Improved belief propagation decoding algorithm based on decoupling representation of Pauli operators for quantum stabilizer codes

Based on decoupling representation of Pauli operators, we propose partially decoupled belief propagation (PDBP) and fully decoupled belief propagation (FDBP) decoding algorithm for quantum LDPC codes. These two algorithms can handle the correlations between the X and Z components of the vectors in s...

Full description

Saved in:

Bibliographic Details
Published in:	Quantum information processing Vol. 24; no. 4; p. 100
Main Authors:	Yi, Zhengzhong, Liang, Zhipeng, Chen, Jiahan, Zhong, Kaixin, Wu, Yulin, Fang, Zhou, Wang, Xuan
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Nature B.V 01.04.2025
Subjects:	Accuracy Algorithms Codes Commuting Decoding Decoupling Error correcting codes Error correction Error correction & detection Operators Parity Representations Simulation
ISSN:	1573-1332, 1570-0755, 1573-1332
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Based on decoupling representation of Pauli operators, we propose partially decoupled belief propagation (PDBP) and fully decoupled belief propagation (FDBP) decoding algorithm for quantum LDPC codes. These two algorithms can handle the correlations between the X and Z components of the vectors in symplectic representation, which are introduced by Pauli Y errors. Hence, they can apply not only to CSS codes, but also to non-CSS codes. For planar surface code and XZZX planar surface code, compared with traditional BP based on symplectic representation, the decoding accuracy of PDBP and FDBP is significantly improved in pure Y noise and depolarizing noise, especially that of FDBP. The impressive performance of FDBP might promote the practical implementation of quantum error correcting codes in engineering.
AbstractList	Based on decoupling representation of Pauli operators, we propose partially decoupled belief propagation (PDBP) and fully decoupled belief propagation (FDBP) decoding algorithm for quantum LDPC codes. These two algorithms can handle the correlations between the X and Z components of the vectors in symplectic representation, which are introduced by Pauli Y errors. Hence, they can apply not only to CSS codes, but also to non-CSS codes. For planar surface code and XZZX planar surface code, compared with traditional BP based on symplectic representation, the decoding accuracy of PDBP and FDBP is significantly improved in pure Y noise and depolarizing noise, especially that of FDBP. The impressive performance of FDBP might promote the practical implementation of quantum error correcting codes in engineering.
ArticleNumber	100
Author	Zhong, Kaixin Fang, Zhou Wu, Yulin Wang, Xuan Chen, Jiahan Yi, Zhengzhong Liang, Zhipeng
Author_xml	– sequence: 1 givenname: Zhengzhong surname: Yi fullname: Yi, Zhengzhong – sequence: 2 givenname: Zhipeng surname: Liang fullname: Liang, Zhipeng – sequence: 3 givenname: Jiahan surname: Chen fullname: Chen, Jiahan – sequence: 4 givenname: Kaixin surname: Zhong fullname: Zhong, Kaixin – sequence: 5 givenname: Yulin surname: Wu fullname: Wu, Yulin – sequence: 6 givenname: Zhou surname: Fang fullname: Fang, Zhou – sequence: 7 givenname: Xuan surname: Wang fullname: Wang, Xuan
BookMark	eNp9kE1LxDAQhoOs4K76BzwFPFfz0SbpURa_YEEPeg5pM10j3aYmqaA3_7nRehAPnmaG931nmGeFFoMfAKETSs4oIfI8UkqZKgirClJKUhdiDy1pJXlBOWeLX_0BWsX4TAijQokl-rjdjcG_gsUN9A46nKfRbE1yfsAWWm_dsMWm3_rg0tMONyZm7482jf2XGmAMEGFIc8p3-N5MvcN-hGCSDxF3PuCXyQxp2uGYTON69w4B5-0Qj9B-Z_oIxz_1ED1eXT6sb4rN3fXt-mJTtEzKVNRUcFVXRsnKCioawoRtykYypaztShCypdy20CpGa5s_lYwaw0tBCa8sA36ITue9-cOXCWLSz34KQz6pOatULWRZl9nFZlcbfIwBOj0GtzPhTVOiv1DrGbXOqPU3ai1ySP0JtW6GkYJx_X_RT6M1h6o
CitedBy_id	crossref_primary_10_1109_TQE_2025_3577769 crossref_primary_10_3390_e27090940
Cites_doi	10.26421/QIC8.10-8 10.1109/18.748992 10.1109/JSAIT.2020.3011758 10.1109/4234.1001666 10.1109/TIT.2015.2422294 10.1109/CCNC.2014.6940497 10.1109/ISIT.2014.6874997 10.1109/26.990903 10.22331/q-2021-11-22-585 10.1103/PhysRevA.86.032324 10.1038/s42254-024-00706-3 10.1109/49.661103 10.1109/18.412683 10.1103/PhysRevA.90.032326 10.1109/18.910572 10.1103/PhysRevResearch.2.043423 10.1038/s41534-022-00623-2 10.1109/26.768759 10.4153/CJM-1965-045-4 10.1109/ISTC57237.2023.10273527 10.1103/PhysRevLett.104.050504 10.1109/ACCESS.2015.2503267 10.1109/GCWkshps50303.2020.9367482 10.1103/PhysRevA.83.052331 10.1038/s41467-021-22274-1 10.1109/ISIT.2018.8437905
ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
Copyright_xml	– notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
DBID	AAYXX CITATION JQ2
DOI	10.1007/s11128-025-04709-6
DatabaseName	CrossRef ProQuest Computer Science Collection
DatabaseTitle	CrossRef ProQuest Computer Science Collection
DatabaseTitleList	ProQuest Computer Science Collection
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1573-1332
ExternalDocumentID	10_1007_s11128_025_04709_6
GroupedDBID	.86 .VR 06D 0R~ 0VY 123 1N0 203 29P 29~ 2J2 2JN 2JY 2KG 2LR 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 8TC 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYXX ABAKF ABBBX ABBRH ABBXA ABDBE ABDBF ABDZT ABECU ABFSG ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACSTC ACZOJ ADHHG ADHIR ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHPBZ AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BGNMA BSONS CITATION CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI ESBYG ESX FEDTE FERAY FFXSO FIGPU FNLPD FRRFC FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS HF~ HG5 HG6 HLICF HMJXF HQYDN HRMNR HVGLF HZ~ I09 IJ- IKXTQ ITM IWAJR IXC IXE IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y MA- NPVJJ NQJWS NU0 O93 O9J OAM P2P P9O PF0 PT4 QOS R89 R9I RNS ROL RPX RSV S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ~A9 AAYZH AESKC JQ2
ID	FETCH-LOGICAL-c277t-9163895a875d616b026db4b7288ddf4e67c13dcec8219d133721aa3461035d2e3
IEDL.DBID	RSV
ISICitedReferencesCount	3
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001451691000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1573-1332 1570-0755
IngestDate	Fri Oct 10 03:41:28 EDT 2025 Tue Nov 18 20:15:31 EST 2025 Sat Nov 29 07:57:16 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c277t-9163895a875d616b026db4b7288ddf4e67c13dcec8219d133721aa3461035d2e3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
PQID	3258967494
PQPubID	2043832
ParticipantIDs	proquest_journals_3258967494 crossref_primary_10_1007_s11128_025_04709_6 crossref_citationtrail_10_1007_s11128_025_04709_6
PublicationCentury	2000
PublicationDate	2025-04-01
PublicationDateYYYYMMDD	2025-04-01
PublicationDate_xml	– month: 04 year: 2025 text: 2025-04-01 day: 01
PublicationDecade	2020
PublicationPlace	Dordrecht
PublicationPlace_xml	– name: Dordrecht
PublicationTitle	Quantum information processing
PublicationYear	2025
Publisher	Springer Nature B.V
Publisher_xml	– name: Springer Nature B.V
References	M-H Hsieh (4709_CR24) 2011; 83 4709_CR1 DJ MacKay (4709_CR6) 1999; 45 JP Bonilla Ataides (4709_CR20) 2021; 12 MP Fossorier (4709_CR32) 1995; 41 J Chen (4709_CR30) 2002; 50 S Bravyi (4709_CR3) 2014; 90 4709_CR23 G Duclos-Cianci (4709_CR4) 2010; 104 4709_CR26 4709_CR5 4709_CR29 AG Fowler (4709_CR21) 2012; 86 K-Y Kuo (4709_CR8) 2022; 8 RJ McEliece (4709_CR27) 1998; 16 P Panteleev (4709_CR13) 2021; 5 J Chen (4709_CR31) 2002; 6 J Edmonds (4709_CR2) 1965; 17 P Iyer (4709_CR25) 2015; 61 4709_CR10 FR Kschischang (4709_CR28) 2001; 47 4709_CR11 J Roffe (4709_CR12) 2020; 2 4709_CR14 4709_CR15 Z Babar (4709_CR7) 2015; 3 K-Y Kuo (4709_CR9) 2020; 1 4709_CR16 4709_CR17 4709_CR18 4709_CR19 MP Fossorier (4709_CR22) 1999; 47
References_xml	– ident: 4709_CR5 – ident: 4709_CR17 – ident: 4709_CR11 doi: 10.26421/QIC8.10-8 – ident: 4709_CR23 – volume: 45 start-page: 399 issue: 2 year: 1999 ident: 4709_CR6 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.748992 – volume: 1 start-page: 487 issue: 2 year: 2020 ident: 4709_CR9 publication-title: IEEE J. Sel. Areas Inf. Theory doi: 10.1109/JSAIT.2020.3011758 – volume: 6 start-page: 208 issue: 5 year: 2002 ident: 4709_CR31 publication-title: IEEE Commun. Lett. doi: 10.1109/4234.1001666 – volume: 61 start-page: 5209 issue: 9 year: 2015 ident: 4709_CR25 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2015.2422294 – ident: 4709_CR29 doi: 10.1109/CCNC.2014.6940497 – ident: 4709_CR15 doi: 10.1109/ISIT.2014.6874997 – volume: 50 start-page: 406 issue: 3 year: 2002 ident: 4709_CR30 publication-title: IEEE Trans. Commun. doi: 10.1109/26.990903 – volume: 5 start-page: 585 year: 2021 ident: 4709_CR13 publication-title: Quantum doi: 10.22331/q-2021-11-22-585 – volume: 86 issue: 3 year: 2012 ident: 4709_CR21 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.86.032324 – ident: 4709_CR1 doi: 10.1038/s42254-024-00706-3 – volume: 16 start-page: 140 issue: 2 year: 1998 ident: 4709_CR27 publication-title: IEEE J. Sel. Areas Commun. doi: 10.1109/49.661103 – volume: 41 start-page: 1379 issue: 5 year: 1995 ident: 4709_CR32 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.412683 – volume: 90 issue: 3 year: 2014 ident: 4709_CR3 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.90.032326 – ident: 4709_CR16 – volume: 47 start-page: 498 issue: 2 year: 2001 ident: 4709_CR28 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.910572 – volume: 2 issue: 4 year: 2020 ident: 4709_CR12 publication-title: Phys. Rev. Res. doi: 10.1103/PhysRevResearch.2.043423 – volume: 8 start-page: 111 issue: 1 year: 2022 ident: 4709_CR8 publication-title: npj Quantum Inf. doi: 10.1038/s41534-022-00623-2 – volume: 47 start-page: 673 issue: 5 year: 1999 ident: 4709_CR22 publication-title: IEEE Trans. Commun. doi: 10.1109/26.768759 – volume: 17 start-page: 449 year: 1965 ident: 4709_CR2 publication-title: Can. J. Math. doi: 10.4153/CJM-1965-045-4 – ident: 4709_CR14 doi: 10.1109/ISTC57237.2023.10273527 – ident: 4709_CR18 doi: 10.1109/ISIT.2014.6874997 – volume: 104 issue: 5 year: 2010 ident: 4709_CR4 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.104.050504 – ident: 4709_CR26 – volume: 3 start-page: 2492 year: 2015 ident: 4709_CR7 publication-title: IEEE Access doi: 10.1109/ACCESS.2015.2503267 – ident: 4709_CR10 doi: 10.1109/GCWkshps50303.2020.9367482 – volume: 83 issue: 5 year: 2011 ident: 4709_CR24 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.83.052331 – volume: 12 start-page: 2172 issue: 1 year: 2021 ident: 4709_CR20 publication-title: Nat. Commun. doi: 10.1038/s41467-021-22274-1 – ident: 4709_CR19 doi: 10.1109/ISIT.2018.8437905
SSID	ssj0021686
Score	2.3758154
Snippet	Based on decoupling representation of Pauli operators, we propose partially decoupled belief propagation (PDBP) and fully decoupled belief propagation (FDBP)...
SourceID	proquest crossref
SourceType	Aggregation Database Enrichment Source Index Database
StartPage	100
SubjectTerms	Accuracy Algorithms Codes Commuting Decoding Decoupling Error correcting codes Error correction Error correction & detection Operators Parity Representations Simulation
Title	Improved belief propagation decoding algorithm based on decoupling representation of Pauli operators for quantum stabilizer codes
URI	https://www.proquest.com/docview/3258967494
Volume	24
WOSCitedRecordID	wos001451691000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAVX databaseName: SpringerLink Contemporary customDbUrl: eissn: 1573-1332 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0021686 issn: 1573-1332 databaseCode: RSV dateStart: 20020401 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3LS8MwGA9jePDifOJjSg7etNg82qRHEYenIfhgt9Im6Rxs3VxbD978z_2StpOBCjuGtiF8v3yvJt_vQ-hS6iiTibJ3qiLu8YSDSlEYgjOQmlHf8FS6ZhNiOJSjUfTYQdd_nuDfFKCNlkWZBp7PhR95ll-bhHWx1tPrKrsioWvrSALBPEi8aFMh8_sU615o3Qg7zzLobbamXbTTRJD4toZ8D3VMvo96bXcG3CjrAfqq_xcYjVMDgWaGYQTWwyGBNWSd1mvhZDqeLyfl2wxbf6Zx86yyhbpj7Cgv2_KkHM8zbG8STvB8YdzxfIEh5sXvFcBTzTAEmvaq7SeswlbKF4foZXD_fPfgNQ0XPEWFKMHw2fglSCCH0SEJU8jPdMpTQaXUOuMmFIowrYySYOc0CBnSxyRhlrKdBZoadoS6-Tw3xwhTqoNIqSxLAX8DYZAkvhYkC30TGKrZCSItALFq2MhtU4xp_MOjbGUcg4xjJ-M4PEFXq28WNRfHv2_3W1zjRi-LmNFARqHgET_daLIztE1rtD2f9FG3XFbmHG2pj3JSLC_cRvwGU1PVhQ
linkProvider	Springer Nature
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Improved+belief+propagation+decoding+algorithm+based+on+decoupling+representation+of+Pauli+operators+for+quantum+stabilizer+codes&rft.jtitle=Quantum+information+processing&rft.au=Yi%2C+Zhengzhong&rft.au=Liang%2C+Zhipeng&rft.au=Chen%2C+Jiahan&rft.au=Zhong%2C+Kaixin&rft.date=2025-04-01&rft.issn=1573-1332&rft.eissn=1573-1332&rft.volume=24&rft.issue=4&rft_id=info:doi/10.1007%2Fs11128-025-04709-6&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11128_025_04709_6
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1573-1332&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1573-1332&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1573-1332&client=summon