Quantum query complexity of Boolean functions under indefinite causal order
The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum syst...
Gespeichert in:
| Veröffentlicht in: | Physical review research Jg. 6; H. 3; S. L032020 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
American Physical Society
26.07.2024
|
| Schlagworte: | |
| ISSN: | 2643-1564, 2643-1564 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. |
|---|---|
| AbstractList | The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several ad hoc computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. Published by the American Physical Society 2024 The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. |
| ArticleNumber | L032020 |
| Author | Mhalla, Mehdi Pocreau, Pierre Abbott, Alastair A. |
| Author_xml | – sequence: 1 givenname: Alastair A. orcidid: 0000-0002-2759-633X surname: Abbott fullname: Abbott, Alastair A. – sequence: 2 givenname: Mehdi orcidid: 0000-0003-4178-5396 surname: Mhalla fullname: Mhalla, Mehdi – sequence: 3 givenname: Pierre orcidid: 0009-0009-1566-0363 surname: Pocreau fullname: Pocreau, Pierre |
| BackLink | https://inria.hal.science/hal-04672768$$DView record in HAL |
| BookMark | eNqNkU1LJDEQhoO44Od_iEcPMyadj06fREVX2QFd8R5qkspOpKejSffg_PvtcWRZPXmpKl7qfSjqPSC7XeqQkBPOppwzcfawWJdHXD1iQchuMdXTGRMVq9gO2a-0FBOutNz9b94jx6U8M8Yqxbk0ap_8-j1A1w9L-jpgXlOXli8tvsV-TVOglym1CB0NQ-f6mLpCh85jpnGsIXaxR-pgKNDSlEf9iPwI0BY8_uiH5Onm-unqdjK7_3l3dTGbOMmrfgKymQMLAhXO9dybpgYBYjMEV9UqjALTykvuxiNBGM244xpDwNoBCHFI7rZYn-DZvuS4hLy2CaJ9F1L-YyH30bVox1c0jTdGe-mlhLlhRnlAoxruG2XcyDrdshbQfkLdXszsRmNS11WtzYqPu8121-VUSsbwz8CZ3eRhv-Rhtf3IY_Sef_G62MPmp32G2H6D8Bflspsy |
| CitedBy_id | crossref_primary_10_4204_EPTCS_426_11 |
| Cites_doi | 10.1038/ncomms2076 10.1016/0034-4877(72)90011-0 10.1088/1367-2630/aafef7 10.1103/PRXQuantum.2.010320 10.1103/PhysRevLett.123.210502 10.1145/502090.502097 10.1103/PhysRevLett.124.190503 10.1103/PhysRevLett.101.060401 10.1137/S0097539796300933 10.1063/5.0075919 10.1103/PhysRevA.88.022318 10.1103/PhysRevLett.127.110402 10.1088/1367-2630/17/10/102001 10.23638/LMCS-15(3:15)2019 10.1103/PRXQuantum.2.030335 10.1016/0024-3795(75)90075-0 10.1006/jcss.2002.1826 10.1103/PhysRevA.80.022339 10.1103/PhysRevLett.130.070803 10.1088/1367-2630/18/9/093020 10.1103/PhysRevA.109.062435 10.1088/1367-2630/aaf352 10.1007/s00453-013-9826-8 10.1103/PhysRevLett.127.200504 10.1016/S0304-3975(01)00144-X 10.1103/PhysRevLett.113.250402 10.1103/PhysRevA.86.040301 10.1103/PhysRevLett.117.100502 10.1038/nphoton.2011.35 10.22331/q-2017-04-26-10 10.1209/0295-5075/83/30004 10.1007/s10957-016-0892-3 10.1038/s41467-023-36893-3 10.1103/PhysRevLett.128.230503 10.1103/PhysRevA.96.052315 10.1016/j.jcss.2005.06.006 10.22331/q-2022-03-31-679 10.1137/050644719 |
| ContentType | Journal Article |
| Copyright | licence_http://creativecommons.org/publicdomain/zero |
| Copyright_xml | – notice: licence_http://creativecommons.org/publicdomain/zero |
| DBID | AAYXX CITATION 1XC VOOES DOA |
| DOI | 10.1103/PhysRevResearch.6.L032020 |
| DatabaseName | CrossRef Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) Open Access: 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 |
| Discipline | Physics |
| EISSN | 2643-1564 |
| ExternalDocumentID | oai_doaj_org_article_02099d886d4d44ab8085dae8591d958c oai:HAL:hal-04672768v1 10_1103_PhysRevResearch_6_L032020 |
| GroupedDBID | 3MX AAFWJ AAYXX AECSF AFGMR AFPKN AGDNE ALMA_UNASSIGNED_HOLDINGS CITATION GROUPED_DOAJ M~E ROL 1XC VOOES |
| ID | FETCH-LOGICAL-c412t-a49ba0f3e5eb6bd897a3a3bd89fc275f897065d41c511a38601c16effe7caa33 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001283826200007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2643-1564 |
| IngestDate | Mon Nov 10 04:35:55 EST 2025 Sat Nov 22 06:20:31 EST 2025 Sat Nov 29 01:36:29 EST 2025 Tue Nov 18 22:26:19 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| License | licence_http://creativecommons.org/publicdomain/zero/: http://creativecommons.org/publicdomain/zero |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c412t-a49ba0f3e5eb6bd897a3a3bd89fc275f897065d41c511a38601c16effe7caa33 |
| ORCID | 0009-0009-1566-0363 0000-0002-2759-633X 0000-0003-4178-5396 |
| OpenAccessLink | https://doaj.org/article/02099d886d4d44ab8085dae8591d958c |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_02099d886d4d44ab8085dae8591d958c hal_primary_oai_HAL_hal_04672768v1 crossref_primary_10_1103_PhysRevResearch_6_L032020 crossref_citationtrail_10_1103_PhysRevResearch_6_L032020 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-07-26 |
| PublicationDateYYYYMMDD | 2024-07-26 |
| PublicationDate_xml | – month: 07 year: 2024 text: 2024-07-26 day: 26 |
| PublicationDecade | 2020 |
| PublicationTitle | Physical review research |
| PublicationYear | 2024 |
| Publisher | American Physical Society |
| Publisher_xml | – name: American Physical Society |
| References | PhysRevResearch.6.L032020Cc9R1 PhysRevResearch.6.L032020Cc11R1 PhysRevResearch.6.L032020Cc34R1 PhysRevResearch.6.L032020Cc8R1 PhysRevResearch.6.L032020Cc12R1 PhysRevResearch.6.L032020Cc33R1 PhysRevResearch.6.L032020Cc7R1 PhysRevResearch.6.L032020Cc13R1 PhysRevResearch.6.L032020Cc6R1 PhysRevResearch.6.L032020Cc14R1 PhysRevResearch.6.L032020Cc5R1 PhysRevResearch.6.L032020Cc15R1 PhysRevResearch.6.L032020Cc4R1 PhysRevResearch.6.L032020Cc16R1 PhysRevResearch.6.L032020Cc37R1 PhysRevResearch.6.L032020Cc3R1 PhysRevResearch.6.L032020Cc17R1 J. Lofberg (PhysRevResearch.6.L032020Cc39R1) 2004 PhysRevResearch.6.L032020Cc18R1 L. K. Grover (PhysRevResearch.6.L032020Cc2R1) 1996 A. Ambainis (PhysRevResearch.6.L032020Cc19R1) 2018 S. Aaronson (PhysRevResearch.6.L032020Cc35R1) 2016 PhysRevResearch.6.L032020Cc30R1 PhysRevResearch.6.L032020Cc32R1 PhysRevResearch.6.L032020Cc10R1 PhysRevResearch.6.L032020Cc31R1 PhysRevResearch.6.L032020Cc22R1 PhysRevResearch.6.L032020Cc45R1 PhysRevResearch.6.L032020Cc23R1 PhysRevResearch.6.L032020Cc44R1 PhysRevResearch.6.L032020Cc25R1 PhysRevResearch.6.L032020Cc46R1 PhysRevResearch.6.L032020Cc26R1 PhysRevResearch.6.L032020Cc27R1 PhysRevResearch.6.L032020Cc29R1 H. Barnum (PhysRevResearch.6.L032020Cc38R1) 2003 S. Aaronson (PhysRevResearch.6.L032020Cc36R1) 2021 PhysRevResearch.6.L032020Cc1R1 PhysRevResearch.6.L032020Cc41R1 PhysRevResearch.6.L032020Cc40R1 PhysRevResearch.6.L032020Cc20R1 PhysRevResearch.6.L032020Cc43R1 PhysRevResearch.6.L032020Cc21R1 PhysRevResearch.6.L032020Cc42R1 |
| References_xml | – ident: PhysRevResearch.6.L032020Cc5R1 doi: 10.1038/ncomms2076 – ident: PhysRevResearch.6.L032020Cc22R1 doi: 10.1016/0034-4877(72)90011-0 – ident: PhysRevResearch.6.L032020Cc41R1 doi: 10.1088/1367-2630/aafef7 – ident: PhysRevResearch.6.L032020Cc12R1 doi: 10.1103/PRXQuantum.2.010320 – ident: PhysRevResearch.6.L032020Cc29R1 doi: 10.1103/PhysRevLett.123.210502 – ident: PhysRevResearch.6.L032020Cc33R1 doi: 10.1145/502090.502097 – ident: PhysRevResearch.6.L032020Cc15R1 doi: 10.1103/PhysRevLett.124.190503 – ident: PhysRevResearch.6.L032020Cc6R1 doi: 10.1103/PhysRevLett.101.060401 – ident: PhysRevResearch.6.L032020Cc1R1 doi: 10.1137/S0097539796300933 – ident: PhysRevResearch.6.L032020Cc13R1 doi: 10.1063/5.0075919 – volume-title: 18th IEEE Annual Conference on Computational Complexity, Proceedings year: 2003 ident: PhysRevResearch.6.L032020Cc38R1 – ident: PhysRevResearch.6.L032020Cc4R1 doi: 10.1103/PhysRevA.88.022318 – ident: PhysRevResearch.6.L032020Cc27R1 doi: 10.1103/PhysRevLett.127.110402 – ident: PhysRevResearch.6.L032020Cc26R1 doi: 10.1088/1367-2630/17/10/102001 – volume-title: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing year: 2021 ident: PhysRevResearch.6.L032020Cc36R1 – ident: PhysRevResearch.6.L032020Cc42R1 doi: 10.23638/LMCS-15(3:15)2019 – ident: PhysRevResearch.6.L032020Cc17R1 doi: 10.1103/PRXQuantum.2.030335 – ident: PhysRevResearch.6.L032020Cc21R1 doi: 10.1016/0024-3795(75)90075-0 – ident: PhysRevResearch.6.L032020Cc20R1 doi: 10.1006/jcss.2002.1826 – ident: PhysRevResearch.6.L032020Cc23R1 doi: 10.1103/PhysRevA.80.022339 – ident: PhysRevResearch.6.L032020Cc31R1 doi: 10.1103/PhysRevLett.130.070803 – ident: PhysRevResearch.6.L032020Cc7R1 doi: 10.1088/1367-2630/18/9/093020 – ident: PhysRevResearch.6.L032020Cc32R1 doi: 10.1103/PhysRevA.109.062435 – volume-title: Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing (STOC 2016) year: 2016 ident: PhysRevResearch.6.L032020Cc35R1 – ident: PhysRevResearch.6.L032020Cc8R1 doi: 10.1088/1367-2630/aaf352 – ident: PhysRevResearch.6.L032020Cc37R1 doi: 10.1007/s00453-013-9826-8 – ident: PhysRevResearch.6.L032020Cc30R1 doi: 10.1103/PhysRevLett.127.200504 – ident: PhysRevResearch.6.L032020Cc18R1 doi: 10.1016/S0304-3975(01)00144-X – volume-title: 2004 IEEE International Symposium on Computer Aided Control Systems Design year: 2004 ident: PhysRevResearch.6.L032020Cc39R1 – ident: PhysRevResearch.6.L032020Cc10R1 doi: 10.1103/PhysRevLett.113.250402 – volume-title: Proceedings of the International Congress of Mathematicians: Rio de Janeiro 2018 year: 2018 ident: PhysRevResearch.6.L032020Cc19R1 – ident: PhysRevResearch.6.L032020Cc9R1 doi: 10.1103/PhysRevA.86.040301 – ident: PhysRevResearch.6.L032020Cc46R1 doi: 10.1103/PhysRevLett.117.100502 – ident: PhysRevResearch.6.L032020Cc43R1 doi: 10.1038/nphoton.2011.35 – ident: PhysRevResearch.6.L032020Cc44R1 doi: 10.22331/q-2017-04-26-10 – volume-title: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing - STOC '96 year: 1996 ident: PhysRevResearch.6.L032020Cc2R1 – ident: PhysRevResearch.6.L032020Cc25R1 doi: 10.1209/0295-5075/83/30004 – ident: PhysRevResearch.6.L032020Cc40R1 doi: 10.1007/s10957-016-0892-3 – ident: PhysRevResearch.6.L032020Cc45R1 doi: 10.1038/s41467-023-36893-3 – ident: PhysRevResearch.6.L032020Cc11R1 doi: 10.1103/PhysRevLett.128.230503 – ident: PhysRevResearch.6.L032020Cc16R1 doi: 10.1103/PhysRevA.96.052315 – ident: PhysRevResearch.6.L032020Cc34R1 doi: 10.1016/j.jcss.2005.06.006 – ident: PhysRevResearch.6.L032020Cc14R1 doi: 10.22331/q-2022-03-31-679 – ident: PhysRevResearch.6.L032020Cc3R1 doi: 10.1137/050644719 |
| SSID | ssj0002511485 |
| Score | 2.3093252 |
| Snippet | The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this... |
| SourceID | doaj hal crossref |
| SourceType | Open Website Open Access Repository Enrichment Source Index Database |
| StartPage | L032020 |
| SubjectTerms | Physics Quantum Physics |
| Title | Quantum query complexity of Boolean functions under indefinite causal order |
| URI | https://inria.hal.science/hal-04672768 https://doaj.org/article/02099d886d4d44ab8085dae8591d958c |
| Volume | 6 |
| WOSCitedRecordID | wos001283826200007&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: 2643-1564 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002511485 issn: 2643-1564 databaseCode: DOA dateStart: 20190101 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: 2643-1564 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002511485 issn: 2643-1564 databaseCode: M~E dateStart: 20190101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA4iKl7EJ64vonit2zZpmh53ZZcFH6jswVvJqyhoV_aFXvztzqRd2fWiBy-lBJK2kyHzTfrlG0LOmU6xqIsKMgu5KkaoQLPEBibRQslUqyKuik2kt7fy8TG7myv1hZywSh64MlwzxLOdVkphueVcaQkYwSqHsms2S6TB1TdMs7lkCtdgBM5cJmvktGK6syYSKh_cdMZnuxAX1752eLgQkLxuP4SZp9m2qg8z3U2yUeND2qrea4ssuXKbrHqephntkKv7CZhi8kphOR9-UE8Id--ApOmgoO3B4MWpkmKs8u5E8YTYkKIiYvGM4JIaNRnB8F5wc5f0u53-ZS-o6yEEhkfxOFA80yosmEucFtrKLFVMMbwpTJwmBTQAoLA8MvD1iknItUwkkBeSGqUY2yPL5aB0-4SiSqDUsSyEc5xnkYL5SQEqcmWjImO2QeTMJrmptcKxZMVL7nOGkOU_zJmLvDZng8TfXd8qwYy_dGqj4b87oOa1bwBPyGtPyH_zhAY5g2lbGKPXus6xLeT4w1nIaXTwH086JOvw1hy3eGNxRJbHw4k7JitmOn4eDU-8J8L15rPzBRJz5X8 |
| 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=Quantum+query+complexity+of+Boolean+functions+under+indefinite+causal+order&rft.jtitle=Physical+review+research&rft.au=Abbott%2C+Alastair+A.&rft.au=Mhalla%2C+Mehdi&rft.au=Pocreau%2C+Pierre&rft.date=2024-07-26&rft.pub=American+Physical+Society&rft.issn=2643-1564&rft.eissn=2643-1564&rft.volume=6&rft.issue=3&rft_id=info:doi/10.1103%2FPhysRevResearch.6.L032020&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai%3AHAL%3Ahal-04672768v1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2643-1564&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2643-1564&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2643-1564&client=summon |