Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution an...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Physical review. X Ročník 7; číslo 2; s. 021027
Hlavní autoři: Yang, Zhi-Cheng, Rahmani, Armin, Shabani, Alireza, Neven, Hartmut, Chamon, Claudio
Médium: Journal Article
Jazyk:angličtina
Vydáno: College Park American Physical Society 18.05.2017
Témata:
Algorithms
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Combinatorial analysis
Computing costs
Control systems
Control theory
Coupling
Data processing
Digital computers
Evolutionary algorithms
Feedback control
Optimization
Parameter identification
Parameterization
Quantum computers
Quantum computing
Quantum phenomena
Quantum theory
Spin glasses
Switches
Thermal baths
Time
ISSN:2160-3308, 2160-3308
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Furthermore, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.
AbstractList We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Furthermore, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.
We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.
ArticleNumber 021027
Author Neven, Hartmut
Chamon, Claudio
Rahmani, Armin
Yang, Zhi-Cheng
Shabani, Alireza
Author_xml – sequence: 1
  givenname: Zhi-Cheng
  surname: Yang
  fullname: Yang, Zhi-Cheng
– sequence: 2
  givenname: Armin
  surname: Rahmani
  fullname: Rahmani, Armin
– sequence: 3
  givenname: Alireza
  surname: Shabani
  fullname: Shabani, Alireza
– sequence: 4
  givenname: Hartmut
  surname: Neven
  fullname: Neven, Hartmut
– sequence: 5
  givenname: Claudio
  surname: Chamon
  fullname: Chamon, Claudio
BackLink https://www.osti.gov/biblio/1357856$$D View this record in Osti.gov
BookMark eNp1kd9KHDEUxoMoaLc-QO-G9nq3-TOZzF6KWBUUt6LSu5B_s3uWmWRNssJ61dfo6_VJjE6FUui5yeHw-z7I931A-z54h9AngmeEYPZ1sdqlW_f0YyZmmBJMxR46oqTBU8Zwu__XfoiOU1rjMg0mtRBHaHGzyTDAM_hl9aAiqAzBq776vlU-b4fqpF-GCHk1pOo-vUKL4HPcqSX43z9_peoaPAyFW0TwBja9-4gOOtUnd_znnaD7b2d3pxfTq5vzy9OTq6mpBc_TuVaO1NRp29i6ZbzGpByoY6SzxFI6bxhzvFUUt1ZR1mllsCHE0K7RthYdm6DL0dcGtZabCIOKOxkUyLdDiEupYgbTO9m4ubW8YVTjec0N1Z1STNuWa6wbSmnx-jx6hZRBJgPZmZUJ3juTJWFctEU9QV9GaBPD49alLNdhG0tWSVLOS6CiJaJQYqRMDClF18ni9hZqjgp6SbB8rUy-VyaFHCsrSvKP8v1T_9e8ADThntw
CitedBy_id crossref_primary_10_1103_RevModPhys_94_015004
crossref_primary_10_1103_PhysRevApplied_22_024009
crossref_primary_10_1103_PhysRevResearch_6_013076
crossref_primary_10_1103_PRXQuantum_2_010101
crossref_primary_10_1103_PhysRevResearch_3_043088
crossref_primary_10_1103_PhysRevResearch_3_043165
crossref_primary_10_1103_PhysRevX_10_021067
crossref_primary_10_1088_2058_9565_ab33c2
crossref_primary_10_1103_PRXQuantum_2_010309
crossref_primary_10_1088_2058_9565_aad3e4
crossref_primary_10_1088_2058_9565_ad895c
crossref_primary_10_1088_2058_9565_ace54a
crossref_primary_10_1103_PhysRevResearch_7_023240
crossref_primary_10_2478_qic_2025_0006
crossref_primary_10_1103_PhysRevA_101_012320
crossref_primary_10_1103_PhysRevLett_129_056801
crossref_primary_10_1103_x72t_bsh4
crossref_primary_10_1103_PhysRevResearch_3_013227
crossref_primary_10_1088_1361_6455_ad46a5
crossref_primary_10_1103_PhysRevLett_126_140502
crossref_primary_10_1088_1367_2630_aaca62
crossref_primary_10_1103_PRXQuantum_2_010338
crossref_primary_10_1103_PhysRevApplied_23_024036
crossref_primary_10_1103_PhysRevResearch_4_023249
crossref_primary_10_1007_s42484_022_00069_x
crossref_primary_10_1103_PhysRevApplied_19_064071
crossref_primary_10_1103_PhysRevLett_126_070505
crossref_primary_10_1103_PhysRevX_8_031086
crossref_primary_10_1103_PhysRevA_111_L050201
crossref_primary_10_1088_1361_6633_ad85f0
crossref_primary_10_1103_PRXQuantum_2_020332
crossref_primary_10_1103_PhysRevResearch_2_033402
crossref_primary_10_1103_PhysRevD_111_034506
crossref_primary_10_1103_PhysRevA_111_042616
crossref_primary_10_1134_S0021364023603056
crossref_primary_10_1103_PhysRevApplied_16_054023
crossref_primary_10_7566_JPSJ_88_061016
crossref_primary_10_1103_PhysRevResearch_6_033336
crossref_primary_10_1103_PRXQuantum_5_020366
crossref_primary_10_1088_2058_9565_aca3ce
crossref_primary_10_1088_1402_4896_acf6e8
crossref_primary_10_1103_PRXQuantum_2_030203
crossref_primary_10_1088_2058_9565_acfbaa
crossref_primary_10_1103_wkys_cd39
crossref_primary_10_1103_PhysRevA_111_062411
crossref_primary_10_1103_PRXQuantum_2_017001
crossref_primary_10_1103_PhysRevA_111_042602
crossref_primary_10_1007_s11128_020_02748_9
crossref_primary_10_1088_1367_2630_ad7b6b
crossref_primary_10_1088_1751_8121_aaecf6
crossref_primary_10_1140_epjqt_s40507_022_00138_x
crossref_primary_10_1103_PhysRevResearch_5_023096
crossref_primary_10_1007_s10479_024_06253_5
crossref_primary_10_1007_s11128_025_04655_3
crossref_primary_10_1103_PhysRevResearch_4_033029
Cites_doi 10.1088/1751-8113/49/16/165304
10.1103/PhysRevLett.115.230501
10.1038/ncomms5213
10.1126/science.aaa4170
10.1049/iet-cta.2009.0508
10.1103/PhysRevA.80.022303
10.1038/srep03589
10.1038/nature17658
10.1103/PhysRevA.88.021601
10.1103/PhysRevA.95.042308
10.1088/1367-2630/18/2/023023
10.1103/PhysRevA.90.052317
10.1063/1.3058756
10.1017/CBO9780511976667
10.1103/PhysRevLett.117.080402
10.1088/1367-2630/14/12/123016
10.1103/PhysRevA.87.043607
10.1103/PhysRevLett.35.1792
10.1126/science.1057726
10.1007/s11128-010-0168-z
10.1142/S0217984913300196
10.1103/PhysRevA.92.042110
10.1109/PROC.1987.13721
10.1103/PhysRevA.94.022309
10.1103/PhysRevA.92.042303
10.1038/543171a
10.1103/PhysRevX.5.041044
10.1103/PhysRevA.95.020501
10.1088/1367-2630/12/7/075008
10.1103/PhysRevX.6.031007
10.1103/PhysRevA.87.033606
10.1088/1367-2630/16/6/065013
10.3389/fphy.2014.00005
10.1103/PhysRevB.91.201404
10.1038/ncomms10327
10.1103/PhysRevE.58.5355
10.1103/PhysRevLett.103.080502
ContentType Journal Article
Copyright 2017. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2017. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
CorporateAuthor Boston Univ., MA (United States)
CorporateAuthor_xml – name: Boston Univ., MA (United States)
DBID AAYXX
CITATION
3V.
7XB
88I
8FE
8FG
8FK
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
GNUQQ
HCIFZ
L6V
M2P
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
OTOTI
DOA
DOI 10.1103/PhysRevX.7.021027
DatabaseName CrossRef
ProQuest Central (Corporate)
ProQuest Central (purchase pre-March 2016)
Science Database (Alumni Edition)
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
Technology collection
ProQuest One Community College
ProQuest Central
ProQuest Central Student
SciTech Premium Collection
ProQuest Engineering Collection
Science Database
Engineering Database
ProQuest Central Premium
ProQuest One Academic (New)
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
ProQuest Central Basic
OSTI.GOV
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
ProQuest Central Student
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest Central Korea
ProQuest Central (New)
Engineering Collection
Engineering Database
ProQuest Science Journals (Alumni Edition)
ProQuest Central Basic
ProQuest Science Journals
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2160-3308
ExternalDocumentID oai_doaj_org_article_6e9dd5632b0945c2bfaa3bd85b0b6222
1357856
10_1103_PhysRevX_7_021027
GroupedDBID 3MX
5VS
88I
AAFWJ
AAYXX
ABJCF
ABSSX
ABUWG
ADBBV
AECSF
AENEX
AFFHD
AFGMR
AFKRA
AFPKN
AGDNE
ALMA_UNASSIGNED_HOLDINGS
AUAIK
AZQEC
BCNDV
BENPR
BGLVJ
CCPQU
CITATION
DWQXO
EBS
EJD
FRP
GNUQQ
GROUPED_DOAJ
HCIFZ
KQ8
M2P
M7S
M~E
OK1
PHGZM
PHGZT
PIMPY
PQGLB
PTHSS
ROL
S7W
3V.
7XB
8FE
8FG
8FK
L6V
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
Q9U
ABCKA
ADETJ
OTOTI
ID FETCH-LOGICAL-c475t-9bae142ebd6d4835401ae12e31fd1d229633e58a208da23fbac0c11c2f6bd47f3
IEDL.DBID M2P
ISICitedReferencesCount 150
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000401662800003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2160-3308
IngestDate Mon Nov 10 04:34:56 EST 2025
Mon Mar 25 05:16:28 EDT 2024
Fri Jul 25 11:42:31 EDT 2025
Tue Nov 18 21:02:13 EST 2025
Sat Nov 29 02:51:00 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
License http://creativecommons.org/licenses/by/3.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c475t-9bae142ebd6d4835401ae12e31fd1d229633e58a208da23fbac0c11c2f6bd47f3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
USDOE
FG02-06ER46316
OpenAccessLink https://www.proquest.com/docview/2550607817?pq-origsite=%requestingapplication%
PQID 2550607817
PQPubID 5161131
ParticipantIDs doaj_primary_oai_doaj_org_article_6e9dd5632b0945c2bfaa3bd85b0b6222
osti_scitechconnect_1357856
proquest_journals_2550607817
crossref_citationtrail_10_1103_PhysRevX_7_021027
crossref_primary_10_1103_PhysRevX_7_021027
PublicationCentury 2000
PublicationDate 2017-05-18
PublicationDateYYYYMMDD 2017-05-18
PublicationDate_xml – month: 05
  year: 2017
  text: 2017-05-18
  day: 18
PublicationDecade 2010
PublicationPlace College Park
PublicationPlace_xml – name: College Park
– name: United States
PublicationTitle Physical review. X
PublicationYear 2017
Publisher American Physical Society
Publisher_xml – name: American Physical Society
References L. S. Pontryagin (PhysRevX.7.021027Cc29R1) 1987
M. A. Nielson (PhysRevX.7.021027Cc44R1) 2010
PhysRevX.7.021027Cc32R1
A. E. Bryson (PhysRevX.7.021027Cc28R1) 1975
PhysRevX.7.021027Cc33R1
PhysRevX.7.021027Cc11R1
PhysRevX.7.021027Cc31R1
PhysRevX.7.021027Cc13R1
PhysRevX.7.021027Cc36R1
PhysRevX.7.021027Cc12R1
PhysRevX.7.021027Cc15R1
PhysRevX.7.021027Cc34R1
PhysRevX.7.021027Cc14R1
PhysRevX.7.021027Cc35R1
PhysRevX.7.021027Cc17R1
PhysRevX.7.021027Cc16R1
PhysRevX.7.021027Cc19R1
PhysRevX.7.021027Cc38R1
PhysRevX.7.021027Cc18R1
PhysRevX.7.021027Cc39R1
PhysRevX.7.021027Cc1R1
PhysRevX.7.021027Cc4R1
PhysRevX.7.021027Cc3R1
PhysRevX.7.021027Cc20R1
PhysRevX.7.021027Cc43R1
PhysRevX.7.021027Cc9R1
H. P. Breuer (PhysRevX.7.021027Cc40R1) 2002
PhysRevX.7.021027Cc22R1
PhysRevX.7.021027Cc41R1
PhysRevX.7.021027Cc21R1
R. F. Stengel (PhysRevX.7.021027Cc30R1) 1994
PhysRevX.7.021027Cc42R1
PhysRevX.7.021027Cc6R1
PhysRevX.7.021027Cc47R1
PhysRevX.7.021027Cc5R1
PhysRevX.7.021027Cc23R1
PhysRevX.7.021027Cc48R1
PhysRevX.7.021027Cc8R1
PhysRevX.7.021027Cc45R1
PhysRevX.7.021027Cc7R1
PhysRevX.7.021027Cc46R1
References_xml – ident: PhysRevX.7.021027Cc5R1
  doi: 10.1088/1751-8113/49/16/165304
– ident: PhysRevX.7.021027Cc8R1
  doi: 10.1103/PhysRevLett.115.230501
– ident: PhysRevX.7.021027Cc15R1
  doi: 10.1038/ncomms5213
– ident: PhysRevX.7.021027Cc9R1
  doi: 10.1126/science.aaa4170
– ident: PhysRevX.7.021027Cc34R1
  doi: 10.1049/iet-cta.2009.0508
– ident: PhysRevX.7.021027Cc45R1
  doi: 10.1103/PhysRevA.80.022303
– ident: PhysRevX.7.021027Cc16R1
  doi: 10.1038/srep03589
– ident: PhysRevX.7.021027Cc43R1
  doi: 10.1038/nature17658
– ident: PhysRevX.7.021027Cc12R1
  doi: 10.1103/PhysRevA.88.021601
– ident: PhysRevX.7.021027Cc20R1
  doi: 10.1103/PhysRevA.95.042308
– ident: PhysRevX.7.021027Cc19R1
  doi: 10.1088/1367-2630/18/2/023023
– ident: PhysRevX.7.021027Cc6R1
  doi: 10.1103/PhysRevA.90.052317
– ident: PhysRevX.7.021027Cc11R1
  doi: 10.1063/1.3058756
– volume-title: Quantum Computation and Quantum Information
  year: 2010
  ident: PhysRevX.7.021027Cc44R1
  doi: 10.1017/CBO9780511976667
– ident: PhysRevX.7.021027Cc42R1
  doi: 10.1103/PhysRevLett.117.080402
– ident: PhysRevX.7.021027Cc46R1
  doi: 10.1088/1367-2630/14/12/123016
– ident: PhysRevX.7.021027Cc13R1
  doi: 10.1103/PhysRevA.87.043607
– ident: PhysRevX.7.021027Cc41R1
  doi: 10.1103/PhysRevLett.35.1792
– ident: PhysRevX.7.021027Cc3R1
  doi: 10.1126/science.1057726
– ident: PhysRevX.7.021027Cc4R1
  doi: 10.1007/s11128-010-0168-z
– ident: PhysRevX.7.021027Cc14R1
  doi: 10.1142/S0217984913300196
– ident: PhysRevX.7.021027Cc39R1
  doi: 10.1103/PhysRevA.92.042110
– ident: PhysRevX.7.021027Cc32R1
  doi: 10.1109/PROC.1987.13721
– ident: PhysRevX.7.021027Cc18R1
  doi: 10.1103/PhysRevA.94.022309
– volume-title: The Theory of Open Quantum Systems
  year: 2002
  ident: PhysRevX.7.021027Cc40R1
– ident: PhysRevX.7.021027Cc17R1
  doi: 10.1103/PhysRevA.92.042303
– volume-title: Applied Optimal Control: Optimization, Estimation and Control
  year: 1975
  ident: PhysRevX.7.021027Cc28R1
– ident: PhysRevX.7.021027Cc48R1
  doi: 10.1038/543171a
– ident: PhysRevX.7.021027Cc22R1
  doi: 10.1103/PhysRevX.5.041044
– ident: PhysRevX.7.021027Cc21R1
  doi: 10.1103/PhysRevA.95.020501
– ident: PhysRevX.7.021027Cc33R1
  doi: 10.1088/1367-2630/12/7/075008
– ident: PhysRevX.7.021027Cc23R1
  doi: 10.1103/PhysRevX.6.031007
– ident: PhysRevX.7.021027Cc38R1
  doi: 10.1103/PhysRevA.87.033606
– ident: PhysRevX.7.021027Cc31R1
  doi: 10.1088/1367-2630/16/6/065013
– ident: PhysRevX.7.021027Cc35R1
  doi: 10.3389/fphy.2014.00005
– volume-title: Optimal Control and Estimation
  year: 1994
  ident: PhysRevX.7.021027Cc30R1
– ident: PhysRevX.7.021027Cc36R1
  doi: 10.1103/PhysRevB.91.201404
– volume-title: Mathematical Theory of Optimal Processes
  year: 1987
  ident: PhysRevX.7.021027Cc29R1
– ident: PhysRevX.7.021027Cc47R1
  doi: 10.1038/ncomms10327
– ident: PhysRevX.7.021027Cc1R1
  doi: 10.1103/PhysRevE.58.5355
– ident: PhysRevX.7.021027Cc7R1
  doi: 10.1103/PhysRevLett.103.080502
SSID ssj0000601477
Score 2.5877638
Snippet We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a...
SourceID doaj
osti
proquest
crossref
SourceType Open Website
Open Access Repository
Aggregation Database
Enrichment Source
Index Database
StartPage 021027
SubjectTerms Algorithms
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Combinatorial analysis
Computing costs
Control systems
Control theory
Coupling
Data processing
Digital computers
Evolutionary algorithms
Feedback control
Optimization
Parameter identification
Parameterization
Quantum computers
Quantum computing
Quantum phenomena
Quantum theory
Spin glasses
Switches
Thermal baths
Time
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA4iCl7EJ1ar7MGTsHWT7Ca7xyqKBx9VtPQW8tSCbcVtBT35N_x7_hIn2a0ogl48LYRsCJN5fJMM3yC0K3MmrStkbAANxJ6BK1aAXGNHM-akZJkLL7rdU35-nvd6RedLqy9fE1bRA1eC22e2MCZjlChIRDJNFKxAlckzlSgGwc1734QXX5KpygcD9Oe8fsbECd33BZVX9qnX4q2Q5vBvgSjw9cNnBHb1wyuHUHO8hBZrjBi1q70toxk7XEHzoVZTl6uocwFmPui_QNCJupDq1td50eUEpDQZRO372xGk_HeDMgoFAVHHl6M_-3ZE769vZXTWH_YHMK8zvWdfQzfHR9eHJ3HdGCHWKc_GcaGkxSmxyjCThpsbDAPEUuwMNoSAUVGb5ZIkuZGEOiV1ojHWxDFlUu7oOpodjoZ2A0W54wCpihQXHJbRsHBiJTGpYdQBctINlEylJHTNGu6bV9yLkD0kVEwFK7ioBNtAe5-_PFSUGb9NPvCi_5zo2a7DAOiAqHVA_KUDDbTlD04AaPDMt9qXCOmxwIHJhzVQc3qeojbQUoA-go7wHPPN_9jBFlogPt57Wte8iWbHjxO7jeb007hfPu4E3fwA9sHrlw
  priority: 102
  providerName: Directory of Open Access Journals
Title Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle
URI https://www.proquest.com/docview/2550607817
https://www.osti.gov/biblio/1357856
https://doaj.org/article/6e9dd5632b0945c2bfaa3bd85b0b6222
Volume 7
WOSCitedRecordID wos000401662800003&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: 2160-3308
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000601477
  issn: 2160-3308
  databaseCode: DOA
  dateStart: 20110101
  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: 2160-3308
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000601477
  issn: 2160-3308
  databaseCode: M~E
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 2160-3308
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000601477
  issn: 2160-3308
  databaseCode: M7S
  dateStart: 20110801
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2160-3308
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000601477
  issn: 2160-3308
  databaseCode: BENPR
  dateStart: 20110801
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 2160-3308
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000601477
  issn: 2160-3308
  databaseCode: PIMPY
  dateStart: 20110801
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Science Database
  customDbUrl:
  eissn: 2160-3308
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000601477
  issn: 2160-3308
  databaseCode: M2P
  dateStart: 20110801
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/sciencejournals
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NbtQwELagBYkL_xVLyyoHTkhpEzuxkxNqUSuQ2CUUqJaT5d-yUne3bLKV4MRr8Ho8CTNeZxFC6oVLItmOFXk842_Go28Iea4qrpyvVWoBDaTIwJVqQK6pZyX3SvHShxvds7diPK4mk7qJAbc2plX2NjEYarswGCM_gAkyjsw04uXl1xSrRuHtaiyhcZNsA7LJMaVrRJtNjAW5Rgoh4mVmnrEDTKs8dVeTfbEfnB3x13EUWPvhtQDt-sc2hwPn5N7__up9cjdCzeRwvTcekBtu_pDcDimfpn1EmndgLWbT73B2JWfgMceoYPJ-BYu9miWHF-cwafdl1iYhryBpMKv9G1Y1-vXjZ5uMpvPpDMY1fbj-Mfl0cvzx1es01ldITSHKLq21cnlBnbbcFiEAlEMDdSz3NreUgm4yV1aKZpVVlHmtTGby3FDPtS2EZztka76YuyckqbwAZFYXeS1gGgMTZ05RW1jOPAAwMyBZv8zSRPJxrIFxIYMTkjHZS0YKuZbMgLzYfHK5Zt64bvARym4zEEmzQ8NieS6jDkruamtLzqgGn7Y0VMNmZNpWpc40B5w0ILsoeQnYAwl0DWYamU7mgRCID8heL20Z9byVf0T99PruXXKHIiBA3tdqj2x1y5V7Rm6Zq27aLodk--h43JwOQ0RgGDYxPsUH6GnejJrPvwFtpP56
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwEB6VAoIL_4ilBXKAC1LaxE7s5IBQ-aladbsEVKq9Gf-WSN3dstktKideg5fgoXgSxt5kEULqrQdOkRJnJMefZ8Yzk28AnsqCSetKGRv0BmLPwBUr9FxjR3PmpGS5Cxndwz4fDIrhsKxW4Gf3L4wvq-x0YlDUZqJ9jHwTBSTMM9PwlydfYt81ymdXuxYaC1js2bOveGRrXuy-wfV9Rsj224PXO3HbVSDWGc9ncamkTTNilWEmC2GPFG8QS1NnUkMIIpLavJAkKYwk1CmpE52mmjimTMYdRbmX4HLm5-VLBUm1jOl4bpOM8zZ5miZ005dxfrCnww2-EQ5X_C_zF7oE4GWCu_kfWxAM3PbN_-3T3IIbrSsdbS2wfxtW7PgOXA0lrbq5C9U71Iaj-hva5uhQTus26hm9nyOY5qNo6_gIJzH7PGqiUDcRVb5q_8x3bfr1_UcT7dfjeoTjqi4dcQ8-Xsh07sPqeDK2DyAqHEfPs8zSkqMYjYITK4nJDKMOHUzdg6RbVqFbcnXf4-NYhENWQkWHBMHFAgk9eL585WTBLHLe4FceK8uBnhQ83JhMj0SrYwSzpTE5o0ThmT3XROFmo8oUuUoUQz-wB2seaQJ9K08QrH0llZ6JNBAesR6sd-gSrR5rxB9oPTz_8RO4tnOw3xf93cHeGlwn3vnxHLfFOqzOpnP7CK7o01ndTB-HLRPBp4sG4m8LaVc3
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=Optimizing+Variational+Quantum+Algorithms+Using+Pontryagin%E2%80%99s+Minimum+Principle&rft.jtitle=Physical+review.+X&rft.au=Yang%2C+Zhi-Cheng&rft.au=Rahmani%2C+Armin&rft.au=Shabani%2C+Alireza&rft.au=Neven%2C+Hartmut&rft.date=2017-05-18&rft.issn=2160-3308&rft.eissn=2160-3308&rft.volume=7&rft.issue=2&rft_id=info:doi/10.1103%2FPhysRevX.7.021027&rft.externalDBID=n%2Fa&rft.externalDocID=10_1103_PhysRevX_7_021027
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2160-3308&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2160-3308&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2160-3308&client=summon