Optimal Parallel Quantum Query Algorithms

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Algorithmica Ročník 79; číslo 2; s. 509 - 529
Hlavní autori:	Jeffery, Stacey, Magniez, Frederic, de Wolf, Ronald
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.10.2017 Springer Nature B.V Springer Verlag
Predmet:	Algorithm Analysis and Problem Complexity Algorithms Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Functions (mathematics) Lower bounds Mathematical analysis Mathematics of Computing Parallel processing Qubits (quantum computing) Queries Theory of Computation Upper bounds Quantum algorithms Lower bounds Query complexity Parallel algorithms
ISSN:	0178-4617, 1432-0541
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a number of problems, specifically Θ ( ( n / p ) 2 / 3 ) p -parallel queries for element distinctness and Θ ( ( n / p ) k / ( k + 1 ) ) for k -sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p -parallel query complexity are polynomially related for all total functions f when p is small compared to f ’s block sensitivity.
AbstractList	We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a number of problems, specifically Θ ( ( n / p ) 2 / 3 ) p -parallel queries for element distinctness and Θ ( ( n / p ) k / ( k + 1 ) ) for k -sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p -parallel query complexity are polynomially related for all total functions f when p is small compared to f ’s block sensitivity. We define the Streaming Communication model that combines the main aspects of communication complexity and streaming. Input arrives as a stream, spread between several agents across a network. Each agent has a bounded memory, which can be updated upon receiving a new bit, or a message from another agent. We provide tight tradeoffs between the necessary resources, i.e., communication between agents and memory, for some of the canonical problems from communication complexity by proving a strong general lower bound technique. Second, we analyze the Approximate Matching problem and show that the complexity of this problem (i.e., the achievable approximation ratio) in the one-way variant of our model is strictly different both from the streaming complexity and the one-way communication complexity thereof. We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a number of problems, specifically Θ ( ( n / p ) 2 / 3 ) p-parallel queries for element distinctness and Θ ( ( n / p ) k / ( k + 1 ) ) for k -sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p-parallel query complexity are polynomially related for all total functions f when p is small compared to f’s block sensitivity.
Author	Jeffery, Stacey de Wolf, Ronald Magniez, Frederic
Author_xml	– sequence: 1 givenname: Stacey surname: Jeffery fullname: Jeffery, Stacey email: sjeffery@caltech.edu organization: Institute for Quantum Information and Matter, California Institute of Technology – sequence: 2 givenname: Frederic surname: Magniez fullname: Magniez, Frederic organization: CNRS, IRIF, Univ Paris Diderot, Sorbonne Paris-Cité – sequence: 3 givenname: Ronald surname: de Wolf fullname: de Wolf, Ronald organization: QuSoft, CWI and University of Amsterdam
BackLink	https://hal.science/hal-03752908$$DView record in HAL
BookMark	eNp9kF1LAkEUhocwSK0f0J3QlRdT58zO56VIZSBYUNfDuB-6su7azBror29kCyKoqwMvz3N4eQekVzd1Tsg1wi0CqLsAwEVCASUFBpIez0gfecIoCI490gdUmnKJ6oIMQtgAIFNG9sl4sWvLratGz867qsqr0cve1e1-G2_uD6NJtWp82a634ZKcF64K-dXXHZK3h_vX6YzOF49P08mcpomAlqZFATrnBhwTGehlVkgjMsGNRi3VUjCdGSyMS02RcpU5gSxjUqDUEmOwTIZk3P1du8rufCznD7ZxpZ1N5vaUQaIEM6A_MLI3Hbvzzfs-D63dNHtfx3oWDeMmYYLLSKmOSn0Tgs8Lm5ata8umbr0rK4tgTxvabkMbN7SnDe0xmvjL_C70n8M6J0S2XuX-R6c_pU_ihIOF
CitedBy_id	crossref_primary_10_1103_PhysRevResearch_4_033034 crossref_primary_10_1007_s11128_018_1930_x
Cites_doi	10.1098/rspa.2012.0686 10.1016/j.ipl.2010.09.009 10.1137/S0097539705447311 10.1145/2897518.2897644 10.1098/rspa.1992.0167 10.1007/978-3-642-39206-1_10 10.1109/CCC.2013.14 10.1109/FOCS.2012.18 10.1145/2213977.2213985 10.1109/SFCS.2000.892140 10.1145/1008731.1008735 10.1109/FOCS.2009.55 10.4086/toc.2005.v001a005 10.1145/2897518.2897524 10.1145/502090.502097 10.1145/1250790.1250867 10.1137/090745854 10.1109/SFCS.1998.743486 10.1145/237814.237866 10.1145/2422436.2422474 10.1137/0220062 10.1016/S0304-3975(01)00144-X 10.1137/S0097539799355053 10.1137/S0097539795293172 10.1103/PhysRevA.60.2746 10.1006/jcss.2002.1826 10.1007/BF01263419 10.1137/S0097539796298637 10.1109/CCC.2013.25 10.1007/s00453-002-0978-1
ContentType	Journal Article
Copyright	Springer Science+Business Media New York 2016 Copyright Springer Science & Business Media 2017 Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml	– notice: Springer Science+Business Media New York 2016 – notice: Copyright Springer Science & Business Media 2017 – notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID	AAYXX CITATION JQ2 1XC
DOI	10.1007/s00453-016-0206-z
DatabaseName	CrossRef ProQuest Computer Science Collection Hyper Article en Ligne (HAL)
DatabaseTitle	CrossRef ProQuest Computer Science Collection
DatabaseTitleList	ProQuest Computer Science Collection
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1432-0541
EndPage	529
ExternalDocumentID	oai:HAL:hal-03752908v1 10_1007_s00453_016_0206_z
GrantInformation_xml	– fundername: European Commission grantid: IST STREP QCS 255961; QALGO 600700 funderid: http://dx.doi.org/10.13039/501100000780 – fundername: European Research Council grantid: QPROGRESS funderid: http://dx.doi.org/10.13039/501100000781 – fundername: Agence Nationale de la Recherche grantid: ANR-12-BS02-005 funderid: http://dx.doi.org/10.13039/501100001665 – fundername: Netherlands Organization for International Cooperation in Higher Education (NL) grantid: Vidi Grant
GroupedDBID	-4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION JQ2 1XC
ID	FETCH-LOGICAL-c350t-cff08e490a25d08bdf695d54981867b528d91f9ac9fc47da512d26516861c47b3
IEDL.DBID	RSV
ISICitedReferencesCount	14
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000406779100011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0178-4617
IngestDate	Tue Oct 14 20:28:30 EDT 2025 Thu Oct 02 16:29:24 EDT 2025 Sat Nov 29 02:20:27 EST 2025 Tue Nov 18 22:36:12 EST 2025 Fri Feb 21 02:40:20 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	Quantum algorithms Lower bounds Query complexity Parallel algorithms
Language	English
License	Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c350t-cff08e490a25d08bdf695d54981867b528d91f9ac9fc47da512d26516861c47b3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-2384-9026
PQID	1924932546
PQPubID	2043795
PageCount	21
ParticipantIDs	hal_primary_oai_HAL_hal_03752908v1 proquest_journals_1924932546 crossref_citationtrail_10_1007_s00453_016_0206_z crossref_primary_10_1007_s00453_016_0206_z springer_journals_10_1007_s00453_016_0206_z
PublicationCentury	2000
PublicationDate	2017-10-01
PublicationDateYYYYMMDD	2017-10-01
PublicationDate_xml	– month: 10 year: 2017 text: 2017-10-01 day: 01
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Algorithmica
PublicationTitleAbbrev	Algorithmica
PublicationYear	2017
Publisher	Springer US Springer Nature B.V Springer Verlag
Publisher_xml	– name: Springer US – name: Springer Nature B.V – name: Springer Verlag
References	Belovs, A., Childs, A., Jeffery, S., Kothari, R., Magniez, F.: Time-efficient quantum walks for 3-distinctness. In: Proceedings of 40th ICALP(1), pp. 105–122 (2013) AmbainisAQuantum lower bounds by quantum argumentsJ. Comput. Syst. Sci.2002644750767191230110.1006/jcss.2002.18261015.68075 Cleve, R., Watrous, J.: Fast parallel circuits for the quantum Fourier transform. In: Proceedings of 41st IEEE FOCS, pp. 526–536 (2000) AmbainisAQuantum walk algorithm for element distinctnessSIAM J. Comput.2007371210239230629010.1137/S00975397054473111134.81010 ZalkaChGrover’s quantum searching algorithm is optimalPhys. Rev. A1999602746275110.1103/PhysRevA.60.2746 MagniezFNayakARolandJSanthaMSearch via quantum walkSIAM J. Comput.2011401142164278320610.1137/0907458541223.05289 Lee, T., Mittal, R., Reichardt, B., Špalek, R., Szegedy, M.: Quantum query complexity of state conversion. In: Proceedings of 52nd IEEE FOCS, pp. 344–353, (2011). arXiv:1011.3020v2 Belovs, A.: Learning-graph-based quantum algorithm for k-distinctness. In: Proceedings of 53rd IEEE FOCS, pp. 207–216 (2012) MontanaroANonadaptive quantum query complexityInf. Process. Lett.20101102411101113277824410.1016/j.ipl.2010.09.009 SimonDOn the power of quantum computationSIAM J. Comput.199726514741483147198910.1137/S00975397962986370883.03024 de BeaudrapNCleveRWatrousJSharp quantum vs. classical query complexity separationsAlgorithmica2002344449461194351710.1007/s00453-002-0978-11012.68220 Aaronson, S., Ben-David, S., Kothari, R.: Separations in query complexity using cheat sheets. In: Proceedings of 48th STOC, pp. 863–876 (2016) MooreCNilssonMParallel quantum computation and quantum codesSIAM J. Comput.2002313799815189645910.1137/S00975397993550531161.81326 Belovs, A.: Adversary lower bound for element distinctness (2012). arXiv:1204.5074 Aaronson, S., Ambainis, A.: Forrelation: a problem that optimally separates quantum from classical computing. In: Proceedings of 47th ACM STOC, pp. 307–316 (2015). arXiv:1411.5729 Ambainis, A., Balodis, K., Belovs, A., Lee, T., Santha, M., Smotrovs, J.: Separations in query complexity based on pointer functions. In: Proceedings of 48th STOC, pp 800–813 (2016) DeutschDJozsaRRapid solution of problems by quantum computationProc. R. Soc. Lond.1992A439553558119643310.1098/rspa.1992.01670792.68058 van Dam, W.: Quantum oracle interrogation: getting all information for almost half the price. In: Proceedings of 39th IEEE FOCS, pp. 362–367 (1998) Ambainis, A., Bačkurs, A., Smotrovs, J., de Wolf, R.: Optimal quantum query bounds for almost all Boolean functions. In: Proceedings of 30th STACS, pp. 446–453 (2013) NisanNCREW PRAMs and decision treesSIAM J. Comput.19912069991007113574410.1137/02200620737.68028 BealsRBuhrmanHCleveRMoscaMde WolfRQuantum lower bounds by polynomialsJ. ACM2001484778797214493010.1145/502090.5020971127.68404 Høyer, P., Lee, T., Špalek, R.: Negative weights make adversaries stronger. In: Proceedings of 39th ACM STOC, pp. 526–535 (2007) JozsaRAngelakisDGChristandlMEkertAAn introduction to measurement based quantum computationQuantum Information Processing2006AmsterdamIOS Press137158 Takahashi, Y., Tani, S.: Collapse of the hierarchy of constant-depth exact quantum circuits. In: Proceedings of 28th IEEE CCC (2013) Grover, L., Radhakrishnan, J.: Quantum search for multiple items using parallel queries (2004). arXiv:quant-ph/0407217 Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th ACM STOC, pp. 212–219 (1996) NisanNSzegedyMOn the degree of Boolean functions as real polynomialsComput. Complex.199444301313131353110.1007/BF012634190829.68047 AaronsonSShiYQuantum lower bounds for the collision and the element distinctness problemsJ. ACM2004514595605214784910.1145/1008731.10087351169.68406 ShorPWPolynomial-time algorithms for prime factorization and discrete logarithms on a quantum computerSIAM J. Comput.199726514841509147199010.1137/S00975397952931721005.11065 BealsRBrierleySGrayOHarrowAKutinSLindenNShepherdDStatherMEfficient distributed quantum computingProc. R. Soc A20134692153302978910.1098/rspa.2012.0686 HøyerPŠpalekRQuantum fan-out is powerfulTheory Comput.20051181103232251510.4086/toc.2005.v001a0051213.68298 GreenFHomerSMooreCPollettCCounting, fanout and the complexity of quantum ACCQuantum Inf. Comput.200221356519075201187.81065 Belovs, A., Lee, T.: Quantum algorithm for k-distinctness with prior knowledge on the input. Technical Report (2011). arXiv:1108.3022 Belovs, A., Rosmanis, A.: On the power of non-adaptive learning graphs. In: Proceedings of 28th IEEE CCC, pp. 44–55 (2013). arXiv:1210.3279v2 Belovs, A., Špalek, R.: Adversary lower bound for the k-sum problem. In: Proceedings of 4th ITCS, pp. 323–328 (2013) BuhrmanHde WolfRComplexity measures and decision tree complexity: a surveyTheor. Comput. Sci.200228812143193488810.1016/S0304-3975(01)00144-X1061.68058 Reichardt, B.: Span programs and quantum query complexity: The general adversary bound is nearly tight for every Boolean function. In: Proceedings of 50th IEEE FOCS, pp. 544–551 (2009) Belovs, A.: Span programs for functions with constant-sized 1-certificates. In: Proceedings of 43rd ACM STOC, pp. 77–84 (2012) GroverLRudolphTHow significant are the known collision and element distinctness quantum algorithms?Quantum Inf. Comput.20044320120620904551175.81056 D Deutsch (206_CR21) 1992; A439 A Ambainis (206_CR4) 2002; 64 R Beals (206_CR9) 2001; 48 F Green (206_CR22) 2002; 2 N Nisan (206_CR34) 1994; 4 206_CR12 206_CR11 R Jozsa (206_CR28) 2006 C Moore (206_CR32) 2002; 31 N Nisan (206_CR33) 1991; 20 R Beals (206_CR8) 2013; 469 206_CR2 206_CR17 N Beaudrap de (206_CR10) 2002; 34 206_CR19 206_CR14 206_CR13 206_CR35 206_CR1 206_CR16 206_CR38 206_CR15 H Buhrman (206_CR18) 2002; 288 206_CR7 206_CR6 F Magniez (206_CR30) 2011; 40 P Høyer (206_CR27) 2005; 1 Ch Zalka (206_CR39) 1999; 60 A Montanaro (206_CR31) 2010; 110 PW Shor (206_CR36) 1997; 26 S Aaronson (206_CR3) 2004; 51 206_CR20 206_CR23 L Grover (206_CR24) 2004; 4 D Simon (206_CR37) 1997; 26 A Ambainis (206_CR5) 2007; 37 206_CR29 206_CR25 206_CR26
References_xml	– reference: AmbainisAQuantum lower bounds by quantum argumentsJ. Comput. Syst. Sci.2002644750767191230110.1006/jcss.2002.18261015.68075 – reference: van Dam, W.: Quantum oracle interrogation: getting all information for almost half the price. In: Proceedings of 39th IEEE FOCS, pp. 362–367 (1998) – reference: GreenFHomerSMooreCPollettCCounting, fanout and the complexity of quantum ACCQuantum Inf. Comput.200221356519075201187.81065 – reference: GroverLRudolphTHow significant are the known collision and element distinctness quantum algorithms?Quantum Inf. Comput.20044320120620904551175.81056 – reference: Belovs, A., Lee, T.: Quantum algorithm for k-distinctness with prior knowledge on the input. Technical Report (2011). arXiv:1108.3022 – reference: BuhrmanHde WolfRComplexity measures and decision tree complexity: a surveyTheor. Comput. Sci.200228812143193488810.1016/S0304-3975(01)00144-X1061.68058 – reference: DeutschDJozsaRRapid solution of problems by quantum computationProc. R. Soc. Lond.1992A439553558119643310.1098/rspa.1992.01670792.68058 – reference: Aaronson, S., Ambainis, A.: Forrelation: a problem that optimally separates quantum from classical computing. In: Proceedings of 47th ACM STOC, pp. 307–316 (2015). arXiv:1411.5729 – reference: Aaronson, S., Ben-David, S., Kothari, R.: Separations in query complexity using cheat sheets. In: Proceedings of 48th STOC, pp. 863–876 (2016) – reference: HøyerPŠpalekRQuantum fan-out is powerfulTheory Comput.20051181103232251510.4086/toc.2005.v001a0051213.68298 – reference: NisanNCREW PRAMs and decision treesSIAM J. Comput.19912069991007113574410.1137/02200620737.68028 – reference: Høyer, P., Lee, T., Špalek, R.: Negative weights make adversaries stronger. In: Proceedings of 39th ACM STOC, pp. 526–535 (2007) – reference: Cleve, R., Watrous, J.: Fast parallel circuits for the quantum Fourier transform. In: Proceedings of 41st IEEE FOCS, pp. 526–536 (2000) – reference: MontanaroANonadaptive quantum query complexityInf. Process. Lett.20101102411101113277824410.1016/j.ipl.2010.09.009 – reference: Belovs, A.: Adversary lower bound for element distinctness (2012). arXiv:1204.5074 – reference: MooreCNilssonMParallel quantum computation and quantum codesSIAM J. Comput.2002313799815189645910.1137/S00975397993550531161.81326 – reference: Belovs, A.: Learning-graph-based quantum algorithm for k-distinctness. In: Proceedings of 53rd IEEE FOCS, pp. 207–216 (2012) – reference: JozsaRAngelakisDGChristandlMEkertAAn introduction to measurement based quantum computationQuantum Information Processing2006AmsterdamIOS Press137158 – reference: NisanNSzegedyMOn the degree of Boolean functions as real polynomialsComput. Complex.199444301313131353110.1007/BF012634190829.68047 – reference: ShorPWPolynomial-time algorithms for prime factorization and discrete logarithms on a quantum computerSIAM J. Comput.199726514841509147199010.1137/S00975397952931721005.11065 – reference: MagniezFNayakARolandJSanthaMSearch via quantum walkSIAM J. Comput.2011401142164278320610.1137/0907458541223.05289 – reference: BealsRBrierleySGrayOHarrowAKutinSLindenNShepherdDStatherMEfficient distributed quantum computingProc. R. Soc A20134692153302978910.1098/rspa.2012.0686 – reference: Ambainis, A., Bačkurs, A., Smotrovs, J., de Wolf, R.: Optimal quantum query bounds for almost all Boolean functions. In: Proceedings of 30th STACS, pp. 446–453 (2013) – reference: Belovs, A., Rosmanis, A.: On the power of non-adaptive learning graphs. In: Proceedings of 28th IEEE CCC, pp. 44–55 (2013). arXiv:1210.3279v2 – reference: Belovs, A.: Span programs for functions with constant-sized 1-certificates. In: Proceedings of 43rd ACM STOC, pp. 77–84 (2012) – reference: Reichardt, B.: Span programs and quantum query complexity: The general adversary bound is nearly tight for every Boolean function. In: Proceedings of 50th IEEE FOCS, pp. 544–551 (2009) – reference: AaronsonSShiYQuantum lower bounds for the collision and the element distinctness problemsJ. ACM2004514595605214784910.1145/1008731.10087351169.68406 – reference: Ambainis, A., Balodis, K., Belovs, A., Lee, T., Santha, M., Smotrovs, J.: Separations in query complexity based on pointer functions. In: Proceedings of 48th STOC, pp 800–813 (2016) – reference: Grover, L., Radhakrishnan, J.: Quantum search for multiple items using parallel queries (2004). arXiv:quant-ph/0407217 – reference: de BeaudrapNCleveRWatrousJSharp quantum vs. classical query complexity separationsAlgorithmica2002344449461194351710.1007/s00453-002-0978-11012.68220 – reference: Belovs, A., Childs, A., Jeffery, S., Kothari, R., Magniez, F.: Time-efficient quantum walks for 3-distinctness. In: Proceedings of 40th ICALP(1), pp. 105–122 (2013) – reference: Lee, T., Mittal, R., Reichardt, B., Špalek, R., Szegedy, M.: Quantum query complexity of state conversion. In: Proceedings of 52nd IEEE FOCS, pp. 344–353, (2011). arXiv:1011.3020v2 – reference: BealsRBuhrmanHCleveRMoscaMde WolfRQuantum lower bounds by polynomialsJ. ACM2001484778797214493010.1145/502090.5020971127.68404 – reference: Belovs, A., Špalek, R.: Adversary lower bound for the k-sum problem. In: Proceedings of 4th ITCS, pp. 323–328 (2013) – reference: AmbainisAQuantum walk algorithm for element distinctnessSIAM J. Comput.2007371210239230629010.1137/S00975397054473111134.81010 – reference: Takahashi, Y., Tani, S.: Collapse of the hierarchy of constant-depth exact quantum circuits. In: Proceedings of 28th IEEE CCC (2013) – reference: Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th ACM STOC, pp. 212–219 (1996) – reference: SimonDOn the power of quantum computationSIAM J. Comput.199726514741483147198910.1137/S00975397962986370883.03024 – reference: ZalkaChGrover’s quantum searching algorithm is optimalPhys. Rev. A1999602746275110.1103/PhysRevA.60.2746 – volume: 469 start-page: 2153 year: 2013 ident: 206_CR8 publication-title: Proc. R. Soc A doi: 10.1098/rspa.2012.0686 – ident: 206_CR15 – volume: 110 start-page: 1110 issue: 24 year: 2010 ident: 206_CR31 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2010.09.009 – volume: 37 start-page: 210 issue: 1 year: 2007 ident: 206_CR5 publication-title: SIAM J. Comput. doi: 10.1137/S0097539705447311 – ident: 206_CR7 – ident: 206_CR13 – ident: 206_CR1 – volume: 4 start-page: 201 issue: 3 year: 2004 ident: 206_CR24 publication-title: Quantum Inf. Comput. – ident: 206_CR2 doi: 10.1145/2897518.2897644 – volume: A439 start-page: 553 year: 1992 ident: 206_CR21 publication-title: Proc. R. Soc. Lond. doi: 10.1098/rspa.1992.0167 – ident: 206_CR14 doi: 10.1007/978-3-642-39206-1_10 – ident: 206_CR16 doi: 10.1109/CCC.2013.14 – ident: 206_CR11 doi: 10.1109/FOCS.2012.18 – ident: 206_CR12 doi: 10.1145/2213977.2213985 – ident: 206_CR19 doi: 10.1109/SFCS.2000.892140 – volume: 51 start-page: 595 issue: 4 year: 2004 ident: 206_CR3 publication-title: J. ACM doi: 10.1145/1008731.1008735 – ident: 206_CR35 doi: 10.1109/FOCS.2009.55 – volume: 1 start-page: 81 issue: 1 year: 2005 ident: 206_CR27 publication-title: Theory Comput. doi: 10.4086/toc.2005.v001a005 – ident: 206_CR6 doi: 10.1145/2897518.2897524 – volume: 48 start-page: 778 issue: 4 year: 2001 ident: 206_CR9 publication-title: J. ACM doi: 10.1145/502090.502097 – ident: 206_CR26 doi: 10.1145/1250790.1250867 – volume: 40 start-page: 142 issue: 1 year: 2011 ident: 206_CR30 publication-title: SIAM J. Comput. doi: 10.1137/090745854 – ident: 206_CR20 doi: 10.1109/SFCS.1998.743486 – start-page: 137 volume-title: Quantum Information Processing year: 2006 ident: 206_CR28 – ident: 206_CR25 doi: 10.1145/237814.237866 – ident: 206_CR17 doi: 10.1145/2422436.2422474 – volume: 20 start-page: 999 issue: 6 year: 1991 ident: 206_CR33 publication-title: SIAM J. Comput. doi: 10.1137/0220062 – volume: 288 start-page: 21 issue: 1 year: 2002 ident: 206_CR18 publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(01)00144-X – ident: 206_CR29 – volume: 31 start-page: 799 issue: 3 year: 2002 ident: 206_CR32 publication-title: SIAM J. Comput. doi: 10.1137/S0097539799355053 – volume: 26 start-page: 1484 issue: 5 year: 1997 ident: 206_CR36 publication-title: SIAM J. Comput. doi: 10.1137/S0097539795293172 – volume: 60 start-page: 2746 year: 1999 ident: 206_CR39 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.60.2746 – volume: 64 start-page: 750 issue: 4 year: 2002 ident: 206_CR4 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2002.1826 – ident: 206_CR23 – volume: 2 start-page: 35 issue: 1 year: 2002 ident: 206_CR22 publication-title: Quantum Inf. Comput. – volume: 4 start-page: 301 issue: 4 year: 1994 ident: 206_CR34 publication-title: Comput. Complex. doi: 10.1007/BF01263419 – volume: 26 start-page: 1474 issue: 5 year: 1997 ident: 206_CR37 publication-title: SIAM J. Comput. doi: 10.1137/S0097539796298637 – ident: 206_CR38 doi: 10.1109/CCC.2013.25 – volume: 34 start-page: 449 issue: 4 year: 2002 ident: 206_CR10 publication-title: Algorithmica doi: 10.1007/s00453-002-0978-1
SSID	ssj0012796
Score	2.2997537
Snippet	We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that... We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that... We define the Streaming Communication model that combines the main aspects of communication complexity and streaming. Input arrives as a stream, spread between...
SourceID	hal proquest crossref springer
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	509
SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Functions (mathematics) Lower bounds Mathematical analysis Mathematics of Computing Parallel processing Qubits (quantum computing) Queries Theory of Computation Upper bounds
Title	Optimal Parallel Quantum Query Algorithms
URI	https://link.springer.com/article/10.1007/s00453-016-0206-z https://www.proquest.com/docview/1924932546 https://hal.science/hal-03752908
Volume	79
WOSCitedRecordID	wos000406779100011&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: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 databaseCode: RSV dateStart: 19970101 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/eLvHCXMwnV1LS8NAEB60evBifWK0ShAvKoE8NtnssYilB6kVH_QWkt2sLfQhSVuwv96dbRKqqKCnwGbyYGZ3Z4aZ_T6AC0ZjQSghFpMstUjicisMBLVEmPoep1L4JNZkE7TTCXs91i3Ocedlt3tZktQ7dXXYDaMP7P3BplmVBi_WYcNHsBlM0R9fqtKBSzUpF9LOW0T557KU-d0rPjmj9T62Qq7EmV9Ko9rjtOr_-tcd2C4CTLO5nBG7sJaO96BekjeYxVreh8t7tVmMlGQ3zpBPZWg-zJSWZyN1TbN3szl8nWSDaX-UH8Bz6_bppm0VvAkW93x7anEp7TAlzI5dX9hhImTAfKV0ptHrEt8NBXMkizmTnFARK58v3MB3gjBw1EDiHUJtPBmnR2AykThOoCTjhCIyeyI4sYXHJAKDUVcaYJcKjHgBKo7cFsOogkPWqoiwkQxVES0MuKoeeVsiavwmfK6sUskhFna7eRfhGJL3uswO544BjdJoUbEC80gnlh6i_RtwXRpp5fZPXzz-k_QJbLno53V3XwNq02yWnsImn08HeXamJ-YHmUba0A
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1ZS8NAEB5sFfTFW4xnEF9UAjk22exjEUvFWise-BaS3awV2ippWtBf7842CSoq6FNgMzmY2d2ZYWa_D-CQ0VgQSojFJEstkrjcCgNBLRGmvsepFD6JNdkE7XTChwfWLc5xj8pu97IkqXfq6rAbRh_Y-4NNsyoNfqvBLEGWHUzRb-6r0oFLNSkX0s5bRPnnspT53Ss-OaNaD1shP8SZX0qj2uM0l_71r8uwWASYZmM6I1ZgJh2uwlJJ3mAWa3kNjq7UZjFQkt04Qz6Vvnk9VloeD9Q1zV7NRv_xOXvKe4PROtw1z25PW1bBm2Bxz7dzi0tphylhduz6wg4TIQPmK6UzjV6X-G4omCNZzJnkhIpY-XzhBr4ThIGjBhJvA-rD52G6CSYTieMESjJOKCKzJ4ITW3hMIjAYdaUBdqnAiBeg4sht0Y8qOGStiggbyVAV0ZsBx9UjL1NEjd-ED5RVKjnEwm412hGOIXmvy-xw4hiwUxotKlbgKNKJpYdo_waclEb6cPunL279SXof5lu3l-2ofd652IYFF32-7vTbgXqejdNdmOOT_GmU7elJ-g7j6920
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD64KeKLd7Fei_iiUtZL2jSPQx0TZc4rvpU2aZywzdF2gv56c7q2qKggPhXS0zackzQnnC_fB7DPaCgIJcRgksUGiWxu-J6ghvBj1-FUCpeEudgE7XT8hwfWLXRO0xLtXpYkJ2cakKVpmDVGQjaqg2-YiSAOCAG0akv8VoNpojYyiOm6vrmvygg2zQW6UILeIGqtLsua373i08JU6yEs8kPO-aVMmq8-rYV_93sR5ovEU29ORsoSTMXDZVgoRR30Yo6vwMGl-okMlGU3TFBnpa9fjZX3xwN1jZNXvdl_fE6est4gXYW71untcdso9BQM7rhmZnApTT8mzAxtV5h-JKTHXBUMlrPaRa7tC2ZJFnImOaEiVLmAsD3X8nzPUg2Rswb14fMwXgediciyPGUZRhQZ2yPBiSkcJpEwjNpSA7N0ZsALsnHUvOgHFU1y7ooAAWboiuBNg8PqkdGEaeM34z0VocoOObLbzYsA21DU12am_2JpsFUGMChmZhrkG04HVQA0OCoD9uH2T1_c-JP1Lsx2T1rBxVnnfBPmbEwFcgDgFtSzZBxvwwx_yZ7SZCcfr-854-aY
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=Optimal+Parallel+Quantum+Query+Algorithms&rft.jtitle=Algorithmica&rft.au=Jeffery%2C+Stacey&rft.au=Magniez%2C+Frederic&rft.au=de+Wolf%2C+Ronald&rft.date=2017-10-01&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=79&rft.issue=2&rft.spage=509&rft.epage=529&rft_id=info:doi/10.1007%2Fs00453-016-0206-z&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00453_016_0206_z
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon