Variational Quantum Computation Integer Factorization Algorithm
The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits...
Gespeichert in:
| Veröffentlicht in: | International journal of theoretical physics Jg. 62; H. 11; S. 245 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
15.11.2023
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 1572-9575, 0020-7748, 1572-9575 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits. Moreover, the precision of continued fraction computations in Shor’s algorithm is influenced by the number of qubits, making it difficult to implement the algorithm on Noisy Intermediate-Scale Quantum (NISQ) computers. To address these issues, this paper proposes variational quantum computation integer factorization (VQCIF) algorithm based on variational quantum algorithm (VQA). Inspired by classical computing, this algorithm utilizes the parallelism of quantum computing to calculate the product of parameterized quantum states. Subsequently, the quantum multi-control gate is used to map the product satisfying
p
q
=
N
onto an auxiliary qubit. Then the variational quantum circuit is adjusted by the optimizer, and it is possible to obtain a prime factor of the integer
N
with a high probability. While maintaining generality, VQCIF has a simple quantum circuit structure and requires only
2
n
+
1
qubits. Furthermore, the time complexity is exponentially accelerated. VQCIF algorithm is implemented using the Qiskit framework, and tests are conducted on factorization instances to demonstrate its feasibility. |
|---|---|
| AbstractList | The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits. Moreover, the precision of continued fraction computations in Shor’s algorithm is influenced by the number of qubits, making it difficult to implement the algorithm on Noisy Intermediate-Scale Quantum (NISQ) computers. To address these issues, this paper proposes variational quantum computation integer factorization (VQCIF) algorithm based on variational quantum algorithm (VQA). Inspired by classical computing, this algorithm utilizes the parallelism of quantum computing to calculate the product of parameterized quantum states. Subsequently, the quantum multi-control gate is used to map the product satisfying pq=N onto an auxiliary qubit. Then the variational quantum circuit is adjusted by the optimizer, and it is possible to obtain a prime factor of the integer N with a high probability. While maintaining generality, VQCIF has a simple quantum circuit structure and requires only 2n+1 qubits. Furthermore, the time complexity is exponentially accelerated. VQCIF algorithm is implemented using the Qiskit framework, and tests are conducted on factorization instances to demonstrate its feasibility. The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits. Moreover, the precision of continued fraction computations in Shor’s algorithm is influenced by the number of qubits, making it difficult to implement the algorithm on Noisy Intermediate-Scale Quantum (NISQ) computers. To address these issues, this paper proposes variational quantum computation integer factorization (VQCIF) algorithm based on variational quantum algorithm (VQA). Inspired by classical computing, this algorithm utilizes the parallelism of quantum computing to calculate the product of parameterized quantum states. Subsequently, the quantum multi-control gate is used to map the product satisfying p q = N onto an auxiliary qubit. Then the variational quantum circuit is adjusted by the optimizer, and it is possible to obtain a prime factor of the integer N with a high probability. While maintaining generality, VQCIF has a simple quantum circuit structure and requires only 2 n + 1 qubits. Furthermore, the time complexity is exponentially accelerated. VQCIF algorithm is implemented using the Qiskit framework, and tests are conducted on factorization instances to demonstrate its feasibility. |
| ArticleNumber | 245 |
| Author | Zhang, Xinglan Zhang, Feng |
| Author_xml | – sequence: 1 givenname: Xinglan surname: Zhang fullname: Zhang, Xinglan organization: Faculty of Information Technology, Beijing University of Technology, Beijing Key Laboratory of Trusted Computing – sequence: 2 givenname: Feng surname: Zhang fullname: Zhang, Feng email: changfeng@emails.bjut.edu.cn organization: Faculty of Information Technology, Beijing University of Technology, Beijing Key Laboratory of Trusted Computing |
| BookMark | eNp9kE1LAzEQhoNUsK3-AU8LnlcnX033JKXYWiiIoF5DNp2tW_ajJtlD_fXGrqB46GGYyfC-4Z1nRAZN2yAh1xRuKYC68xSU4imwWFLE6XBGhlQqlmZSycGf-YKMvN8BQAZiOiT3b8aVJpRtY6rkuTNN6Opk3tb7Lhy3yaoJuEWXLIwNrSs_--2s2sZHeK8vyXlhKo9XP31MXhcPL_PHdP20XM1n69RymoV0AwItZEbGCIg5ZwaZpCpHy4wVhgppZcExUxuBgpscpFKbeJKdAMNC5XxMbvp_96796NAHvWs7F0N7zZkUkwkIClE17VXWtd47LLQt-zuCM2WlKehvXLrHpSMufcSlD9HK_ln3rqyNO5w28d7ko7iJmH5TnXB9AX6jgJo |
| CitedBy_id | crossref_primary_10_1038_s41534_025_01061_6 |
| Cites_doi | 10.1038/s42254-021-00348-9 10.1103/PhysRevA.102.032420 10.1103/PhysRevLett.114.140504 10.1038/nphys3029 10.1007/s11432-022-3492-x 10.1145/359340.359342 10.1103/PhysRevLett.103.150502 10.1007/s11128-023-03869-7 10.1103/PhysRevA.106.042602 10.1007/978-3-030-14082-3_7 10.1103/PhysRevA.52.3457 10.1007/978-3-319-96424-9 10.1145/237814.237866 10.1038/s41598-020-62802-5 10.22331/q-2020-05-25-269 10.1103/PhysRevA.99.032331 10.5555/2011517.2011525 10.1103/PhysRevLett.70.1895 10.1007/s10773-022-05040-x 10.1007/978-94-015-8330-5_4 10.22331/q-2021-10-20-567 10.26421/QIC23.1-2-3 10.1038/s41586-019-0980-2 10.1002/qute.201900070 10.5555/3179553.3179560 10.1038/nature23879 10.22331/q-2018-08-06-79 10.1109/SFCS.1994.365700 10.48550/arXiv.2304.12100 10.1103/PhysRevLett.86.1889 10.1109/ICCCA49541.2020.9250806 10.1142/9789813237230_0001 10.48550/arXiv.1310.6446 10.48550/arXiv.2101.11020 10.1109/JPROC.2018.2884353 10.1103/PhysRevA.103.042415 10.48550/arXiv.2107.09155 10.1109/ICTC46691.2019.8939749 10.1038/srep03023 10.1007/s11128-017-1603-1 10.1017/CBO9780511976667 10.5281/zenodo.8090426 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. |
| DBID | AAYXX CITATION 7XB 8FE 8FG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ M2P P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS Q9U |
| DOI | 10.1007/s10773-023-05473-y |
| DatabaseName | CrossRef ProQuest Central (purchase pre-March 2016) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection Science Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) 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 ProQuest Central Basic |
| DatabaseTitle | CrossRef Advanced Technologies & Aerospace Collection ProQuest Central Student Technology Collection ProQuest Central Basic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Science Journals ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central Advanced Technologies & Aerospace Database ProQuest One Applied & Life Sciences ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Advanced Technologies & Aerospace Collection |
| Database_xml | – sequence: 1 dbid: P5Z name: Advanced Technologies & Aerospace Database url: https://search.proquest.com/hightechjournals sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 1572-9575 |
| ExternalDocumentID | 10_1007_s10773_023_05473_y |
| GrantInformation_xml | – fundername: Beijing Municipal Natural Science Foundation grantid: 4212015 funderid: http://dx.doi.org/10.13039/501100005089 |
| GroupedDBID | -54 -5F -5G -BR -DZ -EM -~C -~X .86 .VR 06D 0R~ 0VY 1N0 203 29J 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADMLS ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. B0M BA0 BGNMA BSONS CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EAD EAP EAS EBLON EBS EIOEI EMK EPL ESBYG ESX FEDTE FERAY FFXSO FIGPU FNLPD FRRFC FWDCC GGCAI GGRSB GJIRD GNWQR GQ3 GQ6 GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y MA- NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P2P P9T PF0 PT4 PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S27 S3B SAP SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UPT UTJUX VC2 W23 W48 WH7 WK8 YLTOR Z45 Z7R Z7U Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ~8M ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ABUFD ACSTC AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AHPBZ AHWEU AIXLP AMVHM ARAPS ATHPR AYFIA AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ M2P PHGZM PHGZT PQGLB 7XB 8FE 8FG P62 PKEHL PQEST PQQKQ PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c319t-d04ec09a5957eeb32ae2517bec2ac4a145c5f3e97d4e43ab0577d077c602ef7b3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001101059200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1572-9575 0020-7748 |
| IngestDate | Sat Sep 27 04:20:53 EDT 2025 Tue Nov 18 22:40:09 EST 2025 Sat Nov 29 06:31:08 EST 2025 Fri Feb 21 02:41:10 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Keywords | Shor’s algorithm Variational quantum algorithm Variational quantum computation integer factorization algorithm Integer factorization Qiskit |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-d04ec09a5957eeb32ae2517bec2ac4a145c5f3e97d4e43ab0577d077c602ef7b3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3254660410 |
| PQPubID | 2043554 |
| ParticipantIDs | proquest_journals_3254660410 crossref_citationtrail_10_1007_s10773_023_05473_y crossref_primary_10_1007_s10773_023_05473_y springer_journals_10_1007_s10773_023_05473_y |
| PublicationCentury | 2000 |
| PublicationDate | 2023-11-15 |
| PublicationDateYYYYMMDD | 2023-11-15 |
| PublicationDate_xml | – month: 11 year: 2023 text: 2023-11-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | International journal of theoretical physics |
| PublicationTitleAbbrev | Int J Theor Phys |
| PublicationYear | 2023 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | LiQHuangYJinSHouXWangXQuantum spectral clustering algorithm for unsupervised learningSci. China Inf. Sci.20226510445513810.1007/s11432-022-3492-x BeauregardSCircuit for shor’s algorithm using 2n+3 qubitsQuantum Info. Comput.200332175185196558810.5555/2011517.20115251152.81676 Xiao, L., Qiu, D., Luo, L., Mateus, P.: Distributed Quantum-classical Hybrid Shor’s Algorithm (2023). https://doi.org/10.48550/arXiv.2304.12100 RivestRLShamirAAdlemanLA method for obtaining digital signatures and public-key cryptosystemsCommun. ACM.197821212012670010310.1145/359340.3593420368.94005 AraujoIFParkDKLudermirTBOliveiraWRPetruccioneFSilvaAJConfigurable sublinear circuits for quantum state preparationQuantum Inf. Process.20232221232023QuIP...22..123A455168610.1007/s11128-023-03869-71509.81237 LaRoseRCoyleBRobust data encodings for quantum classifiersPhys. Rev. A.20201022020PhRvA.102c2420L10.1103/PhysRevA.102.032420 BarencoABennettCHCleveRDiVincenzoDPMargolusNShorPSleatorTSmolinJAWeinfurterHElementary gates for quantum computationPhys Rev A.199552534571995PhRvA..52.3457B10.1103/PhysRevA.52.3457 Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the twenty-eighth annual acm symposium on theory of computing. STOC ’96, pp. 212–219. Association for Computing Machinery, New York, NY, USA (1996). https://doi.org/10.1145/237814.237866 KerenidisILandmanJQuantum spectral clusteringPhys. Rev. A.20211032021PhRvA.103d2415K425681610.1103/PhysRevA.103.042415 Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum. 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79 Benenti, G., Casati, G., Rossini, D., Strini, G.: Principles of Quantum Computation and Information. World Scientific, Singapore (2019). https://doi.org/10.1142/9789813237230_0001 Schuld, M., Petruccione, F.: Supervised Learning with Quantum Computers vol. 17. Springer, Switzerland (2018). https://doi.org/10.1007/978-3-319-96424-9 SchuldMBergholmVGogolinCIzaacJKilloranNEvaluating analytic gradients on quantum hardwarePhys. Rev. A.2019992019PhRvA..99c2331S10.1103/PhysRevA.99.032331 LiZLiuXXuNDuJExperimental realization of a quantum support vector machinePhys. Rev. Lett.20151142015PhRvL.114n0504L10.1103/PhysRevLett.114.140504 SimSJohnsonPDAspuru-GuzikAExpressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithmsAdv. Quantum Technol.2019212190007010.1002/qute.201900070 Stokes, J., Izaac, J., Killoran, N., Carleo, G.: Quantum Natural Gradient. Quantum. 4, 269 (2020). https://doi.org/10.22331/q-2020-05-25-269 LiHJiangNZhangRWangZWangHQuantum support vector machine based on gradient descentInt. J. Theor. Phys.202261392440271910.1007/s10773-022-05040-x1490.81049 Schuld, M.: Supervised quantum machine learning models are kernel methods. arXiv preprint arXiv:2101.11020. (2021) https://doi.org/10.48550/arXiv.2101.11020 Gacon, J., Zoufal, C., Carleo, G., Woerner, S.: Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information. Quantum. 5, 567 (2021). https://doi.org/10.22331/q-2021-10-20-567 BennettCHBrassardGCrépeauCJozsaRPeresAWoottersWKTeleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channelsPhys Rev Lett.1993701318951993PhRvL..70.1895B120824710.1103/PhysRevLett.70.18951051.81505 WangBHuFYaoHWangCPrime factorization algorithm based on parameter optimization of ising modelSci. Rep.202010171062020NatSR..10.7106W10.1038/s41598-020-62802-5 Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th annual symposium on foundations of computer science, pp. 124–134 (1994). https://doi.org/10.1109/SFCS.1994.365700 MaslovDNamYKimJAn outlook for quantum computing [point of view]Proc. IEEE.2019107151010.1109/JPROC.2018.2884353 SilvaAJParkDKLinear-depth quantum circuits for multiqubit controlled gatesPhys. Rev. A.20221062022PhRvA.106d2602D451129510.1103/PhysRevA.106.042602 LloydSMohseniMRebentrostPQuantum principal component analysisNat. Phys.201410963163310.1038/nphys3029 Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University press, Cambridge (2010). https://doi.org/10.1017/CBO9780511976667 WeinsteinYSPraviaMAFortunatoEMLloydSCoryDGImplementation of the quantum fourier transformPhys. Rev. Lett.200186188918912001PhRvL..86.1889W10.1103/PhysRevLett.86.1889 GellerMRZhouZFactoring 51 and 85 with 8 qubitsSci Rep.20133130232013NatSR...3E3023G10.1038/srep03023 Häner, T., Roetteler, M., Svore, K.M.: Factoring using 2n+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2n + 2$$\end{document} qubits with toffoli based modular multiplication. Quantum Info. Comput. 17(7–8), 673–684 (2017). https://doi.org/10.5555/3179553.3179560 Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. nature. 549(7671), 242–246 (2017). https://doi.org/10.1038/nature23879 Choi, J., Kim, J.: A tutorial on quantum approximate optimization algorithm (qaoa): Fundamentals and applications. In: 2019 international conference on information and communication technology convergence (ICTC), pp. 138–142 (2019). https://doi.org/10.1109/ICTC46691.2019.8939749 Treinish, M., Gambetta, J., Thomas, S., qiskit-bot, Nation, P., Kassebaum, P., Arellano, E., Rodríguez, D.M., Puente González, S., Bello, L., Lishman, J., Hu, S., Garrison, J., Huang, J., Krsulich, K., Yu, J., Gacon, J., Marques, M., McKay, D., Gomez, J., Capelluto, L., Wood, S., Travis-S-IBM, Mitchell, A., Panigrahi, A., Hartman, K., lerongil, Rahman, R.I., Itoko, T., Pozas-Kerstjens, A.: Qiskit/qiskit-metapackage: Qiskit 0.43.2. https://doi.org/10.5281/zenodo.8090426 CerezoMArrasmithABabbushRBenjaminSCEndoSFujiiKMcCleanJRMitaraiKYuanXCincioLVariational quantum algorithms.Nat. Rev. Phys.20213962564410.1038/s42254-021-00348-9 HarrowAWHassidimALloydSQuantum algorithm for linear systems of equationsPhys. Rev. Lett.20091032009PhRvL.103o0502H255168810.1103/PhysRevLett.103.150502 Anschuetz, E., Olson, J., Aspuru-Guzik, A., Cao, Y.: Variational quantum factoring. In: Feld, S., Linnhoff-Popien, C. (eds.) Quantum Technology and Optimization Problems, pp. 74–85. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14082-3_7 Ruiz-PerezLGarcia-EscartinJCQuantum arithmetic with the quantum fourier transformQuantum Inf. Process.201716114364200710.1007/s11128-017-1603-11373.81150 Gamel, O., James, D.F.V.: Simplified Factoring Algorithms for Validating Small-Scale Quantum Information Processing Technologies (2013). https://doi.org/10.48550/arXiv.1310.6446 Bhatia, V., Ramkumar, K.R.: An efficient quantum computing technique for cracking rsa using shor’s algorithm. In: 2020 IEEE 5th international conference on computing communication and automation (ICCCA), pp. 89–94 (2020). https://doi.org/10.1109/ICCCA49541.2020.9250806 HavlíčekVCórcolesADTemmeKHarrowAWKandalaAChowJMGambettaJMSupervised learning with quantum-enhanced feature spacesNature.201956777472092122019Natur.567..209H10.1038/s41586-019-0980-2 Powell, M.J.: A Direct Search Optimization Method that Models the Objective and Constraint Functions by Linear Interpolation. Springer, Dordrecht (1994). https://doi.org/10.1007/978-94-015-8330-5_4 Ghosh, K.: Encoding classical data into a quantum computer (2021). https://doi.org/10.48550/arXiv.2107.09155 Xiao, L., Qiu, D., Luo, L., Mateus, P.: Distributed shor’s algorithm. Quantum Inform. Comput. 23(1-2), 27–44 (2023). https://doi.org/10.26421/QIC23.1-2-3 H Li (5473_CR7) 2022; 61 D Maslov (5473_CR2) 2019; 107 S Lloyd (5473_CR8) 2014; 10 5473_CR30 S Sim (5473_CR33) 2019; 2 RL Rivest (5473_CR11) 1978; 21 5473_CR12 5473_CR34 YS Weinstein (5473_CR40) 2001; 86 5473_CR4 5473_CR14 5473_CR36 5473_CR3 5473_CR15 5473_CR37 5473_CR16 5473_CR38 MR Geller (5473_CR17) 2013; 3 5473_CR18 5473_CR19 S Beauregard (5473_CR13) 2003; 3 M Schuld (5473_CR35) 2019; 99 AW Harrow (5473_CR5) 2009; 103 AJ Silva (5473_CR41) 2022; 106 R LaRose (5473_CR32) 2020; 102 M Cerezo (5473_CR25) 2021; 3 V Havlíček (5473_CR31) 2019; 567 5473_CR1 CH Bennett (5473_CR20) 1993; 70 L Ruiz-Perez (5473_CR39) 2017; 16 5473_CR22 Q Li (5473_CR10) 2022; 65 5473_CR23 Z Li (5473_CR6) 2015; 114 5473_CR24 5473_CR26 5473_CR27 5473_CR28 I Kerenidis (5473_CR9) 2021; 103 IF Araujo (5473_CR29) 2023; 22 A Barenco (5473_CR42) 1995; 52 B Wang (5473_CR21) 2020; 10 |
| References_xml | – reference: LloydSMohseniMRebentrostPQuantum principal component analysisNat. Phys.201410963163310.1038/nphys3029 – reference: Anschuetz, E., Olson, J., Aspuru-Guzik, A., Cao, Y.: Variational quantum factoring. In: Feld, S., Linnhoff-Popien, C. (eds.) Quantum Technology and Optimization Problems, pp. 74–85. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14082-3_7 – reference: Xiao, L., Qiu, D., Luo, L., Mateus, P.: Distributed Quantum-classical Hybrid Shor’s Algorithm (2023). https://doi.org/10.48550/arXiv.2304.12100 – reference: Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum. 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79 – reference: Gacon, J., Zoufal, C., Carleo, G., Woerner, S.: Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information. Quantum. 5, 567 (2021). https://doi.org/10.22331/q-2021-10-20-567 – reference: MaslovDNamYKimJAn outlook for quantum computing [point of view]Proc. IEEE.2019107151010.1109/JPROC.2018.2884353 – reference: Choi, J., Kim, J.: A tutorial on quantum approximate optimization algorithm (qaoa): Fundamentals and applications. In: 2019 international conference on information and communication technology convergence (ICTC), pp. 138–142 (2019). https://doi.org/10.1109/ICTC46691.2019.8939749 – reference: Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University press, Cambridge (2010). https://doi.org/10.1017/CBO9780511976667 – reference: WangBHuFYaoHWangCPrime factorization algorithm based on parameter optimization of ising modelSci. Rep.202010171062020NatSR..10.7106W10.1038/s41598-020-62802-5 – reference: WeinsteinYSPraviaMAFortunatoEMLloydSCoryDGImplementation of the quantum fourier transformPhys. Rev. Lett.200186188918912001PhRvL..86.1889W10.1103/PhysRevLett.86.1889 – reference: LiHJiangNZhangRWangZWangHQuantum support vector machine based on gradient descentInt. J. Theor. Phys.202261392440271910.1007/s10773-022-05040-x1490.81049 – reference: Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. nature. 549(7671), 242–246 (2017). https://doi.org/10.1038/nature23879 – reference: CerezoMArrasmithABabbushRBenjaminSCEndoSFujiiKMcCleanJRMitaraiKYuanXCincioLVariational quantum algorithms.Nat. Rev. Phys.20213962564410.1038/s42254-021-00348-9 – reference: LaRoseRCoyleBRobust data encodings for quantum classifiersPhys. Rev. A.20201022020PhRvA.102c2420L10.1103/PhysRevA.102.032420 – reference: RivestRLShamirAAdlemanLA method for obtaining digital signatures and public-key cryptosystemsCommun. ACM.197821212012670010310.1145/359340.3593420368.94005 – reference: SilvaAJParkDKLinear-depth quantum circuits for multiqubit controlled gatesPhys. Rev. A.20221062022PhRvA.106d2602D451129510.1103/PhysRevA.106.042602 – reference: GellerMRZhouZFactoring 51 and 85 with 8 qubitsSci Rep.20133130232013NatSR...3E3023G10.1038/srep03023 – reference: Benenti, G., Casati, G., Rossini, D., Strini, G.: Principles of Quantum Computation and Information. World Scientific, Singapore (2019). https://doi.org/10.1142/9789813237230_0001 – reference: BarencoABennettCHCleveRDiVincenzoDPMargolusNShorPSleatorTSmolinJAWeinfurterHElementary gates for quantum computationPhys Rev A.199552534571995PhRvA..52.3457B10.1103/PhysRevA.52.3457 – reference: BennettCHBrassardGCrépeauCJozsaRPeresAWoottersWKTeleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channelsPhys Rev Lett.1993701318951993PhRvL..70.1895B120824710.1103/PhysRevLett.70.18951051.81505 – reference: Treinish, M., Gambetta, J., Thomas, S., qiskit-bot, Nation, P., Kassebaum, P., Arellano, E., Rodríguez, D.M., Puente González, S., Bello, L., Lishman, J., Hu, S., Garrison, J., Huang, J., Krsulich, K., Yu, J., Gacon, J., Marques, M., McKay, D., Gomez, J., Capelluto, L., Wood, S., Travis-S-IBM, Mitchell, A., Panigrahi, A., Hartman, K., lerongil, Rahman, R.I., Itoko, T., Pozas-Kerstjens, A.: Qiskit/qiskit-metapackage: Qiskit 0.43.2. https://doi.org/10.5281/zenodo.8090426 – reference: BeauregardSCircuit for shor’s algorithm using 2n+3 qubitsQuantum Info. Comput.200332175185196558810.5555/2011517.20115251152.81676 – reference: SimSJohnsonPDAspuru-GuzikAExpressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithmsAdv. Quantum Technol.2019212190007010.1002/qute.201900070 – reference: Powell, M.J.: A Direct Search Optimization Method that Models the Objective and Constraint Functions by Linear Interpolation. Springer, Dordrecht (1994). https://doi.org/10.1007/978-94-015-8330-5_4 – reference: Häner, T., Roetteler, M., Svore, K.M.: Factoring using 2n+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2n + 2$$\end{document} qubits with toffoli based modular multiplication. Quantum Info. Comput. 17(7–8), 673–684 (2017). https://doi.org/10.5555/3179553.3179560 – reference: KerenidisILandmanJQuantum spectral clusteringPhys. Rev. A.20211032021PhRvA.103d2415K425681610.1103/PhysRevA.103.042415 – reference: Gamel, O., James, D.F.V.: Simplified Factoring Algorithms for Validating Small-Scale Quantum Information Processing Technologies (2013). https://doi.org/10.48550/arXiv.1310.6446 – reference: Schuld, M.: Supervised quantum machine learning models are kernel methods. arXiv preprint arXiv:2101.11020. (2021) https://doi.org/10.48550/arXiv.2101.11020 – reference: LiQHuangYJinSHouXWangXQuantum spectral clustering algorithm for unsupervised learningSci. China Inf. Sci.20226510445513810.1007/s11432-022-3492-x – reference: Ghosh, K.: Encoding classical data into a quantum computer (2021). https://doi.org/10.48550/arXiv.2107.09155 – reference: Stokes, J., Izaac, J., Killoran, N., Carleo, G.: Quantum Natural Gradient. Quantum. 4, 269 (2020). https://doi.org/10.22331/q-2020-05-25-269 – reference: HarrowAWHassidimALloydSQuantum algorithm for linear systems of equationsPhys. Rev. Lett.20091032009PhRvL.103o0502H255168810.1103/PhysRevLett.103.150502 – reference: HavlíčekVCórcolesADTemmeKHarrowAWKandalaAChowJMGambettaJMSupervised learning with quantum-enhanced feature spacesNature.201956777472092122019Natur.567..209H10.1038/s41586-019-0980-2 – reference: Bhatia, V., Ramkumar, K.R.: An efficient quantum computing technique for cracking rsa using shor’s algorithm. In: 2020 IEEE 5th international conference on computing communication and automation (ICCCA), pp. 89–94 (2020). https://doi.org/10.1109/ICCCA49541.2020.9250806 – reference: Ruiz-PerezLGarcia-EscartinJCQuantum arithmetic with the quantum fourier transformQuantum Inf. Process.201716114364200710.1007/s11128-017-1603-11373.81150 – reference: Xiao, L., Qiu, D., Luo, L., Mateus, P.: Distributed shor’s algorithm. Quantum Inform. Comput. 23(1-2), 27–44 (2023). https://doi.org/10.26421/QIC23.1-2-3 – reference: Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th annual symposium on foundations of computer science, pp. 124–134 (1994). https://doi.org/10.1109/SFCS.1994.365700 – reference: LiZLiuXXuNDuJExperimental realization of a quantum support vector machinePhys. Rev. Lett.20151142015PhRvL.114n0504L10.1103/PhysRevLett.114.140504 – reference: Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the twenty-eighth annual acm symposium on theory of computing. STOC ’96, pp. 212–219. Association for Computing Machinery, New York, NY, USA (1996). https://doi.org/10.1145/237814.237866 – reference: AraujoIFParkDKLudermirTBOliveiraWRPetruccioneFSilvaAJConfigurable sublinear circuits for quantum state preparationQuantum Inf. Process.20232221232023QuIP...22..123A455168610.1007/s11128-023-03869-71509.81237 – reference: Schuld, M., Petruccione, F.: Supervised Learning with Quantum Computers vol. 17. Springer, Switzerland (2018). https://doi.org/10.1007/978-3-319-96424-9 – reference: SchuldMBergholmVGogolinCIzaacJKilloranNEvaluating analytic gradients on quantum hardwarePhys. Rev. A.2019992019PhRvA..99c2331S10.1103/PhysRevA.99.032331 – volume: 3 start-page: 625 issue: 9 year: 2021 ident: 5473_CR25 publication-title: Nat. Rev. Phys. doi: 10.1038/s42254-021-00348-9 – volume: 102 year: 2020 ident: 5473_CR32 publication-title: Phys. Rev. A. doi: 10.1103/PhysRevA.102.032420 – volume: 114 year: 2015 ident: 5473_CR6 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.114.140504 – volume: 10 start-page: 631 issue: 9 year: 2014 ident: 5473_CR8 publication-title: Nat. Phys. doi: 10.1038/nphys3029 – volume: 65 issue: 10 year: 2022 ident: 5473_CR10 publication-title: Sci. China Inf. Sci. doi: 10.1007/s11432-022-3492-x – volume: 21 start-page: 120 issue: 2 year: 1978 ident: 5473_CR11 publication-title: Commun. ACM. doi: 10.1145/359340.359342 – volume: 103 year: 2009 ident: 5473_CR5 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.103.150502 – volume: 22 start-page: 123 issue: 2 year: 2023 ident: 5473_CR29 publication-title: Quantum Inf. Process. doi: 10.1007/s11128-023-03869-7 – volume: 106 year: 2022 ident: 5473_CR41 publication-title: Phys. Rev. A. doi: 10.1103/PhysRevA.106.042602 – ident: 5473_CR22 doi: 10.1007/978-3-030-14082-3_7 – volume: 52 start-page: 3457 issue: 5 year: 1995 ident: 5473_CR42 publication-title: Phys Rev A. doi: 10.1103/PhysRevA.52.3457 – ident: 5473_CR27 doi: 10.1007/978-3-319-96424-9 – ident: 5473_CR4 doi: 10.1145/237814.237866 – volume: 10 start-page: 7106 issue: 1 year: 2020 ident: 5473_CR21 publication-title: Sci. Rep. doi: 10.1038/s41598-020-62802-5 – ident: 5473_CR36 doi: 10.22331/q-2020-05-25-269 – volume: 99 year: 2019 ident: 5473_CR35 publication-title: Phys. Rev. A. doi: 10.1103/PhysRevA.99.032331 – volume: 3 start-page: 175 issue: 2 year: 2003 ident: 5473_CR13 publication-title: Quantum Info. Comput. doi: 10.5555/2011517.2011525 – volume: 70 start-page: 1895 issue: 13 year: 1993 ident: 5473_CR20 publication-title: Phys Rev Lett. doi: 10.1103/PhysRevLett.70.1895 – volume: 61 start-page: 92 issue: 3 year: 2022 ident: 5473_CR7 publication-title: Int. J. Theor. Phys. doi: 10.1007/s10773-022-05040-x – ident: 5473_CR38 doi: 10.1007/978-94-015-8330-5_4 – ident: 5473_CR37 doi: 10.22331/q-2021-10-20-567 – ident: 5473_CR18 doi: 10.26421/QIC23.1-2-3 – volume: 567 start-page: 209 issue: 7747 year: 2019 ident: 5473_CR31 publication-title: Nature. doi: 10.1038/s41586-019-0980-2 – volume: 2 start-page: 1900070 issue: 12 year: 2019 ident: 5473_CR33 publication-title: Adv. Quantum Technol. doi: 10.1002/qute.201900070 – ident: 5473_CR15 doi: 10.5555/3179553.3179560 – ident: 5473_CR34 doi: 10.1038/nature23879 – ident: 5473_CR24 doi: 10.22331/q-2018-08-06-79 – ident: 5473_CR3 doi: 10.1109/SFCS.1994.365700 – ident: 5473_CR19 doi: 10.48550/arXiv.2304.12100 – volume: 86 start-page: 1889 year: 2001 ident: 5473_CR40 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.86.1889 – ident: 5473_CR1 doi: 10.1109/ICCCA49541.2020.9250806 – ident: 5473_CR12 doi: 10.1142/9789813237230_0001 – ident: 5473_CR16 doi: 10.48550/arXiv.1310.6446 – ident: 5473_CR28 doi: 10.48550/arXiv.2101.11020 – volume: 107 start-page: 5 issue: 1 year: 2019 ident: 5473_CR2 publication-title: Proc. IEEE. doi: 10.1109/JPROC.2018.2884353 – volume: 103 year: 2021 ident: 5473_CR9 publication-title: Phys. Rev. A. doi: 10.1103/PhysRevA.103.042415 – ident: 5473_CR30 doi: 10.48550/arXiv.2107.09155 – ident: 5473_CR23 doi: 10.1109/ICTC46691.2019.8939749 – volume: 3 start-page: 3023 issue: 1 year: 2013 ident: 5473_CR17 publication-title: Sci Rep. doi: 10.1038/srep03023 – volume: 16 start-page: 1 year: 2017 ident: 5473_CR39 publication-title: Quantum Inf. Process. doi: 10.1007/s11128-017-1603-1 – ident: 5473_CR14 doi: 10.1017/CBO9780511976667 – ident: 5473_CR26 doi: 10.5281/zenodo.8090426 |
| SSID | ssj0009048 |
| Score | 2.3463938 |
| Snippet | The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem.... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 245 |
| SubjectTerms | Algorithms Circuits Complexity Computers Elementary Particles Factorization Integers Machine learning Mathematical and Computational Physics Optimization techniques Physics Physics and Astronomy Prime numbers Quantum computing Quantum Field Theory Quantum Physics Qubits (quantum computing) Theoretical |
| SummonAdditionalLinks | – databaseName: ProQuest Central dbid: BENPR link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1JS8NAFH5oq-DFXaxWycGbBrPMZDKnUqXFg5QqKr2FyWSqQjebVOi_900yMSjYi7esw_DeLG-Z930AFzELJPGFshUVnk1wE7FDLpkthirB8UQVjXPI_HvW64WDAe-bgFtqjlWWa2K-UCdTqWPk174Gbg8c4jqt2YetWaN0dtVQaKxDXSOVkRrUbzq9_mMFu-uQYi1GJwkNndCUzZjiOcZ0DlOfXyN4tfy5NVX25q8Uab7zdHf-2-dd2DY2p9UuBskerKnJPmzmZz9legCtF_SXTUzQeligqBdjq2B7yJ9aOmqI_bK6OTePKdy02qNXvMnexofw3O083d7ZhlfBljjhMjtxiJIOF5RTptCZ9oTSwGWoTU9IIlxCJR36irOEKNRjjCYdS1BYMnA8NWSxfwS1yXSijsFyYnQ5uETRB4LEAROxm3DlqzDkwzDmogFuKdJIGtBxzX0xiiq4ZK2GCNUQ5WqIlg24_P5nVkBurPy6Wco-MtMvjSrBN-Cq1F71-u_WTla3dgpbmm5e1yK6tAm1bL5QZ7AhP7P3dH5uBt8Xi5DgCA priority: 102 providerName: ProQuest |
| Title | Variational Quantum Computation Integer Factorization Algorithm |
| URI | https://link.springer.com/article/10.1007/s10773-023-05473-y https://www.proquest.com/docview/3254660410 |
| Volume | 62 |
| WOSCitedRecordID | wos001101059200001&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: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1572-9575 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009048 issn: 1572-9575 databaseCode: P5Z dateStart: 20230101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1572-9575 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009048 issn: 1572-9575 databaseCode: BENPR dateStart: 20230101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1572-9575 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009048 issn: 1572-9575 databaseCode: M2P dateStart: 20230101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLink customDbUrl: eissn: 1572-9575 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009048 issn: 1572-9575 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/eLvHCXMwnV3dS8MwED_cpuCL3-J0jj74poV-JE3zJFM2fNBRp47hS0nTVIVtytoJ---9dK1TUUFfSj-SNtxH75Lc_Q7gKGKeJK5QpqLCMQkaEdPnkpkiUTHKE1U0yiHzL1m36w8GPCiSwtIy2r3cksz_1B-S3RjTe4463ozg2awCNTR3vlbH3k1_AbWLQlmkx3zf77MJWviVX7ZCcwvTWf_f2DZgrfAojdZcBDZhSY23YCWP7JTpNpz2cTZcrPgZ11Mk5HRkzGs55HcNvSaIXzI6eeWdIi3TaA0f8CJ7HO3AXad9e35hFlUTTInqlJmxRZS0uKCcMoVTZUcoDUuGvHKEJMImVNLEVZzFRCGXInTYWIzDl57lqIRF7i5Ux89jtQeGFeGEgkubE0-QyGMismOuXOX7PPEjLupgl4QMZQEpritbDMMFGLImTIiECXPChLM6HL_3eZkDavzaulHyJyyUKw1djeHvWcS26nBS8mPx-Oe37f-t-QGs6uLyOvPQpg2oZpOpOoRl-Zo9pZMm1M7a3aDXhMqVE-AxoPfNXBDfAG9x11w |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3JTsMwEB2VAoILO6JQIAc4QUQWJ44PqKqAiqqLigSIW3AcFyp1owuoP8U3Ms5CBBLcOHDLasV-L-MZexaAo4C6gthc6tLhlk5wEtE9JqjO2zJEPjnSCaKU-XXabHoPD6yVg_c0Fka5VaYyMRLU4UCoNfIzWyVudw1iGqXhi66qRqnd1bSERkyLmpy9ock2Pq9eIr7HllW5ur241pOqArpAuk300CBSGIw7zKESTUmLS5W2C_ticUG4SRzhtG3JaEgk9iJAhYaGBqXCNSzZpoGN7c7BPEFLSP1XDauVJfk1SCz50SRDtcpLgnSSUD1K1Y6p8pYjeDT7OhFm2u23Ddlonqus_rcRWoOVRKPWyvEvsA452d-AxcizVYw3oXTPR51kxVO7mSKRpj0trmURXdXUmiiOg1aJKg8lYalaufuEJ5Pn3hbc_cnXb0O-P-jLHdCMAA0qJkxGXE4Cl_LADJm0peexthcwXgAzhdAXSUp1Vdmj62fJoBXsPsLuR7D7swKcfL4zjBOK_Pp0McXaT4TL2M-ALsBpypbs9s-t7f7e2iEsXd826n692qztwbKlyKocHp0i5CejqdyHBfE66YxHBxHtNXj8axZ9AGa3PO8 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDLZgPMSFN2IwoAduUNFH2jQnNAEViGkaAqbdqjRNAWkr09Yh7d_j9EEHAiTErY-kjWxHtmP7M8BxSF1BbC516XBLJ6hEdI8JqvNYRihPjnTCDDK_Rdttr9djnZkq_izbvQxJ5jUNCqUpSc-GUXw2U_hGqYo_qtwzglfTeVggqmmQ8tfvuxXsLgpoUSrz_bzP6qiyMb-ERTNt46_9f53rsFpYmlozF40NmJPJJixlGZ9ivAXnXfSSi5NA7W6CBJ4MtLzHQ_ZUU2eF-FfNzzryFOWaWrP_hDfp82AbHv2rh4trveimoAvcZqkeGUQKg3GHOVSiC21xqeDKkIcWF4SbxBFObEtGIyKReyEacjTC5QvXsGRMQ3sHaslrIndBM0J0NJgwGXE5CV3KQzNi0paex2IvZLwOZknUQBRQ46rjRT-oQJIVYQIkTJARJpjW4eRjzjAH2vh1dKPkVVBsunFgK2x_10A5qMNpyZvq9c9f2_vb8CNY7lz6QeumfbsPK6r_vCpONJ0G1NLRRB7AonhLX8ajw0wW3wH3kd-a |
| 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=Variational+Quantum+Computation+Integer+Factorization+Algorithm&rft.jtitle=International+journal+of+theoretical+physics&rft.au=Zhang%2C+Xinglan&rft.au=Zhang%2C+Feng&rft.date=2023-11-15&rft.issn=1572-9575&rft.eissn=1572-9575&rft.volume=62&rft.issue=11&rft_id=info:doi/10.1007%2Fs10773-023-05473-y&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10773_023_05473_y |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1572-9575&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1572-9575&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1572-9575&client=summon |