Counterdiabaticity and the quantum approximate optimization algorithm
The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the p → ∞ limit the final state is an exact maximal eigenstate in accordance with the a...
Uložené v:
| Vydané v: | Quantum (Vienna, Austria) Ročník 6; s. 635 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
27.01.2022
|
| ISSN: | 2521-327X, 2521-327X |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the
p
→
∞
limit the final state is an exact maximal eigenstate in accordance with the adiabatic theorem. In this work, the connection between QAOA and adiabaticity is made explicit by inspecting the regime of
p
large but finite. By connecting QAOA to counterdiabatic (CD) evolution, we construct CD-QAOA angles which mimic a counterdiabatic schedule by matching Trotter "error" terms to approximate adiabatic gauge potentials which suppress diabatic excitations arising from finite ramp speed. In our construction, these "error" terms are helpful, not detrimental, to QAOA. Using this matching to link QAOA with quantum adiabatic algorithms (QAA), we show that the approximation ratio converges to one at least as
1
−
C
(
p
)
∼
1
/
p
μ
. We show that transfer of parameters between graphs, and interpolating angles for
p
+
1
given
p
are both natural byproducts of CD-QAOA matching. Optimization of CD-QAOA angles is equivalent to optimizing a continuous adiabatic schedule. Finally, we show that, using a property of variational adiabatic gauge potentials, QAOA is at least counterdiabatic, not just adiabatic, and has better performance than finite time adiabatic evolution. We demonstrate the method on three examples: a 2 level system, an Ising chain, and the MaxCut problem. |
|---|---|
| AbstractList | The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the
p
→
∞
limit the final state is an exact maximal eigenstate in accordance with the adiabatic theorem. In this work, the connection between QAOA and adiabaticity is made explicit by inspecting the regime of
p
large but finite. By connecting QAOA to counterdiabatic (CD) evolution, we construct CD-QAOA angles which mimic a counterdiabatic schedule by matching Trotter "error" terms to approximate adiabatic gauge potentials which suppress diabatic excitations arising from finite ramp speed. In our construction, these "error" terms are helpful, not detrimental, to QAOA. Using this matching to link QAOA with quantum adiabatic algorithms (QAA), we show that the approximation ratio converges to one at least as
1
−
C
(
p
)
∼
1
/
p
μ
. We show that transfer of parameters between graphs, and interpolating angles for
p
+
1
given
p
are both natural byproducts of CD-QAOA matching. Optimization of CD-QAOA angles is equivalent to optimizing a continuous adiabatic schedule. Finally, we show that, using a property of variational adiabatic gauge potentials, QAOA is at least counterdiabatic, not just adiabatic, and has better performance than finite time adiabatic evolution. We demonstrate the method on three examples: a 2 level system, an Ising chain, and the MaxCut problem. The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the $p\to\infty$ limit the final state is an exact maximal eigenstate in accordance with the adiabatic theorem. In this work, the connection between QAOA and adiabaticity is made explicit by inspecting the regime of $p$ large but finite. By connecting QAOA to counterdiabatic (CD) evolution, we construct CD-QAOA angles which mimic a counterdiabatic schedule by matching Trotter "error" terms to approximate adiabatic gauge potentials which suppress diabatic excitations arising from finite ramp speed. In our construction, these "error" terms are helpful, not detrimental, to QAOA. Using this matching to link QAOA with quantum adiabatic algorithms (QAA), we show that the approximation ratio converges to one at least as $1-C(p)\sim 1/p^{\mu}$. We show that transfer of parameters between graphs, and interpolating angles for $p+1$ given $p$ are both natural byproducts of CD-QAOA matching. Optimization of CD-QAOA angles is equivalent to optimizing a continuous adiabatic schedule. Finally, we show that, using a property of variational adiabatic gauge potentials, QAOA is at least counterdiabatic, not just adiabatic, and has better performance than finite time adiabatic evolution. We demonstrate the method on three examples: a 2 level system, an Ising chain, and the MaxCut problem. |
| ArticleNumber | 635 |
| Author | Love, Peter J. Wurtz, Jonathan |
| Author_xml | – sequence: 1 givenname: Jonathan surname: Wurtz fullname: Wurtz, Jonathan organization: Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA – sequence: 2 givenname: Peter J. surname: Love fullname: Love, Peter J. organization: Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA |
| BookMark | eNp1kN1KAzEQhYNUsNY-gHf7AqvJZH_SSylVCwVvFLwLs0m2TdndtNkUrE9vulUQwasZhvkO55xrMupcZwi5ZfQOgHN2v0-BAqSUpVCmBc8vyBhyYCmH8n30a78i077fUkpBlEUhsjFZzN2hC8ZrixUGq2w4JtjpJGxMsj9gFw5tgruddx-2xWAStwu2tZ_x1XUJNmvnbdi0N-SyxqY30-85IW-Pi9f5c7p6eVrOH1apyoCGVGlqahCcillhuCiNUFiAqLCgJjMYTekctaAoWGWyIgfEmeZQ1wKrvMo1n5DlWVc73Mqdj578UTq0cjg4v5boY4rGyMgzOis4KFDZSVUprEDrMotLOWiVZy3lXd97U8sYfsgVPNpGMiqHcuVensqVlEkoZSw3kuwP-ePkf-YLr4-AwA |
| CitedBy_id | crossref_primary_10_1103_PhysRevApplied_23_014045 crossref_primary_10_1103_PhysRevResearch_4_043204 crossref_primary_10_1007_s10288_023_00549_1 crossref_primary_10_1103_PhysRevLett_131_060602 crossref_primary_10_1088_2058_9565_ad895c crossref_primary_10_1103_PhysRevApplied_19_024027 crossref_primary_10_3390_e25081238 crossref_primary_10_1088_2058_9565_ace54a crossref_primary_10_1103_PhysRevResearch_7_023240 crossref_primary_10_1016_j_physa_2024_129990 crossref_primary_10_1088_1367_2630_ad313e crossref_primary_10_1103_PhysRevResearch_7_013243 crossref_primary_10_1088_1361_6455_ad38f1 crossref_primary_10_1088_1367_2630_acb22c crossref_primary_10_1103_PhysRevResearch_4_013141 crossref_primary_10_1002_andp_202300275 crossref_primary_10_1088_2058_9565_ad60f2 crossref_primary_10_1038_s41598_022_14767_w crossref_primary_10_1016_j_physrep_2024_03_002 crossref_primary_10_1103_PhysRevResearch_5_023147 crossref_primary_10_1038_s41534_025_01070_5 crossref_primary_10_1088_2058_9565_ade6a5 crossref_primary_10_1103_PhysRevA_111_032612 crossref_primary_10_1103_PhysRevResearch_6_023171 crossref_primary_10_1103_PhysRevApplied_22_054037 crossref_primary_10_1088_1367_2630_ad1536 crossref_primary_10_1103_PhysRevA_108_042411 crossref_primary_10_1103_PhysRevA_111_062406 crossref_primary_10_1038_s41534_024_00906_w crossref_primary_10_3390_e26121057 crossref_primary_10_1103_PhysRevA_107_062406 crossref_primary_10_1038_s41534_023_00718_4 crossref_primary_10_3390_e26100877 crossref_primary_10_1088_2058_9565_aca3ce crossref_primary_10_1038_s41534_024_00825_w crossref_primary_10_1103_PhysRevX_14_011032 crossref_primary_10_1103_PhysRevApplied_20_014024 crossref_primary_10_1103_wkys_cd39 crossref_primary_10_1103_PhysRevA_111_062411 crossref_primary_10_1103_PRXQuantum_4_010312 crossref_primary_10_1103_x9hw_xhvj crossref_primary_10_1103_PhysRevA_111_012215 crossref_primary_10_1088_2058_9565_ad200a crossref_primary_10_1109_TQE_2024_3443660 crossref_primary_10_1103_PhysRevA_111_L010401 crossref_primary_10_1007_s10479_024_06253_5 crossref_primary_10_1103_PRXQuantum_5_037001 crossref_primary_10_1103_PhysRevResearch_4_L042030 crossref_primary_10_1103_PhysRevResearch_4_033028 |
| Cites_doi | 10.1088/1367-2630/16/6/065013 10.1103/PhysRevA.97.062343 10.1073/pnas.1619826114 10.1103/PhysRevB.101.195138 10.1038/nature10012 10.1103/PhysRevLett.119.060201 10.1103/physrevlett.101.076801 10.1103/PhysRevLett.122.020601 10.1103/physrevlett.109.015701 10.1103/PhysRevLett.123.090602 10.22331/q-2021-06-17-479 10.1103/PhysRevLett.126.070505 10.1103/PhysRevX.10.041017 10.1103/PhysRevLett.102.220401 10.1103/PhysRevA.78.052508 10.1007/11526216_2 10.22331/q-2018-08-06-79 10.1088/2058-9565/ab8c2b 10.1103/PhysRevA.91.043421 10.1103/physrevx.7.021027 10.1103/physrevx.10.021067 10.3389/fphy.2014.00005 10.1142/s0217751x1430018x 10.1103/PhysRevA.103.042612 10.1103/PhysRevLett.95.245701 10.1103/PhysRevLett.103.080502 10.1007/BF01343193 10.1103/PhysRevA.69.062302 10.1103/RevModPhys.90.015002 10.3389/fict.2017.00002 10.1103/RevModPhys.91.045001 10.1016/j.physrep.2017.07.001 10.22331/q-2021-07-01-491 10.1088/1751-8113/42/36/365303 10.1103/PhysRevResearch.3.013102 10.1103/PhysRevLett.105.123003 10.1016/j.physrep.2008.11.001 10.1103/PhysRevB.72.045141 10.1017/CBO9780511973765 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.22331/q-2022-01-27-635 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| EISSN | 2521-327X |
| ExternalDocumentID | oai_doaj_org_article_e46109632c2c45ad8ccab2dd74cca75d 10_22331_q_2022_01_27_635 |
| GroupedDBID | AAFWJ AAYXX AFPKN ALMA_UNASSIGNED_HOLDINGS CITATION GROUPED_DOAJ M~E |
| ID | FETCH-LOGICAL-c420t-cd0ef2830896e387e8ca628ba60e4ea287d5ad80a81be4652aa9d32ff8ab5b5d3 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 73 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000748924100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2521-327X |
| IngestDate | Fri Oct 03 12:53:34 EDT 2025 Tue Nov 18 22:34:29 EST 2025 Sat Nov 29 03:16:33 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c420t-cd0ef2830896e387e8ca628ba60e4ea287d5ad80a81be4652aa9d32ff8ab5b5d3 |
| OpenAccessLink | https://doaj.org/article/e46109632c2c45ad8ccab2dd74cca75d |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_e46109632c2c45ad8ccab2dd74cca75d crossref_citationtrail_10_22331_q_2022_01_27_635 crossref_primary_10_22331_q_2022_01_27_635 |
| PublicationCentury | 2000 |
| PublicationDate | 2022-01-27 |
| PublicationDateYYYYMMDD | 2022-01-27 |
| PublicationDate_xml | – month: 01 year: 2022 text: 2022-01-27 day: 27 |
| PublicationDecade | 2020 |
| PublicationTitle | Quantum (Vienna, Austria) |
| PublicationYear | 2022 |
| Publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| Publisher_xml | – name: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| References | 22 44 23 45 24 46 25 47 26 27 28 29 30 31 10 32 11 33 12 34 13 35 14 36 15 37 16 38 17 39 18 19 0 1 2 3 4 5 6 7 8 9 40 41 20 42 21 43 |
| References_xml | – ident: 2 – ident: 22 doi: 10.1088/1367-2630/16/6/065013 – ident: 24 doi: 10.1103/PhysRevA.97.062343 – ident: 34 doi: 10.1073/pnas.1619826114 – ident: 0 – ident: 36 doi: 10.1103/PhysRevB.101.195138 – ident: 29 doi: 10.1038/nature10012 – ident: 9 doi: 10.1103/PhysRevLett.119.060201 – ident: 12 doi: 10.1103/physrevlett.101.076801 – ident: 44 doi: 10.1103/PhysRevLett.122.020601 – ident: 41 doi: 10.1103/physrevlett.109.015701 – ident: 26 doi: 10.1103/PhysRevLett.123.090602 – ident: 43 doi: 10.22331/q-2021-06-17-479 – ident: 17 doi: 10.1103/PhysRevLett.126.070505 – ident: 33 doi: 10.1103/PhysRevX.10.041017 – ident: 5 doi: 10.1103/PhysRevLett.102.220401 – ident: 8 doi: 10.1103/PhysRevA.78.052508 – ident: 37 doi: 10.1007/11526216_2 – ident: 1 doi: 10.22331/q-2018-08-06-79 – ident: 18 doi: 10.1088/2058-9565/ab8c2b – ident: 25 doi: 10.1103/PhysRevA.91.043421 – ident: 16 doi: 10.1103/physrevx.7.021027 – ident: 14 doi: 10.1103/physrevx.10.021067 – ident: 45 – ident: 20 – ident: 42 – ident: 3 doi: 10.3389/fphy.2014.00005 – ident: 10 doi: 10.1142/s0217751x1430018x – ident: 47 doi: 10.1103/PhysRevA.103.042612 – ident: 40 doi: 10.1103/PhysRevLett.95.245701 – ident: 21 doi: 10.1103/PhysRevLett.103.080502 – ident: 19 doi: 10.1007/BF01343193 – ident: 13 – ident: 15 – ident: 11 doi: 10.1103/PhysRevA.69.062302 – ident: 4 doi: 10.1103/RevModPhys.90.015002 – ident: 28 doi: 10.3389/fict.2017.00002 – ident: 7 doi: 10.1103/RevModPhys.91.045001 – ident: 32 doi: 10.1016/j.physrep.2017.07.001 – ident: 6 doi: 10.22331/q-2021-07-01-491 – ident: 31 doi: 10.1088/1751-8113/42/36/365303 – ident: 30 doi: 10.1103/PhysRevResearch.3.013102 – ident: 39 doi: 10.1103/PhysRevLett.105.123003 – ident: 46 – ident: 38 doi: 10.1016/j.physrep.2008.11.001 – ident: 35 doi: 10.1103/PhysRevB.72.045141 – ident: 27 doi: 10.1017/CBO9780511973765 – ident: 23 |
| SSID | ssj0002876684 |
| Score | 2.5389748 |
| Snippet | The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut.... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| StartPage | 635 |
| Title | Counterdiabaticity and the quantum approximate optimization algorithm |
| URI | https://doaj.org/article/e46109632c2c45ad8ccab2dd74cca75d |
| Volume | 6 |
| WOSCitedRecordID | wos000748924100001&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: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2521-327X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002876684 issn: 2521-327X databaseCode: DOA dateStart: 20170101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2521-327X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002876684 issn: 2521-327X databaseCode: M~E dateStart: 20170101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV05T8MwFLZQxcCCQIC45YEJyWrqOyOgVgxQMYDUzfIVDvWgpUVM_HaenUA7wcISRZGT2N-z897n2N9D6Iy6EBUvPVEaBjkHWkscc4HQqlSVi7aqYhZxvVH9vh4MyruVVF9pTVgtD1wD145ZEFwy6qnnwgYNr3Q0BMXhRImQvr6FKlfI1EueMlJSal7_xgQPyDrtKXQImpYhEKqIzOndlo5oRa8_O5beFtpsIkJ8UddkG63F8Q7qpr3i0OQ0NZo0VSFWxsD5MYRreLoANBYjnOXAP54h5Ix4AiN_1GypxHb4OAHO_zTaRQ-97v3VNWkyHhDPaTEnPhSxSpJcupSRaRW1t5JqZ2URebTQqpAgKCwEmwCMoNaWgdGq0tYJJwLbQ63xZBz3ES559FwmBiE8tzo48OwsSgHehwF04gAV3803vpEDT1kphgZoQUbMTE1CzBQdQ5UBxA7Q-c8tr7UWxm-FLxOmPwWTjHW-AMY1jXHNX8Y9_I-HHKGNpeWPUWs-W8QTtO7f589vs9Pcb-B4-9n9AjXlynI |
| linkProvider | Directory of Open Access Journals |
| 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=Counterdiabaticity+and+the+quantum+approximate+optimization+algorithm&rft.jtitle=Quantum+%28Vienna%2C+Austria%29&rft.au=Jonathan+Wurtz&rft.au=Peter+J.+Love&rft.date=2022-01-27&rft.pub=Verein+zur+F%C3%B6rderung+des+Open+Access+Publizierens+in+den+Quantenwissenschaften&rft.eissn=2521-327X&rft.volume=6&rft.spage=635&rft_id=info:doi/10.22331%2Fq-2022-01-27-635&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_e46109632c2c45ad8ccab2dd74cca75d |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2521-327X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2521-327X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2521-327X&client=summon |