Exponential suppression of bit or phase flip errors with repetitive quantum error correction Article Swipe

View

Zijun Chen , Kevin J. Satzinger , Juan Atalaya , Alexander N. Korotkov , A. Dunsworth , D. Sank , Chris Quintana , Matt McEwen , R. Barends , Paul V. Klimov , Sabrina Hong , Cody Jones , Andre Petukhov , Dvir Kafri , Sean Demura , Brian Burkett , Craig Gidney , Austin G. Fowler , Harald Putterman , I. L. Aleǐner , Frank Arute , Kunal Arya , Ryan Babbush , Joseph C. Bardin , Andreas Bengtsson , Alexandre Bourassa , Michael Broughton , Bob B. Buckley , David A. Buell , Nicholas Bushnell , Benjamin Chiaro , Roberto Collins , William Courtney , Alan R. Derk , Daniel Eppens , Catherine Erickson , Edward Farhi , Brooks Foxen , Marissa Giustina , Jonathan A. Gross , Matthew P. Harrigan , Sean D. Harrington , J. Hilton , Alan Ho , Trent Huang , William J. Huggins , L. B. Ioffe , Sergei V. Isakov , E. Jeffrey , Jiang Zhang , Kostyantyn Kechedzhi , Seon Kim , Fedor Kostritsa , David Landhuis , Pavel Laptev , Erik Lucero , Orion Martin , Jarrod R. McClean , Trevor McCourt , Xiao Mi , Kevin C. Miao , Masoud Mohseni , Wojciech Mruczkiewicz , Josh Mutus , Ofer Naaman , M. Neeley , Charles Neill , Michael Newman , Murphy Yuezhen Niu , Thomas E. O’Brien , Alex Opremcak , Eric Ostby , Bálint Pató , Nicholas Redd , P. Roushan , Nicholas C. Rubin , Vladimir Shvarts , Doug Strain , Marco Szalay , Matthew D. Trevithick , Benjamin Villalonga , T. White , Z. Jamie Yao , P. Yeh , Adam Zalcman , Hartmut Neven , Sergio Boixo , Vadim Smelyanskiy , Yu Chen , A. Megrant , J. Kelly ·

YOU? · · 2021 · Open Access ·

Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.

Related Topics

Error Detection And Correction

Concepts

Qubit Quantum error correction Error detection and correction Computer science Quantum computer Algorithm Word error rate Quantum Topology (electrical circuits) Quantum mechanics Physics Mathematics Speech recognition Combinatorics

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/pdf/2102.06132.pdf
OA Status: green
Cited By: 10
Related Works: 20
OpenAlex ID: https://openalex.org/W3127785863

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W3127785863

Canonical identifier for this work in OpenAlex
Title: Exponential suppression of bit or phase flip errors with repetitive quantum error correction

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2021

Year of publication
Publication date: 2021-02-11

Full publication date if available
Authors: Zijun Chen, Kevin J. Satzinger, Juan Atalaya, Alexander N. Korotkov, A. Dunsworth, D. Sank, Chris Quintana, Matt McEwen, R. Barends, Paul V. Klimov, Sabrina Hong, Cody Jones, Andre Petukhov, Dvir Kafri, Sean Demura, Brian Burkett, Craig Gidney, Austin G. Fowler, Harald Putterman, I. L. Aleǐner, Frank Arute, Kunal Arya, Ryan Babbush, Joseph C. Bardin, Andreas Bengtsson, Alexandre Bourassa, Michael Broughton, Bob B. Buckley, David A. Buell, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Alan R. Derk, Daniel Eppens, Catherine Erickson, Edward Farhi, Brooks Foxen, Marissa Giustina, Jonathan A. Gross, Matthew P. Harrigan, Sean D. Harrington, J. Hilton, Alan Ho, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, E. Jeffrey, Jiang Zhang, Kostyantyn Kechedzhi, Seon Kim, Fedor Kostritsa, David Landhuis, Pavel Laptev, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Xiao Mi, Kevin C. Miao, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, M. Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O’Brien, Alex Opremcak, Eric Ostby, Bálint Pató, Nicholas Redd, P. Roushan, Nicholas C. Rubin, Vladimir Shvarts, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, T. White, Z. Jamie Yao, P. Yeh, Adam Zalcman, Hartmut Neven, Sergio Boixo, Vadim Smelyanskiy, Yu Chen, A. Megrant, J. Kelly

List of authors in order
Landing page: https://arxiv.org/pdf/2102.06132.pdf

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2102.06132.pdf

Direct OA link when available
Concepts: Qubit, Quantum error correction, Error detection and correction, Computer science, Quantum computer, Algorithm, Word error rate, Quantum, Topology (electrical circuits), Quantum mechanics, Physics, Mathematics, Speech recognition, Combinatorics

Top concepts (fields/topics) attached by OpenAlex
Cited by: 10

Total citation count in OpenAlex
Citations by year (recent): 2022: 1, 2021: 9

Per-year citation counts (last 5 years)
Related works (count): 20

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W3127785863
doi
ids.mag	3127785863
ids.openalex	https://openalex.org/W3127785863
fwci
type	preprint
title	Exponential suppression of bit or phase flip errors with repetitive quantum error correction
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10682
topics[0].field.id	https://openalex.org/fields/17
topics[0].field.display_name	Computer Science
topics[0].score	0.9991999864578247
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/1702
topics[0].subfield.display_name	Artificial Intelligence
topics[0].display_name	Quantum Computing Algorithms and Architecture
topics[1].id	https://openalex.org/T10558
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.9973000288009644
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2208
topics[1].subfield.display_name	Electrical and Electronic Engineering
topics[1].display_name	Advancements in Semiconductor Devices and Circuit Design
topics[2].id	https://openalex.org/T10472
topics[2].field.id	https://openalex.org/fields/22
topics[2].field.display_name	Engineering
topics[2].score	0.9966999888420105
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2208
topics[2].subfield.display_name	Electrical and Electronic Engineering
topics[2].display_name	Semiconductor materials and devices
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C203087015
concepts[0].level	3
concepts[0].score	0.7611101269721985
concepts[0].wikidata	https://www.wikidata.org/wiki/Q378201
concepts[0].display_name	Qubit
concepts[1].id	https://openalex.org/C51003876
concepts[1].level	4
concepts[1].score	0.7105410099029541
concepts[1].wikidata	https://www.wikidata.org/wiki/Q1536431
concepts[1].display_name	Quantum error correction
concepts[2].id	https://openalex.org/C103088060
concepts[2].level	2
concepts[2].score	0.7038747668266296
concepts[2].wikidata	https://www.wikidata.org/wiki/Q1062839
concepts[2].display_name	Error detection and correction
concepts[3].id	https://openalex.org/C41008148
concepts[3].level	0
concepts[3].score	0.6190019845962524
concepts[3].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[3].display_name	Computer science
concepts[4].id	https://openalex.org/C58053490
concepts[4].level	3
concepts[4].score	0.5612960457801819
concepts[4].wikidata	https://www.wikidata.org/wiki/Q176555
concepts[4].display_name	Quantum computer
concepts[5].id	https://openalex.org/C11413529
concepts[5].level	1
concepts[5].score	0.45073288679122925
concepts[5].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[5].display_name	Algorithm
concepts[6].id	https://openalex.org/C40969351
concepts[6].level	2
concepts[6].score	0.449752539396286
concepts[6].wikidata	https://www.wikidata.org/wiki/Q3516228
concepts[6].display_name	Word error rate
concepts[7].id	https://openalex.org/C84114770
concepts[7].level	2
concepts[7].score	0.42213842272758484
concepts[7].wikidata	https://www.wikidata.org/wiki/Q46344
concepts[7].display_name	Quantum
concepts[8].id	https://openalex.org/C184720557
concepts[8].level	2
concepts[8].score	0.3265763521194458
concepts[8].wikidata	https://www.wikidata.org/wiki/Q7825049
concepts[8].display_name	Topology (electrical circuits)
concepts[9].id	https://openalex.org/C62520636
concepts[9].level	1
concepts[9].score	0.3144870698451996
concepts[9].wikidata	https://www.wikidata.org/wiki/Q944
concepts[9].display_name	Quantum mechanics
concepts[10].id	https://openalex.org/C121332964
concepts[10].level	0
concepts[10].score	0.2936558723449707
concepts[10].wikidata	https://www.wikidata.org/wiki/Q413
concepts[10].display_name	Physics
concepts[11].id	https://openalex.org/C33923547
concepts[11].level	0
concepts[11].score	0.27141743898391724
concepts[11].wikidata	https://www.wikidata.org/wiki/Q395
concepts[11].display_name	Mathematics
concepts[12].id	https://openalex.org/C28490314
concepts[12].level	1
concepts[12].score	0.0
concepts[12].wikidata	https://www.wikidata.org/wiki/Q189436
concepts[12].display_name	Speech recognition
concepts[13].id	https://openalex.org/C114614502
concepts[13].level	1
concepts[13].score	0.0
concepts[13].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[13].display_name	Combinatorics
keywords[0].id	https://openalex.org/keywords/qubit
keywords[0].score	0.7611101269721985
keywords[0].display_name	Qubit
keywords[1].id	https://openalex.org/keywords/quantum-error-correction
keywords[1].score	0.7105410099029541
keywords[1].display_name	Quantum error correction
keywords[2].id	https://openalex.org/keywords/error-detection-and-correction
keywords[2].score	0.7038747668266296
keywords[2].display_name	Error detection and correction
keywords[3].id	https://openalex.org/keywords/computer-science
keywords[3].score	0.6190019845962524
keywords[3].display_name	Computer science
keywords[4].id	https://openalex.org/keywords/quantum-computer
keywords[4].score	0.5612960457801819
keywords[4].display_name	Quantum computer
keywords[5].id	https://openalex.org/keywords/algorithm
keywords[5].score	0.45073288679122925
keywords[5].display_name	Algorithm
keywords[6].id	https://openalex.org/keywords/word-error-rate
keywords[6].score	0.449752539396286
keywords[6].display_name	Word error rate
keywords[7].id	https://openalex.org/keywords/quantum
keywords[7].score	0.42213842272758484
keywords[7].display_name	Quantum
keywords[8].id	https://openalex.org/keywords/topology
keywords[8].score	0.3265763521194458
keywords[8].display_name	Topology (electrical circuits)
keywords[9].id	https://openalex.org/keywords/quantum-mechanics
keywords[9].score	0.3144870698451996
keywords[9].display_name	Quantum mechanics
keywords[10].id	https://openalex.org/keywords/physics
keywords[10].score	0.2936558723449707
keywords[10].display_name	Physics
keywords[11].id	https://openalex.org/keywords/mathematics
keywords[11].score	0.27141743898391724
keywords[11].display_name	Mathematics
language	en
locations[0].id	mag:3127785863
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url
locations[0].version	submittedVersion
locations[0].raw_type
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name	arXiv (Cornell University)
locations[0].landing_page_url	http://arxiv.org/pdf/2102.06132.pdf
authorships[0].author.id	https://openalex.org/A5101609780
authorships[0].author.orcid	https://orcid.org/0000-0001-8642-1604
authorships[0].author.display_name	Zijun Chen
authorships[0].author_position	first
authorships[0].raw_author_name	Zijun Chen
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5055747836
authorships[1].author.orcid	https://orcid.org/0000-0001-5865-0813
authorships[1].author.display_name	Kevin J. Satzinger
authorships[1].author_position	middle
authorships[1].raw_author_name	Kevin J. Satzinger
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5078672240
authorships[2].author.orcid	https://orcid.org/0000-0003-3055-2730
authorships[2].author.display_name	Juan Atalaya
authorships[2].author_position	middle
authorships[2].raw_author_name	Juan Atalaya
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5036734283
authorships[3].author.orcid	https://orcid.org/0000-0002-4787-718X
authorships[3].author.display_name	Alexander N. Korotkov
authorships[3].author_position	middle
authorships[3].raw_author_name	Alexander N. Korotkov
authorships[3].is_corresponding	False
authorships[4].author.id	https://openalex.org/A5072846859
authorships[4].author.orcid	https://orcid.org/0000-0002-9508-3069
authorships[4].author.display_name	A. Dunsworth
authorships[4].author_position	middle
authorships[4].raw_author_name	Andrew Dunsworth
authorships[4].is_corresponding	False
authorships[5].author.id	https://openalex.org/A5022797632
authorships[5].author.orcid	https://orcid.org/0000-0001-8188-364X
authorships[5].author.display_name	D. Sank
authorships[5].author_position	middle
authorships[5].raw_author_name	Daniel Sank
authorships[5].is_corresponding	False
authorships[6].author.id	https://openalex.org/A5042184175
authorships[6].author.orcid	https://orcid.org/0000-0003-4408-8318
authorships[6].author.display_name	Chris Quintana
authorships[6].author_position	middle
authorships[6].raw_author_name	Chris Quintana
authorships[6].is_corresponding	False
authorships[7].author.id	https://openalex.org/A5056613045
authorships[7].author.orcid	https://orcid.org/0000-0002-9544-141X
authorships[7].author.display_name	Matt McEwen
authorships[7].author_position	middle
authorships[7].raw_author_name	Matt McEwen
authorships[7].is_corresponding	False
authorships[8].author.id	https://openalex.org/A5112394419
authorships[8].author.orcid
authorships[8].author.display_name	R. Barends
authorships[8].author_position	middle
authorships[8].raw_author_name	Rami Barends
authorships[8].is_corresponding	False
authorships[9].author.id	https://openalex.org/A5055445003
authorships[9].author.orcid	https://orcid.org/0000-0002-9481-4456
authorships[9].author.display_name	Paul V. Klimov
authorships[9].author_position	middle
authorships[9].raw_author_name	Paul V. Klimov
authorships[9].is_corresponding	False
authorships[10].author.id	https://openalex.org/A5044081449
authorships[10].author.orcid	https://orcid.org/0000-0001-7421-5635
authorships[10].author.display_name	Sabrina Hong
authorships[10].author_position	middle
authorships[10].raw_author_name	Sabrina Hong
authorships[10].is_corresponding	False
authorships[11].author.id	https://openalex.org/A5109982819
authorships[11].author.orcid
authorships[11].author.display_name	Cody Jones
authorships[11].author_position	middle
authorships[11].raw_author_name	Cody Jones
authorships[11].is_corresponding	False
authorships[12].author.id	https://openalex.org/A5105551481
authorships[12].author.orcid
authorships[12].author.display_name	Andre Petukhov
authorships[12].author_position	middle
authorships[12].raw_author_name	Andre Petukhov
authorships[12].is_corresponding	False
authorships[13].author.id	https://openalex.org/A5066301431
authorships[13].author.orcid	https://orcid.org/0000-0001-9160-5176
authorships[13].author.display_name	Dvir Kafri
authorships[13].author_position	middle
authorships[13].raw_author_name	Dvir Kafri
authorships[13].is_corresponding	False
authorships[14].author.id	https://openalex.org/A5017376512
authorships[14].author.orcid	https://orcid.org/0000-0003-3727-7380
authorships[14].author.display_name	Sean Demura
authorships[14].author_position	middle
authorships[14].raw_author_name	Sean Demura
authorships[14].is_corresponding	False
authorships[15].author.id	https://openalex.org/A5082137581
authorships[15].author.orcid	https://orcid.org/0000-0001-8474-6317
authorships[15].author.display_name	Brian Burkett
authorships[15].author_position	middle
authorships[15].raw_author_name	Brian Burkett
authorships[15].is_corresponding	False
authorships[16].author.id	https://openalex.org/A5109590205
authorships[16].author.orcid
authorships[16].author.display_name	Craig Gidney
authorships[16].author_position	middle
authorships[16].raw_author_name	Craig Gidney
authorships[16].is_corresponding	False
authorships[17].author.id	https://openalex.org/A5010185866
authorships[17].author.orcid	https://orcid.org/0000-0002-9048-2896
authorships[17].author.display_name	Austin G. Fowler
authorships[17].author_position	middle
authorships[17].raw_author_name	Austin G. Fowler
authorships[17].is_corresponding	False
authorships[18].author.id	https://openalex.org/A5027882429
authorships[18].author.orcid	https://orcid.org/0000-0002-5841-181X
authorships[18].author.display_name	Harald Putterman
authorships[18].author_position	middle
authorships[18].raw_author_name	Harald Putterman
authorships[18].is_corresponding	False
authorships[19].author.id	https://openalex.org/A5029037357
authorships[19].author.orcid	https://orcid.org/0000-0002-9096-254X
authorships[19].author.display_name	I. L. Aleǐner
authorships[19].author_position	middle
authorships[19].raw_author_name	Igor Aleiner
authorships[19].is_corresponding	False
authorships[20].author.id	https://openalex.org/A5014090748
authorships[20].author.orcid	https://orcid.org/0000-0002-7179-0631
authorships[20].author.display_name	Frank Arute
authorships[20].author_position	middle
authorships[20].raw_author_name	Frank Arute
authorships[20].is_corresponding	False
authorships[21].author.id	https://openalex.org/A5080222383
authorships[21].author.orcid	https://orcid.org/0000-0002-6486-7100
authorships[21].author.display_name	Kunal Arya
authorships[21].author_position	middle
authorships[21].raw_author_name	Kunal Arya
authorships[21].is_corresponding	False
authorships[22].author.id	https://openalex.org/A5059699271
authorships[22].author.orcid	https://orcid.org/0000-0001-6979-9533
authorships[22].author.display_name	Ryan Babbush
authorships[22].author_position	middle
authorships[22].raw_author_name	Ryan Babbush
authorships[22].is_corresponding	False
authorships[23].author.id	https://openalex.org/A5078045247
authorships[23].author.orcid	https://orcid.org/0000-0002-6523-6730
authorships[23].author.display_name	Joseph C. Bardin
authorships[23].author_position	middle
authorships[23].raw_author_name	Joseph C. Bardin
authorships[23].is_corresponding	False
authorships[24].author.id	https://openalex.org/A5046123254
authorships[24].author.orcid	https://orcid.org/0000-0001-5264-4025
authorships[24].author.display_name	Andreas Bengtsson
authorships[24].author_position	middle
authorships[24].raw_author_name	Andreas Bengtsson
authorships[24].is_corresponding	False
authorships[25].author.id	https://openalex.org/A5067644085
authorships[25].author.orcid	https://orcid.org/0000-0002-8517-7475
authorships[25].author.display_name	Alexandre Bourassa
authorships[25].author_position	middle
authorships[25].raw_author_name	Alexandre Bourassa
authorships[25].is_corresponding	False
authorships[26].author.id	https://openalex.org/A5014321658
authorships[26].author.orcid	https://orcid.org/0009-0008-1725-9488
authorships[26].author.display_name	Michael Broughton
authorships[26].author_position	middle
authorships[26].raw_author_name	Michael Broughton
authorships[26].is_corresponding	False
authorships[27].author.id	https://openalex.org/A5021629913
authorships[27].author.orcid	https://orcid.org/0000-0001-5139-7931
authorships[27].author.display_name	Bob B. Buckley
authorships[27].author_position	middle
authorships[27].raw_author_name	Bob B. Buckley
authorships[27].is_corresponding	False
authorships[28].author.id	https://openalex.org/A5047982487
authorships[28].author.orcid
authorships[28].author.display_name	David A. Buell
authorships[28].author_position	middle
authorships[28].raw_author_name	David A. Buell
authorships[28].is_corresponding	False
authorships[29].author.id	https://openalex.org/A5053250307
authorships[29].author.orcid	https://orcid.org/0000-0001-7445-1654
authorships[29].author.display_name	Nicholas Bushnell
authorships[29].author_position	middle
authorships[29].raw_author_name	Nicholas Bushnell
authorships[29].is_corresponding	False
authorships[30].author.id	https://openalex.org/A5114048040
authorships[30].author.orcid
authorships[30].author.display_name	Benjamin Chiaro
authorships[30].author_position	middle
authorships[30].raw_author_name	Benjamin Chiaro
authorships[30].is_corresponding	False
authorships[31].author.id	https://openalex.org/A5048515902
authorships[31].author.orcid	https://orcid.org/0000-0002-6164-0007
authorships[31].author.display_name	Roberto Collins
authorships[31].author_position	middle
authorships[31].raw_author_name	Roberto Collins
authorships[31].is_corresponding	False
authorships[32].author.id	https://openalex.org/A5113443645
authorships[32].author.orcid
authorships[32].author.display_name	William Courtney
authorships[32].author_position	middle
authorships[32].raw_author_name	William Courtney
authorships[32].is_corresponding	False
authorships[33].author.id	https://openalex.org/A5023691782
authorships[33].author.orcid
authorships[33].author.display_name	Alan R. Derk
authorships[33].author_position	middle
authorships[33].raw_author_name	Alan R. Derk
authorships[33].is_corresponding	False
authorships[34].author.id	https://openalex.org/A5021226061
authorships[34].author.orcid	https://orcid.org/0000-0001-7134-5733
authorships[34].author.display_name	Daniel Eppens
authorships[34].author_position	middle
authorships[34].raw_author_name	Daniel Eppens
authorships[34].is_corresponding	False
authorships[35].author.id	https://openalex.org/A5103248638
authorships[35].author.orcid	https://orcid.org/0000-0002-7432-5946
authorships[35].author.display_name	Catherine Erickson
authorships[35].author_position	middle
authorships[35].raw_author_name	Catherine Erickson
authorships[35].is_corresponding	False
authorships[36].author.id	https://openalex.org/A5036253306
authorships[36].author.orcid
authorships[36].author.display_name	Edward Farhi
authorships[36].author_position	middle
authorships[36].raw_author_name	Edward Farhi
authorships[36].is_corresponding	False
authorships[37].author.id	https://openalex.org/A5012506742
authorships[37].author.orcid	https://orcid.org/0000-0002-3732-168X
authorships[37].author.display_name	Brooks Foxen
authorships[37].author_position	middle
authorships[37].raw_author_name	Brooks Foxen
authorships[37].is_corresponding	False
authorships[38].author.id	https://openalex.org/A5042731148
authorships[38].author.orcid	https://orcid.org/0000-0002-1283-2862
authorships[38].author.display_name	Marissa Giustina
authorships[38].author_position	middle
authorships[38].raw_author_name	Marissa Giustina
authorships[38].is_corresponding	False
authorships[39].author.id	https://openalex.org/A5020576151
authorships[39].author.orcid	https://orcid.org/0000-0001-7049-6206
authorships[39].author.display_name	Jonathan A. Gross
authorships[39].author_position	middle
authorships[39].raw_author_name	Jonathan A. Gross
authorships[39].is_corresponding	False
authorships[40].author.id	https://openalex.org/A5055936203
authorships[40].author.orcid	https://orcid.org/0000-0001-9412-0553
authorships[40].author.display_name	Matthew P. Harrigan
authorships[40].author_position	middle
authorships[40].raw_author_name	Matthew P. Harrigan
authorships[40].is_corresponding	False
authorships[41].author.id	https://openalex.org/A5087127700
authorships[41].author.orcid	https://orcid.org/0000-0003-0521-8378
authorships[41].author.display_name	Sean D. Harrington
authorships[41].author_position	middle
authorships[41].raw_author_name	Sean D. Harrington
authorships[41].is_corresponding	False
authorships[42].author.id	https://openalex.org/A5006515965
authorships[42].author.orcid
authorships[42].author.display_name	J. Hilton
authorships[42].author_position	middle
authorships[42].raw_author_name	Jeremy Hilton
authorships[42].is_corresponding	False
authorships[43].author.id	https://openalex.org/A5070979642
authorships[43].author.orcid
authorships[43].author.display_name	Alan Ho
authorships[43].author_position	middle
authorships[43].raw_author_name	Alan Ho
authorships[43].is_corresponding	False
authorships[44].author.id	https://openalex.org/A5104082891
authorships[44].author.orcid	https://orcid.org/0009-0000-4650-8115
authorships[44].author.display_name	Trent Huang
authorships[44].author_position	middle
authorships[44].raw_author_name	Trent Huang
authorships[44].is_corresponding	False
authorships[45].author.id	https://openalex.org/A5024111873
authorships[45].author.orcid	https://orcid.org/0000-0003-2735-1380
authorships[45].author.display_name	William J. Huggins
authorships[45].author_position	middle
authorships[45].raw_author_name	William J. Huggins
authorships[45].is_corresponding	False
authorships[46].author.id	https://openalex.org/A5072120756
authorships[46].author.orcid	https://orcid.org/0000-0002-8777-6789
authorships[46].author.display_name	L. B. Ioffe
authorships[46].author_position	middle
authorships[46].raw_author_name	L. B. Ioffe
authorships[46].is_corresponding	False
authorships[47].author.id	https://openalex.org/A5070406226
authorships[47].author.orcid
authorships[47].author.display_name	Sergei V. Isakov
authorships[47].author_position	middle
authorships[47].raw_author_name	Sergei V. Isakov
authorships[47].is_corresponding	False
authorships[48].author.id	https://openalex.org/A5113537118
authorships[48].author.orcid
authorships[48].author.display_name	E. Jeffrey
authorships[48].author_position	middle
authorships[48].raw_author_name	Evan Jeffrey
authorships[48].is_corresponding	False
authorships[49].author.id	https://openalex.org/A5100422956
authorships[49].author.orcid	https://orcid.org/0000-0003-0435-655X
authorships[49].author.display_name	Jiang Zhang
authorships[49].author_position	middle
authorships[49].raw_author_name	Zhang Jiang
authorships[49].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	http://arxiv.org/pdf/2102.06132.pdf
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Exponential suppression of bit or phase flip errors with repetitive quantum error correction
has_fulltext	False
is_retracted	False
updated_date	2025-10-10T17:16:08.811792
primary_topic.id	https://openalex.org/T10682
primary_topic.field.id	https://openalex.org/fields/17
primary_topic.field.display_name	Computer Science
primary_topic.score	0.9991999864578247
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1702
primary_topic.subfield.display_name	Artificial Intelligence
primary_topic.display_name	Quantum Computing Algorithms and Architecture
related_works	https://openalex.org/W3137855080, https://openalex.org/W2268399401, https://openalex.org/W3184667711, https://openalex.org/W2010108838, https://openalex.org/W3181925377, https://openalex.org/W2023217289, https://openalex.org/W2920155300, https://openalex.org/W3047518884, https://openalex.org/W3099908417, https://openalex.org/W3089170382, https://openalex.org/W2502126115, https://openalex.org/W3198901288, https://openalex.org/W3013543845, https://openalex.org/W2583795980, https://openalex.org/W3126520678, https://openalex.org/W3043310711, https://openalex.org/W2356565615, https://openalex.org/W2950317667, https://openalex.org/W3041379827, https://openalex.org/W1803716641
cited_by_count	10
counts_by_year[0].year	2022
counts_by_year[0].cited_by_count	1
counts_by_year[1].year	2021
counts_by_year[1].cited_by_count	9
locations_count	1
best_oa_location.id	mag:3127785863
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url
best_oa_location.version	submittedVersion
best_oa_location.raw_type
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name	arXiv (Cornell University)
best_oa_location.landing_page_url	http://arxiv.org/pdf/2102.06132.pdf
primary_location.id	mag:3127785863
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url
primary_location.version	submittedVersion
primary_location.raw_type
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name	arXiv (Cornell University)
primary_location.landing_page_url	http://arxiv.org/pdf/2102.06132.pdf
publication_date	2021-02-11
publication_year	2021
referenced_works_count	0
abstract_inverted_index.5	148
abstract_inverted_index.a	82, 117, 166, 182, 196, 223, 236
abstract_inverted_index.1D	112, 214
abstract_inverted_index.2D	118, 198, 216
abstract_inverted_index.50	158
abstract_inverted_index.We	163
abstract_inverted_index.as	67
abstract_inverted_index.be	57
abstract_inverted_index.by	44, 137
abstract_inverted_index.in	20, 116, 181
abstract_inverted_index.is	96, 155
abstract_inverted_index.of	3, 70, 101, 120, 127, 145, 160, 179
abstract_inverted_index.on	203, 235
abstract_inverted_index.or	129
abstract_inverted_index.so	53
abstract_inverted_index.to	40, 149
abstract_inverted_index.we	110, 191
abstract_inverted_index.21.	150
abstract_inverted_index.QEC	85, 185
abstract_inverted_index.and	59, 93, 175, 207, 215
abstract_inverted_index.are	63, 80, 91, 234
abstract_inverted_index.bit	128
abstract_inverted_index.but	24
abstract_inverted_index.can	56
abstract_inverted_index.for	17, 168, 186
abstract_inverted_index.low	10
abstract_inverted_index.per	135
abstract_inverted_index.the	1, 21, 68, 76, 89, 143, 177, 187, 204, 210
abstract_inverted_index.two	104
abstract_inverted_index.Many	14
abstract_inverted_index.also	86, 164
abstract_inverted_index.both	213
abstract_inverted_index.call	16
abstract_inverted_index.code	200
abstract_inverted_index.from	147, 212
abstract_inverted_index.grid	119
abstract_inverted_index.have	29
abstract_inverted_index.high	173
abstract_inverted_index.many	50, 99
abstract_inverted_index.more	138
abstract_inverted_index.near	33
abstract_inverted_index.over	98, 157
abstract_inverted_index.path	238
abstract_inverted_index.same	205
abstract_inverted_index.show	208
abstract_inverted_index.than	139
abstract_inverted_index.that	54, 75, 88, 94, 209, 231
abstract_inverted_index.then	64
abstract_inverted_index.this	42, 152
abstract_inverted_index.when	141
abstract_inverted_index.will	6
abstract_inverted_index.with	172, 219
abstract_inverted_index.(QEC)	38
abstract_inverted_index.Here,	109
abstract_inverted_index.These	228
abstract_inverted_index.agree	218
abstract_inverted_index.below	81
abstract_inverted_index.codes	114, 217
abstract_inverted_index.error	12, 18, 31, 36, 78, 102, 134, 153, 161, 170, 193, 226
abstract_inverted_index.fault	240
abstract_inverted_index.first	188
abstract_inverted_index.local	92
abstract_inverted_index.major	105
abstract_inverted_index.qubit	202
abstract_inverted_index.rates	19, 32, 79
abstract_inverted_index.round	136
abstract_inverted_index.small	197
abstract_inverted_index.time.	189
abstract_inverted_index.using	195, 222
abstract_inverted_index.which	123
abstract_inverted_index.across	49
abstract_inverted_index.bridge	41
abstract_inverted_index.device	183
abstract_inverted_index.divide	43
abstract_inverted_index.errors	55, 62, 90, 180
abstract_inverted_index.grows,	73
abstract_inverted_index.method	167
abstract_inverted_index.model.	227
abstract_inverted_index.number	69, 144
abstract_inverted_index.qubits	52, 72, 122, 146, 233
abstract_inverted_index.rates.	13
abstract_inverted_index.rounds	100, 159
abstract_inverted_index.simple	224
abstract_inverted_index.stable	156
abstract_inverted_index.viable	237
abstract_inverted_index.Logical	61
abstract_inverted_index.Quantum	35
abstract_inverted_index.certain	83
abstract_inverted_index.device,	206
abstract_inverted_index.errors,	131
abstract_inverted_index.logical	11, 47, 133, 201
abstract_inverted_index.perform	192
abstract_inverted_index.quantum	4, 26, 46, 242
abstract_inverted_index.regime,	23
abstract_inverted_index.require	7
abstract_inverted_index.results	211
abstract_inverted_index.surface	199
abstract_inverted_index.towards	239
abstract_inverted_index.Finally,	190
abstract_inverted_index.detected	58
abstract_inverted_index.embedded	115
abstract_inverted_index.findings	229
abstract_inverted_index.locality	178
abstract_inverted_index.physical	30, 51, 71, 77
abstract_inverted_index.promises	39
abstract_inverted_index.provided	74
abstract_inverted_index.reducing	132
abstract_inverted_index.requires	87
abstract_inverted_index.tolerant	241
abstract_inverted_index.Realizing	0
abstract_inverted_index.achieving	8
abstract_inverted_index.analyzing	169
abstract_inverted_index.computing	5
abstract_inverted_index.detection	194
abstract_inverted_index.implement	111
abstract_inverted_index.introduce	165
abstract_inverted_index.numerical	220
abstract_inverted_index.platforms	27
abstract_inverted_index.potential	2
abstract_inverted_index.typically	28
abstract_inverted_index.$10^{-15}$	22
abstract_inverted_index.$10^{-3}$.	34
abstract_inverted_index.Crucially,	151
abstract_inverted_index.computing.	243
abstract_inverted_index.corrected.	60
abstract_inverted_index.correction	37
abstract_inverted_index.increasing	142
abstract_inverted_index.maintained	97
abstract_inverted_index.performing	184
abstract_inverted_index.phase-flip	130
abstract_inverted_index.precision,	174
abstract_inverted_index.repetition	113
abstract_inverted_index.suppressed	66
abstract_inverted_index.threshold.	84
abstract_inverted_index.$100\times$	140
abstract_inverted_index.challenges.	108
abstract_inverted_index.correction,	103
abstract_inverted_index.correction.	162
abstract_inverted_index.demonstrate	124, 230
abstract_inverted_index.exponential	125
abstract_inverted_index.information	48
abstract_inverted_index.outstanding	106
abstract_inverted_index.performance	95
abstract_inverted_index.simulations	221
abstract_inverted_index.suppression	126, 154
abstract_inverted_index.applications	15
abstract_inverted_index.characterize	176
abstract_inverted_index.correlations	171
abstract_inverted_index.depolarizing	225
abstract_inverted_index.distributing	45
abstract_inverted_index.experimental	107
abstract_inverted_index.sufficiently	9
abstract_inverted_index.exponentially	65
abstract_inverted_index.superconducting	121, 232
abstract_inverted_index.state-of-the-art	25
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	91
sustainable_development_goals[0].id	https://metadata.un.org/sdg/16
sustainable_development_goals[0].score	0.5199999809265137
sustainable_development_goals[0].display_name	Peace, Justice and strong institutions
citation_normalized_percentile