Parallel time integration using Batched BLAS (Basic Linear Algebra Subprograms) routines
We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform the integration of all time steps in parallel. The performance boost is especially prominent for small to medium-sized quantum systems. The d...
Saved in:
| Published in: | Computer physics communications Vol. 270; p. 108181 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.01.2022
|
| Subjects: | |
| ISSN: | 0010-4655, 1879-2944 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform the integration of all time steps in parallel. The performance boost is especially prominent for small to medium-sized quantum systems. The devised algorithm can largely be implemented using the recently-specified batched versions of the BLAS routines, and can therefore be easily ported to a variety of platforms. Our PARAllelized Matrix Exponentiation for Numerical Time evolution (PARAMENT) implementation runs on CUDA-enabled graphics processing units.
Program Title: PARAMENT
CPC Library link to program files:https://doi.org/10.17632/zy5v4xs89d.1
Developer's repository link:https://github.com/parament-integrator/parament
Licensing provisions: Apache 2.0
Programming language: C / CUDA / Python
Nature of problem: Time-integration of the Schrödinger equation with a time-dependent Hamiltonian for quantum systems with a small Hilbert space but many time-steps.
Solution method: A 4th order Magnus integrator, highly parallelized on a GPU, implemented using a small subset of BLAS functions for improved portability. |
|---|---|
| AbstractList | We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform the integration of all time steps in parallel. The performance boost is especially prominent for small to medium-sized quantum systems. The devised algorithm can largely be implemented using the recently-specified batched versions of the BLAS routines, and can therefore be easily ported to a variety of platforms. Our PARAllelized Matrix Exponentiation for Numerical Time evolution (PARAMENT) implementation runs on CUDA-enabled graphics processing units.
Program Title: PARAMENT
CPC Library link to program files:https://doi.org/10.17632/zy5v4xs89d.1
Developer's repository link:https://github.com/parament-integrator/parament
Licensing provisions: Apache 2.0
Programming language: C / CUDA / Python
Nature of problem: Time-integration of the Schrödinger equation with a time-dependent Hamiltonian for quantum systems with a small Hilbert space but many time-steps.
Solution method: A 4th order Magnus integrator, highly parallelized on a GPU, implemented using a small subset of BLAS functions for improved portability. |
| ArticleNumber | 108181 |
| Author | Welter, Pol Herb, Konstantin |
| Author_xml | – sequence: 1 givenname: Konstantin surname: Herb fullname: Herb, Konstantin email: science@rashbw.de – sequence: 2 givenname: Pol orcidid: 0000-0002-3666-7400 surname: Welter fullname: Welter, Pol |
| BookMark | eNp9kE1LAzEQhoNUsK3-AG856mFrskl2s3hqxS9YUKiCt5DNTmrKdrckqeC_N7WePPQ0zLw8A-8zQaN-6AGhS0pmlNDiZj0zWzPLSU7TLqmkJ2hMZVllecX5CI0JoSTjhRBnaBLCmhBSlhUbo49X7XXXQYej2wB2fYSV19ENPd4F16_wQkfzCS1e1PMlvlro4AyuXQ_a43m3gsZrvNw1Wz8kbBOusR92McXhHJ1a3QW4-JtT9P5w_3b3lNUvj8938zozjJOYWQOiYJoZU0grWkmgZYxZyY0UQnMrGlsVUjBelUBYa6tcNzy3hKRbAY1lU1Qe_ho_hODBKuPib4HotesUJWovSK1VEqT2gtRBUCLpP3Lr3Ub776PM7YGBVOnLgVfBOOgNtM6Diaod3BH6B3XYgBk |
| CitedBy_id | crossref_primary_10_1038_s41467_025_55956_1 crossref_primary_10_1016_j_future_2024_06_004 |
| Cites_doi | 10.1016/j.cpc.2018.02.019 10.1090/S0025-5718-1955-0071856-0 10.1023/A:1022311628317 10.1016/j.cpc.2012.11.019 10.1016/j.jmr.2004.11.004 10.1016/j.procs.2017.05.138 10.1002/cpa.3160070404 10.1016/j.parco.2010.01.006 10.1016/j.jpdc.2004.03.021 10.1016/j.jcp.2011.04.006 10.1016/j.physrep.2008.11.001 10.1137/S00361445024180 10.1088/1361-6633/aa5170 10.1063/1.448136 10.1145/322217.322232 |
| ContentType | Journal Article |
| Copyright | 2021 The Authors |
| Copyright_xml | – notice: 2021 The Authors |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.cpc.2021.108181 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 1879-2944 |
| ExternalDocumentID | 10_1016_j_cpc_2021_108181 S0010465521002939 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARLI AAXUO AAYFN ABBOA ABFNM ABMAC ABNEU ABQEM ABQYD ABXDB ABYKQ ACDAQ ACFVG ACGFS ACLVX ACNNM ACRLP ACSBN ACZNC ADBBV ADECG ADEZE ADJOM ADMUD AEBSH AEKER AENEX AFKWA AFTJW AFZHZ AGHFR AGUBO AGYEJ AHHHB AHZHX AI. AIALX AIEXJ AIKHN AITUG AIVDX AJBFU AJOXV AJSZI ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG ATOGT AVWKF AXJTR AZFZN BBWZM BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FLBIZ FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HLZ HME HMV HVGLF HZ~ IHE IMUCA J1W KOM LG9 LZ4 M38 M41 MO0 N9A NDZJH O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SBC SCB SDF SDG SES SEW SHN SPC SPCBC SPD SPG SSE SSK SSQ SSV SSZ T5K TN5 UPT VH1 WUQ ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c340t-fce563a3cc68f5d80ed333f84c855a4f5bf96853497e03df92ab42f008536ebf3 |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000708648400007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0010-4655 |
| IngestDate | Sat Nov 29 07:00:17 EST 2025 Tue Nov 18 22:29:45 EST 2025 Fri Feb 23 02:44:52 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | GPU programming Batched BLAS Magnus integrators Parallel time integration Schrödinger equation Exponential integrators |
| Language | English |
| License | This is an open access article under the CC BY license. |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c340t-fce563a3cc68f5d80ed333f84c855a4f5bf96853497e03df92ab42f008536ebf3 |
| ORCID | 0000-0002-3666-7400 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.cpc.2021.108181 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_cpc_2021_108181 crossref_primary_10_1016_j_cpc_2021_108181 elsevier_sciencedirect_doi_10_1016_j_cpc_2021_108181 |
| PublicationCentury | 2000 |
| PublicationDate | January 2022 2022-01-00 |
| PublicationDateYYYYMMDD | 2022-01-01 |
| PublicationDate_xml | – month: 01 year: 2022 text: January 2022 |
| PublicationDecade | 2020 |
| PublicationTitle | Computer physics communications |
| PublicationYear | 2022 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Silveri, Tuorila, Thuneberg, Paraoanu (br0160) 2017; 80 Moler, Loan (br0030) 2003; 45 Blanes, Casas, Oteo, Ros (br0120) 2009; 470 Alvermann, Fehske (br0150) 2011; 230 Clenshaw (br0070) 1955; 9 Tal-Ezer, Kosloff (br0050) 1984; 81 Anderson, Bai, Bischof, Blackford, Demmel, Dongarra, Du Croz, Greenbaum, Hammarling, McKenney, Sorensen (br0040) 1999 Dongarra, Hammarling, Higham, Relton, Valero-Lara, Zounon (br0020) 2017; 108 Magnus (br0110) 1954; 7 Blanes, Casas, Ros (br0140) 2000; 40 Ladner, Fischer (br0090) 1980; 27 Johansson, Nation, Nori (br0180) 2013; 184 Creffield (br0190) 2003; 67 Reuther, Kepner, Byun, Samsi, Arcand, Bestor, Bergeron, Gadepally, Houle, Hubbell, Jones, Klein, Milechin, Mullen, Prout, Rosa, Yee, Michaleas (br0170) 2018 Irony, Toledo, Tiskin (br0100) 2004; 64 Slichter (br0010) 1990 Auckenthaler, Bader, Huckle, Spörl, Waldherr (br0080) 2010; 36 Khaneja, Reiss, Kehlet, Schulte-Herbrüggen, Glaser (br0200) 2005; 172 Auer, Einkemmer, Kandolf, Ostermann (br0130) 2018; 228 Lubich (br0060) 2008 Slichter (10.1016/j.cpc.2021.108181_br0010) 1990 Blanes (10.1016/j.cpc.2021.108181_br0140) 2000; 40 Tal-Ezer (10.1016/j.cpc.2021.108181_br0050) 1984; 81 Alvermann (10.1016/j.cpc.2021.108181_br0150) 2011; 230 Auckenthaler (10.1016/j.cpc.2021.108181_br0080) 2010; 36 Reuther (10.1016/j.cpc.2021.108181_br0170) 2018 Anderson (10.1016/j.cpc.2021.108181_br0040) 1999 Lubich (10.1016/j.cpc.2021.108181_br0060) 2008 Magnus (10.1016/j.cpc.2021.108181_br0110) 1954; 7 Moler (10.1016/j.cpc.2021.108181_br0030) 2003; 45 Silveri (10.1016/j.cpc.2021.108181_br0160) 2017; 80 Creffield (10.1016/j.cpc.2021.108181_br0190) 2003; 67 Blanes (10.1016/j.cpc.2021.108181_br0120) 2009; 470 Irony (10.1016/j.cpc.2021.108181_br0100) 2004; 64 Johansson (10.1016/j.cpc.2021.108181_br0180) 2013; 184 Khaneja (10.1016/j.cpc.2021.108181_br0200) 2005; 172 Dongarra (10.1016/j.cpc.2021.108181_br0020) 2017; 108 Clenshaw (10.1016/j.cpc.2021.108181_br0070) 1955; 9 Ladner (10.1016/j.cpc.2021.108181_br0090) 1980; 27 Auer (10.1016/j.cpc.2021.108181_br0130) 2018; 228 |
| References_xml | – volume: 172 start-page: 296 year: 2005 end-page: 305 ident: br0200 publication-title: J. Magn. Res. – volume: 108 start-page: 495 year: 2017 end-page: 504 ident: br0020 publication-title: Proc. Comput. Sci. – volume: 9 start-page: 118 year: 1955 end-page: 120 ident: br0070 publication-title: Math. Comput. – volume: 45 start-page: 3 year: 2003 end-page: 49 ident: br0030 publication-title: SIAM Rev. – volume: 64 start-page: 1017 year: 2004 end-page: 1026 ident: br0100 publication-title: J. Parallel Distrib. Comput. – volume: 40 start-page: 434 year: 2000 end-page: 450 ident: br0140 publication-title: BIT Numer. Math. – volume: 67 year: 2003 ident: br0190 publication-title: Phys. Rev. B – volume: 81 start-page: 3967 year: 1984 end-page: 3971 ident: br0050 publication-title: J. Chem. Phys. – year: 2008 ident: br0060 article-title: From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis – volume: 36 start-page: 359 year: 2010 end-page: 369 ident: br0080 publication-title: Parallel Comput. – volume: 7 start-page: 649 year: 1954 end-page: 673 ident: br0110 publication-title: Commun. Pure Appl. Math. – year: 2018 ident: br0170 publication-title: 2018 IEEE High Performance Extreme Computing Conference (HPEC) – volume: 27 start-page: 831 year: 1980 end-page: 838 ident: br0090 publication-title: J. ACM – volume: 470 start-page: 151 year: 2009 end-page: 238 ident: br0120 publication-title: Phys. Rep. – volume: 184 start-page: 1234 year: 2013 end-page: 1240 ident: br0180 publication-title: Comput. Phys. Commun. – year: 1990 ident: br0010 article-title: Principles of Magnetic Resonance – volume: 228 start-page: 115 year: 2018 end-page: 122 ident: br0130 publication-title: Comput. Phys. Commun. – volume: 80 year: 2017 ident: br0160 publication-title: Rep. Prog. Phys. – year: 1999 ident: br0040 article-title: LAPACK Users' Guide – volume: 230 start-page: 5930 year: 2011 end-page: 5956 ident: br0150 publication-title: J. Comput. Phys. – volume: 228 start-page: 115 year: 2018 ident: 10.1016/j.cpc.2021.108181_br0130 publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2018.02.019 – volume: 9 start-page: 118 issue: 51 year: 1955 ident: 10.1016/j.cpc.2021.108181_br0070 publication-title: Math. Comput. doi: 10.1090/S0025-5718-1955-0071856-0 – volume: 67 year: 2003 ident: 10.1016/j.cpc.2021.108181_br0190 publication-title: Phys. Rev. B – year: 1990 ident: 10.1016/j.cpc.2021.108181_br0010 – volume: 40 start-page: 434 issue: 3 year: 2000 ident: 10.1016/j.cpc.2021.108181_br0140 publication-title: BIT Numer. Math. doi: 10.1023/A:1022311628317 – volume: 184 start-page: 1234 issue: 4 year: 2013 ident: 10.1016/j.cpc.2021.108181_br0180 publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2012.11.019 – volume: 172 start-page: 296 issue: 2 year: 2005 ident: 10.1016/j.cpc.2021.108181_br0200 publication-title: J. Magn. Res. doi: 10.1016/j.jmr.2004.11.004 – year: 1999 ident: 10.1016/j.cpc.2021.108181_br0040 – volume: 108 start-page: 495 year: 2017 ident: 10.1016/j.cpc.2021.108181_br0020 publication-title: Proc. Comput. Sci. doi: 10.1016/j.procs.2017.05.138 – volume: 7 start-page: 649 issue: 4 year: 1954 ident: 10.1016/j.cpc.2021.108181_br0110 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160070404 – volume: 36 start-page: 359 issue: 5–6 year: 2010 ident: 10.1016/j.cpc.2021.108181_br0080 publication-title: Parallel Comput. doi: 10.1016/j.parco.2010.01.006 – year: 2008 ident: 10.1016/j.cpc.2021.108181_br0060 – volume: 64 start-page: 1017 issue: 9 year: 2004 ident: 10.1016/j.cpc.2021.108181_br0100 publication-title: J. Parallel Distrib. Comput. doi: 10.1016/j.jpdc.2004.03.021 – volume: 230 start-page: 5930 issue: 15 year: 2011 ident: 10.1016/j.cpc.2021.108181_br0150 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.04.006 – volume: 470 start-page: 151 issue: 5–6 year: 2009 ident: 10.1016/j.cpc.2021.108181_br0120 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2008.11.001 – volume: 45 start-page: 3 issue: 1 year: 2003 ident: 10.1016/j.cpc.2021.108181_br0030 publication-title: SIAM Rev. doi: 10.1137/S00361445024180 – volume: 80 issue: 5 year: 2017 ident: 10.1016/j.cpc.2021.108181_br0160 publication-title: Rep. Prog. Phys. doi: 10.1088/1361-6633/aa5170 – volume: 81 start-page: 3967 issue: 9 year: 1984 ident: 10.1016/j.cpc.2021.108181_br0050 publication-title: J. Chem. Phys. doi: 10.1063/1.448136 – year: 2018 ident: 10.1016/j.cpc.2021.108181_br0170 – volume: 27 start-page: 831 issue: 4 year: 1980 ident: 10.1016/j.cpc.2021.108181_br0090 publication-title: J. ACM doi: 10.1145/322217.322232 |
| SSID | ssj0007793 |
| Score | 2.4023752 |
| Snippet | We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 108181 |
| SubjectTerms | Batched BLAS Exponential integrators GPU programming Magnus integrators Parallel time integration Schrödinger equation |
| Title | Parallel time integration using Batched BLAS (Basic Linear Algebra Subprograms) routines |
| URI | https://dx.doi.org/10.1016/j.cpc.2021.108181 |
| Volume | 270 |
| WOSCitedRecordID | wos000708648400007&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-2944 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007793 issn: 0010-4655 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtZ3Pa9swFMfFlm6wy-h-0XZb0WGH_cDF0Q9bOiajpRuj5NBBbsaWpbFinJCko39-35NkxyttWQ-7GGNsReijPD89PX8fIR9c7cY2tSoxFYcFSq15olmpEi4yU0mDof7aF5vIz87UfK5nsWbr2pcTyNtWXV3p5X9FDdcANn46-wDcfaNwAc4BOhwBOxz_CfysXGF9lMaXje_lIJDypY8LTEsEVX-Z_pjgGl5NSwCFa3OU9Jk0v3AnGe1JzNxaY9xgtYAOtzHdsNM1iPUgYnBkjdnp229Nelf9FLh5axIc0U7p228GNbEqyGzRDKMPjA2iD9Gigh1HDbahRWWhFki0iWNUzRvfaq5D5ODiyCxRTZKNj7b3_i2NfeOV1ScSdjlqFwU0UWATRWjiMdlhudRqRHYm347n3_u3c55HIebY726n2-f83ejH7b7KwP843yXP48KBTgLwF-SRbV-Sp7Mw9q_IvMNOETsdYKceO43YKWKnHz10GqDTCJ0OoH-iHfLX5OfJ8fnX0yRWzUgMF-kmccbKjJfcmEw5WavU1pxzp4RRUpbCycrpDJw0oXOb8trBX7MSzKHvzTNbOf6GjNpFa_cIVVK4UsOKt7ZGKM1UZrliNtdaSO14uU_SbnwKEyXlsbJJU9zJZZ987h9ZBj2V-24W3aAX0SEMjl4BE-juxw4e8htvybPtvH5HRpvVpX1Pnpg_m9_r1WGcPddeg37b |
| linkProvider | Elsevier |
| 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=Parallel+time+integration+using+Batched+BLAS+%28Basic+Linear+Algebra+Subprograms%29+routines&rft.jtitle=Computer+physics+communications&rft.au=Herb%2C+Konstantin&rft.au=Welter%2C+Pol&rft.date=2022-01-01&rft.issn=0010-4655&rft.volume=270&rft.spage=108181&rft_id=info:doi/10.1016%2Fj.cpc.2021.108181&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cpc_2021_108181 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0010-4655&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0010-4655&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0010-4655&client=summon |