid.org/0000-0002-1310-9174</orcidid><orcidid>https://orcid.org/0000-0002-7473-6745</orcidid><orcidid>https://orcid.org/0000-0002-8497-6363</orcidid><orcidid>https://orcid.org/0000-0001-5139-7931</orcidid><orcidid>https://orcid.org/0000-0002-3000-6732</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0036-8075 |
| ispartof | Science (American Association for the Advancement of Science), 2021-12, Vol.374 (6572), p.1237-1241 |
| issn | 0036-8075 1095-9203 |
| language | eng |
| recordid | cdi_pubmed_primary_34855491 |
| source | Science Magazine; Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" /> |
| subjects | Braiding Circuits Entropy Error correction Excitation Ground state Interferometry Microprocessors Multidisciplinary Sciences Order parameters Quantum entanglement Science & Technology Science & Technology - Other Topics Scientific Concepts Spin liquid Topology |
| title | Realizing topologically ordered states on a quantum processor |
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