Relevant bibliographies by topics / Shor Algorithm

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Shor Algorithm'

Author: Grafiati
Published: 28 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Shor Algorithm"

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Monz, T., D. Nigg, E. A. Martinez, M. F. Brandl, P. Schindler, R. Rines, S. X. Wang, I. L. Chuang, and R. Blatt. "Realization of a scalable Shor algorithm." Science 351, no. 6277 (March 3, 2016): 1068–70. http://dx.doi.org/10.1126/science.aad9480.

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Cherckesova, Larissa, Olga Safaryan, Pavel Razumov, Irina Pilipenko, Yuriy Ivanov, and Ivan Smirnov. "Speed improvement of the quantum factorization algorithm of P. Shor by upgrade its classical part." E3S Web of Conferences 224 (2020): 01016. http://dx.doi.org/10.1051/e3sconf/202022401016.

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This report discusses Shor’s quantum factorization algorithm and ρ–Pollard’s factorization algorithm. Shor’s quantum factorization algorithm consists of classical and quantum parts. In the classical part, it is proposed to use Euclidean algorithm, to find the greatest common divisor (GCD), but now exist large number of modern algorithms for finding GCD. Results of calculations of 8 algorithms were considered, among which algorithm with lowest execution rate of task was identified, which allowed the quantum algorithm as whole to work faster, which in turn provides greater potential for practical application of Shor’s quantum algorithm. Standard quantum Shor’s algorithm was upgraded by replacing the binary algorithm with iterative shift algorithm, canceling random number generation operation, using additive chain algorithm for raising to power. Both Shor’s algorithms (standard and upgraded) are distinguished by their high performance, which proves much faster and insignificant increase in time in implementation of data processing. In addition, it was possible to modernize Shor’s quantum algorithm in such way that its efficiency turned out to be higher than standard algorithm because classical part received an improvement, which allows an increase in speed by 12%.
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AVILA, M. A. "MINIMAL EXECUTION TIME OF SHOR'S ALGORITHM AT LOW TEMPERATURES." International Journal of Quantum Information 07, no. 01 (February 2009): 287–96. http://dx.doi.org/10.1142/s0219749909004475.

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The minimal time, T Shor , in which a one-way quantum computer can execute Shor's algorithm is derived. In the absence of an external magnetic field, this quantity diverges at very small temperatures. This result coincides with that of Anders et al. obtained simultaneously to ours but using thermodynamical arguments. Such divergence contradicts the common belief that it is possible to do quantum computation at low temperatures. It is shown that in the presence of a weak external magnetic field, T Shor becomes a quantized quantity which vanishes at zero temperature. Decoherence is not a problem because T Shor /τ dec < 10-9, where τdec is decoherence time.
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Lerner, E. Yu. "Prime witnesses in the Shor algorithm and the Miller-Rabin algorithm." Russian Mathematics 52, no. 12 (December 2008): 36–40. http://dx.doi.org/10.3103/s1066369x08120062.

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Hlukhov, V. "CAPACITIVE COMPLEXITY OF DETERMINING GCD IN THE SHOR S ALGORITHM." ELECTRICAL AND COMPUTER SYSTEMS 33, no. 108 (November 30, 2020): 26–32. http://dx.doi.org/10.15276/eltecs.32.108.2020.3.

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The article analyzes the results of finding the period r of the function y = axmodM (a is a random number) which is used in the Shor's factorization algorithm for quantum computers. The module M is the product of two primes p and q. The article analyzes the solutions r obtained for various a, for which the capacitive complexity H of finding the greatest common divisor GCD(ar/2 + 1, M) is the least. A digital quantum computer is a classic processor and its digital quantum coprocessor. A digital quantum coprocessor with hundreds and thousands of digital qubits can be implemented in one programmable logic integrated circuit FPGA. In the Shor’s algorithm, the factorization problem of the number M reduces to the problem of determining the period r of the function y. It is known that GCD(ar/2 + 1, M) can be a divisor of the number M The task of the quantum coprocessor in implementing the Shor’s algorithm is to find the period r. After that it is necessary to find the GCD. Since for random a the problem of finding the period r has many solutions, these solutions can be compared by the value of one of the arguments when finding the GCD - the number ar / 2 . In this case, H = (rlog2a)/2 is taken for analysis. It approximately represents the bit depth of binary codes that a classic computer will have to process when determining the GCD. H can vary over a wide range from tens to thousands of bits even for small values of M. In this research the period r, which ensures the least complexity of the subsequent task of finding the GCD, is most often a solution for a = 3 and a = 2, but it can also occur often with other values of a. To clarify the revealed patterns, especially for large M, it is necessary to conduct additional research.
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Ekerå, Martin. "On post-processing in the quantum algorithm for computing short discrete logarithms." Designs, Codes and Cryptography 88, no. 11 (August 6, 2020): 2313–35. http://dx.doi.org/10.1007/s10623-020-00783-2.

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Abstract We revisit the quantum algorithm for computing short discrete logarithms that was recently introduced by Ekerå and Håstad. By carefully analyzing the probability distribution induced by the algorithm, we show its success probability to be higher than previously reported. Inspired by our improved understanding of the distribution, we propose an improved post-processing algorithm that is considerably more efficient, enables better tradeoffs to be achieved, and requires fewer runs, than the original post-processing algorithm. To prove these claims, we construct a classical simulator for the quantum algorithm by sampling the probability distribution it induces for given logarithms. This simulator is in itself a key contribution. We use it to demonstrate that Ekerå–Håstad achieves an advantage over Shor, not only in each individual run, but also overall, when targeting cryptographically relevant instances of RSA and Diffie–Hellman with short exponents.
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Kiseliova, O. M., O. M. Prytomanova, and V. H. Padalko. "APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS." EurasianUnionScientists 6, no. 2(71) (2020): 30–35. http://dx.doi.org/10.31618/esu.2413-9335.2020.6.71.615.

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An algorithm for constructing a multiplicatively weighted Voronoi diagram involving fuzzy parameters with the optimal location of a finite number of generator points in a limited set of n-dimensional Euclidean space 𝐸𝑛 has been suggested in the paper. The algorithm has been developed based on the synthesis of methods of solving the problems of optimal set partitioning theory involving neurofuzzy technologies modifications of N.Z. Shor 𝑟 -algorithm for solving nonsmooth optimization problems.
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Plesa, Mihail-Iulian, and Togan Mihai. "A New Quantum Encryption Scheme." Advanced Journal of Graduate Research 4, no. 1 (June 22, 2018): 59–67. http://dx.doi.org/10.21467/ajgr.4.1.59-67.

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The model of quantum computation has advanced very quickly in the last years. This model brings with it an efficient algorithm for factoring, namely the Shor algorithm. This means that the public key infrastructure will soon be obsolete. In this paper we propose a new quantum cryptographic scheme which aims to replace the RSA algorithm from current public key infrastructures. We analyze the security of our scheme and also, we describe the implementation of the scheme using IBM Q SDK, qiskit. We run a number of experiments in order to build a proof of concept application that uses the proposed scheme.
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Ghisi, F., and S. V. Ulyanov. "The information role of entanglement and interference operators in Shor quantum algorithm gate dynamics." Journal of Modern Optics 47, no. 12 (October 2000): 2079–90. http://dx.doi.org/10.1080/09500340008235130.

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Ulyanov, F. Ghisi, S. V. "The information role of entanglement and interference operators in Shor quantum algorithm gate dynamics." Journal of Modern Optics 47, no. 12 (October 15, 2000): 2079–90. http://dx.doi.org/10.1080/095003400419933.

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Dissertations / Theses on the topic "Shor Algorithm"

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MARTINS, ROBERTO CINTRA. "SHOR S FACTORING ALGORITHM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=35511@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
A dissertação apresenta detalhadamente o algoritmo de fatoração de Shor, tanto em termos de sua execução passo a passo como mediante sua representação em forma de circuito, abordando aspectos tanto de sua parte clássica como de sua parte quântica. Inicialmente são apresentados aspectos de teoria dos números indispensáveis para a compreensão do algoritmo e em seguida são desenvolvidos conceitos e propriedades de mecânica quântica e de informação quântica pertinentes. Em atenção ao caráter eminentemente estocástico do algoritmo realiza-se um estudo de sua fonte estocástica e demonstram-se os principais teoremas que embasam a avaliação de sua probabilidade de sucesso. Desenvolvem-se exemplos de simulação clássica do algoritmo. Finalmente, a eficiência do algoritmo de fatoração de Shor é comparada com a de algoritmos clássicos.
The dissertation presents in detail Shor s factoring algorithm, including its execution step by step and its representation in the form of a circuit, addressing aspects of both its classical and its quantum parts. Aspects of number theory indispensable to understand the algorithm are presented, followed by a development of concepts and properties of quantum mechanics and quantum information. Considering the eminently stochastic character of the algorithm, a study of its stochastic source is carried out and the main theorems that support the evaluation of its probability of success are proved. Examples of classical simulation of the algorithm are developed. Finally, the efficiency of Shor s factoring algorithm is compared with that of classical algorithms.
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Nwaokocha, Martyns. "Shorův algoritmus v kvantové kryptografii." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445457.

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Kryptografie je velmi důležitým aspektem našeho každodenního života, protože poskytuje teoretický základ informační bezpečnosti. Kvantové výpočty a informace se také stávají velmi důležitou oblastí vědy kvůli mnoha aplikačním oblastem včetně kryptologie a konkrétněji v kryptografii veřejných klíčů. Obtížnost čísel do hlavních faktorů je základem některých důležitých veřejných kryptosystémů, jejichž klíčem je kryptosystém RSA . Shorův kvantový faktoringový al-goritmus využívá zejména kvantový interferenční účinek kvantového výpočtu k faktorovým semi-prime číslům v polynomiálním čase na kvantovém počítači. Ačkoli kapacita současných kvantových počítačů vykonávat Shorův algoritmus je velmi omezená, existuje mnoho rozsáhlých základních vědeckých výzkumů o různých technikách optimalizace algoritmu, pokud jde o faktory, jako je počet qubitů, hloubka obvodu a počet bran. v této práci jsou diskutovány, analyzovány a porovnávány různé varianty Shorova factoringového algoritmu a kvantových obvodů. Některé varianty Shorova algoritmu jsou také simulované a skutečně prováděné na simulátorech a kvantových počítačích na platformě IBM QuantumExperience. Výsledky simulace jsou porovnávány z hlediska jejich složitosti a míry úspěšnosti. Organizace práce je následující: Kapitola 1 pojednává o některých klíčových historických výsledcích kvantové kryptografie, uvádí problém diskutovaný v této práci a představuje cíle, kterých má být dosaženo. Kapitola 2 shrnuje matematické základy kvantového výpočtu a kryptografie veřejných klíčů a popisuje notaci použitou v celé práci. To také vysvětluje, jak lze k rozbití kryptosystému RSA použít realizovatelný algoritmus pro vyhledávání objednávek nebo factoring. Kapitola 3 představuje stavební kameny Shorova algoritmu, včetně kvantové Fourierovy transformace, kvantového odhadu fází, modulární exponentiace a Shorova algoritmu. Zde jsou také uvedeny a porovnány různé varianty optimalizace kvantových obvodů. Kapitola 4 představuje výsledky simulací různých verzí Shorova algoritmu. V kapitole 5 pojednejte o dosažení cílů disertační práce, shrňte výsledky výzkumu a nastíňte budoucí směry výzkumu.
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Nyman, Peter. "Representation of Quantum Algorithms with Symbolic Language and Simulation on Classical Computer." Licentiate thesis, Växjö University, School of Mathematics and Systems Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2329.

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Utvecklandet av kvantdatorn är ett ytterst lovande projekt som kombinerar teoretisk och experimental kvantfysik, matematik, teori om kvantinformation och datalogi. Under första steget i utvecklandet av kvantdatorn låg huvudintresset på att skapa några algoritmer med framtida tillämpningar, klargöra grundläggande frågor och utveckla en experimentell teknologi för en leksakskvantdator som verkar på några kvantbitar. Då dominerade förväntningarna om snabba framsteg bland kvantforskare. Men det verkar som om dessa stora förväntningar inte har besannats helt. Många grundläggande och tekniska problem som dekoherens hos kvantbitarna och instabilitet i kvantstrukturen skapar redan vid ett litet antal register tvivel om en snabb utveckling av kvantdatorer som verkligen fungerar. Trots detta kan man inte förneka att stora framsteg gjorts inom kvantteknologin. Det råder givetvis ett stort gap mellan skapandet av en leksakskvantdator med 10-15 kvantregister och att t.ex. tillgodose de tekniska förutsättningarna för det projekt på 100 kvantregister som aviserades för några år sen i USA. Det är också uppenbart att svårigheterna ökar ickelinjärt med ökningen av antalet register. Därför är simulering av kvantdatorer i klassiska datorer en viktig del av kvantdatorprojektet. Självklart kan man inte förvänta sig att en kvantalgoritm skall lösa ett NP-problem i polynomisk tid i en klassisk dator. Detta är heller inte syftet med klassisk simulering. Den klassiska simuleringen av kvantdatorer kommer att täcka en del av gapet mellan den teoretiskt matematiska formuleringen av kvantmekaniken och ett förverkligande av en kvantdator. Ett av de viktigaste problemen i vetenskapen om kvantdatorn är att utveckla ett nytt symboliskt språk för kvantdatorerna och att anpassa redan existerande symboliska språk för klassiska datorer till kvantalgoritmer. Denna avhandling ägnas åt en anpassning av det symboliska språket Mathematica till kända kvantalgoritmer och motsvarande simulering i klassiska datorer. Konkret kommer vi att representera Simons algoritm, Deutsch-Joszas algoritm, Grovers algoritm, Shors algoritm och kvantfelrättande koder i det symboliska språket Mathematica. Vi använder samma stomme i alla dessa algoritmer. Denna stomme representerar de karaktäristiska egenskaperna i det symboliska språkets framställning av kvantdatorn och det är enkelt att inkludera denna stomme i framtida algoritmer.


Quantum computing is an extremely promising project combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. At the first stage of development of quantum computing the main attention was paid to creating a few algorithms which might have applications in the future, clarifying fundamental questions and developing experimental technologies for toy quantum computers operating with a few quantum bits. At that time expectations of quick progress in the quantum computing project dominated in the quantum community. However, it seems that such high expectations were not totally justified. Numerous fundamental and technological problems such as the decoherence of quantum bits and the instability of quantum structures even with a small number of registers led to doubts about a quick development of really working quantum computers. Although it can not be denied that great progress had been made in quantum technologies, it is clear that there is still a huge gap between the creation of toy quantum computers with 10-15 quantum registers and, e.g., satisfying the technical conditions of the project of 100 quantum registers announced a few years ago in the USA. It is also evident that difficulties increase nonlinearly with an increasing number of registers. Therefore the simulation of quantum computations on classical computers became an important part of the quantum computing project. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in "quantum computer science" is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present thesis is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon's algorithm, the Deutsch-Josza algorithm, Grover's algorithm, Shor's algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.

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Drobouchevitch, Inna G. "Design and analysis of algorithms for short-route shop scheduling problems." Thesis, University of Greenwich, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285392.

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Blum, Christian. "Metaheuristics for Group Shop Scheduling." Doctoral thesis, Universite Libre de Bruxelles, 2002. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211345.

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Ta, Quang-Chieu. "Matheuristic algorithms for minimizing total tardiness in flow shop scheduling problems." Thesis, Tours, 2015. http://www.theses.fr/2015TOUR4002/document.

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Nous considérons dans cette thèse un problème d’ordonnancement de flow-shop de permutation où un ensemble de travaux doit être ordonnancé sur un ensemble de machines. Les travaux doivent être ordonnancés sur les machines dans le même ordre. L’objectif est de minimiser le retard total. Nous proposons des algorithmes heuristiques et des nouvelles matheuristiques pour ce problème. Les matheuristiques sont un nouveau type d’algorithmes approchés qui ont été proposés pour résoudre des problèmes d’optimisation combinatoire. Les méthodes importent de la résolution exacte au sein des approches (méta) heuristiques. Ce type de méthode de résolution a reçu un grand intérêt en raison de leurs très bonnes performances pour résoudre des problèmes difficiles. Nous présentons d’abord les concepts de base d’un problème d’ordonnancement. Nous donnons aussi une brève introduction à la théorie de l’ordonnancement et nous présentons un panel de méthodes de résolution. Enfin, nous considérons un problème où un flow shop de permutation à m-machine et un problème de tournées de véhicules sont intégrés, avec pour objectif la minimisation de la somme des retards. Nous proposons un codage direct d’une solution et une méthode de voisinage. Les résultats montrent que l’algorithme Tabou améliore grandement la solution initiale donnée par EDD et où chaque voyage ne délivre qu’un travail
We consider in this thesis a permutation flow shop scheduling problem where a set of jobs have to be scheduled on a set of machines. The jobs have to be processed on the machines in the same order. The objective is to minimize the total tardiness. We propose heuristic algorithms and many new matheuristic algorithms for this problem. The matheuristic methods are a new type of approximated algorithms that have been proposed for solving combinatorial optimization problems. These methods embed exact resolution into (meta)heuristic approaches. This type of resolution method has received a great interest because of their very good performances for solving some difficult problems. We present the basic concepts and components of a scheduling problem and the aspects related to these components. We also give a brief introduction to the theory of scheduling and present an overview of resolution methods. Finally, we consider a problem where m-machine permutation flow shop scheduling problem and a vehicle routing problem are integrated and the objective is to minimize the total tardiness. We introduce a direct coding for a complete solution and a Tabu search for finding a sequence and trips. The results show that the TS greatly improves the initial solution given by EDD heuristic where each trip serves only one job at a time
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Bandini, Michele. "Crittografia quantistica e algoritmo di Shor." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17073/.

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In questo elaborato si cerca di dare un'idea di come funzioni un computer quantistico, portando come esempio l'Algoritmo di Shor per la fattorizzazione: si cerca di chiarirne la matematica e la fisica che vi stanno dietro e l'importanza applicativa e storica che ha avuto. Brevi cenni sull'odierna tecnologia dei calcolatori quantistici.
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Kugel, Felix. "Das Shor-Verfahren als stochastischer Algorithmus." [S.l.] : [s.n.], 2006. http://137.193.200.177/ediss/kugel-felix/meta.html.

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Weyer, Anne. "The Brute Force Algorithm." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1555605680617133.

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Larabi, Mohand. "Le problème de job-shop avec transport : modélisation et optimisation." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2010. http://tel.archives-ouvertes.fr/tel-00625528.

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Dans cette thèse nous nous sommes intéressés à l'extension du problème job-shop en ajoutant la contrainte du transport des jobs entre les différentes machines. Dans cette étude nous avons retenu l'existence de deux types de robots, les robots de capacité de chargement unitaire (capacité=1 veut dire qu'un robot ne peut transporter qu'un seul job à la fois) et les robots de capacité de chargement non unitaire (capacité>1 veut dire qu'un robot peut transporter plusieurs job à la fois). Nous avons traité cette extension en deux étapes. Ainsi, la première étape est consacrée au problème du job-shop avec plusieurs robots de capacité de chargement unitaire et en seconde étape en ajoutant la capacité de chargement non unitaire aux robots. Pour les deux problèmes étudiés nous avons proposé :* Une modélisation linéaire ;* Une modélisation sous forme de graphe disjonctif ;* Plusieurs heuristiques de construction de solutions ;* Plusieurs recherches locales qui améliorent les solutions obtenues ;* Utilisation des algorithmes génétiques / mémétiques comme schéma global d'optimisation ;* De nouveaux benchmarks, des résultats de test de nos approches sur nos benchmarks et ceux de la littérature et ces résultats sont commentés et comparés à ceux de la littérature. Les résultats obtenus montrent la pertinence de notre modélisation ainsi que sa qualité.
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Books on the topic "Shor Algorithm"

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Song, Yingsheng. Genetic algorithms for job shop scheduling. [S.l: The Author], 2002.

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Asquith, Paul. Short sales and trade classification algorithms. Cambridge, MA: National Bureau of Economic Research, 2008.

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George, Vairaktarakis, ed. Flow shop scheduling: Theoretical results, algorithms, and applications. New York: Springer Verlag, 2013.

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Dapporto, Paolo, Paola Paoli, Patrizia Rossi, and Annalisa Guerri. The UTN program. Florence: Firenze University Press, 2001. http://dx.doi.org/10.36253/88-8453-032-6.

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We give an algorithm which goal is to find the energy barrier between a given pair of points in a graph which represents the conformational space of a molecule. If the conformational space is homeomorphic to an -dimensional torus, then the graph can be chosen of a particular form. The UTN software, which implements the algorithm in this case, is described in detail. Finally we focus on applications: to show how UTN works, some examples are carried on in detail, with the additional support of graphical animation1 in the twodimensional case. The source code of the program and some data of the examples are available to the reader.
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Burstein, Joseph. Exact numerical solutions of nonlinear differential equations, short algorithms: After three centuries of approximate methods. Boston: Metrics Press, 2002.

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Jin tian bu xue ji qi xue xi, ming tian jiu bei ji qi qu dai: Cong Python ru shou + yan suan fa. Taibei Shi: Jia kui zi xun fa xing, 2017.

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1974-, Zomorodian Afra J., ed. Advances in applied and computational topology: American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana. Providence, R.I: American Mathematical Society, 2012.

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Daji, Qiao, and SpringerLink (Online service), eds. Quality, Reliability, Security and Robustness in Heterogeneous Networks: 7th International Conference on Heterogeneous Networking for Quality, Reliability, Security and Robustness, QShine 2010, and Dedicated Short Range Communications Workshop, DSRC 2010, Houston, TX, USA, November 17-19, 2010, Revised Selected Papers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Tschinkel, Yuri, Carlo Gasbarri, Steven Lu, and Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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Levitin, Anany, and Maria Levitin. Algorithmic Puzzles. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780199740444.001.0001.

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While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.
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Book chapters on the topic "Shor Algorithm"

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LaPierre, Ray. "Shor Algorithm." In The Materials Research Society Series, 177–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69318-3_13.

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Raj, Gaurav, Dheerendra Singh, and Abhishek Madaan. "Analysis of Classical and Quantum Computing Based on Grover and Shor Algorithm." In Smart Computing and Informatics, 413–23. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5547-8_43.

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Brucker, Peter. "Shop Scheduling Problems." In Scheduling Algorithms, 145–228. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03612-9_6.

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Brucker, Peter. "Shop Scheduling Problems." In Scheduling Algorithms, 143–224. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-662-03088-2_6.

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Brucker, Peter. "Shop Scheduling Problems." In Scheduling Algorithms, 155–239. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04550-3_6.

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Brucker, Peter. "Shop Scheduling Problems." In Scheduling Algorithms, 155–239. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24804-0_6.

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van Heerdt, Gerco, Clemens Kupke, Jurriaan Rot, and Alexandra Silva. "Learning Weighted Automata over Principal Ideal Domains." In Lecture Notes in Computer Science, 602–21. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_31.

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AbstractIn this paper, we study active learning algorithms for weighted automata over a semiring. We show that a variant of Angluin’s seminal $$\mathtt {L}^{\!\star }$$ L ⋆ algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.
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Amram, Gal, Suguman Bansal, Dror Fried, Lucas Martinelli Tabajara, Moshe Y. Vardi, and Gera Weiss. "Adapting Behaviors via Reactive Synthesis." In Computer Aided Verification, 870–93. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81685-8_41.

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AbstractIn the Adapter Design Pattern, a programmer implements a Target interface by constructing an Adapter that accesses an existing Adaptee code. In this work, we present a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an Adaptee and a Target transducers, and the aim is to synthesize an Adapter transducer that, when composed with the Adaptee, generates a behavior that is equivalent to the behavior of the Target. One use of such an algorithm is to synthesize controllers that achieve similar goals on different hardware platforms. While this problem can be solved with existing synthesis algorithms, current state-of-the-art tools fail to scale. To cope with the computational complexity of the problem, we introduce a special form of specification format, called Separated GR(k), which can be solved with a scalable synthesis algorithm but still allows for a large set of realistic specifications. We solve the realizability and the synthesis problems for Separated GR(k), and show how to exploit the separated nature of our specification to construct better algorithms, in terms of time complexity, than known algorithms for GR(k) synthesis. We then describe a tool, called SGR(k), that we have implemented based on the above approach and show, by experimental evaluation, how our tool outperforms current state-of-the-art tools on various benchmarks and test-cases.
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Mattfeld, Dirk C. "Evolutionary Algorithms." In Evolutionary Search and the Job Shop, 49–64. Heidelberg: Physica-Verlag HD, 1996. http://dx.doi.org/10.1007/978-3-662-11712-5_4.

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Bagchi, Tapan P. "Job Shop Scheduling." In Multiobjective Scheduling by Genetic Algorithms, 109–35. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5237-6_5.

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Conference papers on the topic "Shor Algorithm"

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Yimsiriwattana, Anocha, and Samuel J. Lomonaco Jr. "Distributed quantum computing: a distributed Shor algorithm." In Defense and Security, edited by Eric Donkor, Andrew R. Pirich, and Howard E. Brandt. SPIE, 2004. http://dx.doi.org/10.1117/12.546504.

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Zhang, Xin, YaQian Zhao, RenGang Li, XueLei Li, ZhenHua Guo, XiaoMin Zhu, and Gang Dong. "The Quantum Shor Algorithm Simulated on FPGA." In 2019 IEEE Intl Conf on Parallel & Distributed Processing with Applications, Big Data & Cloud Computing, Sustainable Computing & Communications, Social Computing & Networking (ISPA/BDCloud/SocialCom/SustainCom). IEEE, 2019. http://dx.doi.org/10.1109/ispa-bdcloud-sustaincom-socialcom48970.2019.00082.

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Chuang, Issac. "Experimental realization of a Shor-type quantum algorithm." In International Conference on Quantum Information. Washington, D.C.: OSA, 2001. http://dx.doi.org/10.1364/icqi.2001.fqipa3.

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Young, Rupert, Philip Birch, and Chris Chatwin. "A simplification of the Shor quantum factorization algorithm employing a quantum Hadamard transform." In Pattern Recognition and Tracking XXIX, edited by Mohammad S. Alam. SPIE, 2018. http://dx.doi.org/10.1117/12.2309468.

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CHOFFRUT, CHRISTIAN. "A SHORT INTRODUCTION TO AUTOMATIC GROUP THEORY." In Semigroups, Algorithms, Automata and Languages. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776884_0004.

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Li, Qinbin, Bingsheng He, and Dawn Song. "Practical One-Shot Federated Learning for Cross-Silo Setting." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/205.

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Federated learning enables multiple parties to collaboratively learn a model without exchanging their data. While most existing federated learning algorithms need many rounds to converge, one-shot federated learning (i.e., federated learning with a single communication round) is a promising approach to make federated learning applicable in cross-silo setting in practice. However, existing one-shot algorithms only support specific models and do not provide any privacy guarantees, which significantly limit the applications in practice. In this paper, we propose a practical one-shot federated learning algorithm named FedKT. By utilizing the knowledge transfer technique, FedKT can be applied to any classification models and can flexibly achieve differential privacy guarantees. Our experiments on various tasks show that FedKT can significantly outperform the other state-of-the-art federated learning algorithms with a single communication round.
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Scott, David, and L. A. Thomsen. "A Global Algorithm for Pore Pressure Prediction." In Middle East Oil Show. Society of Petroleum Engineers, 1993. http://dx.doi.org/10.2118/25674-ms.

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Morris, Christopher, Matthias Fey, and Nils Kriege. "The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/618.

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In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for (supervised) machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine learning setting. We discuss the theoretical background, show how to use it for supervised graph- and node classification, discuss recent extensions, and its connection to neural architectures. Moreover, we give an overview of current applications and future directions to stimulate research.
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Ambainis, Andris. "Quantum algorithms a decade after shor." In the thirty-sixth annual ACM symposium. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1007352.1007354.

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Snover, Matthew, Bonnie Dorr, and Richard Schwartz. "A lexically-driven algorithm for disfluency detection." In HLT-NAACL 2004: Short Papers. Morristown, NJ, USA: Association for Computational Linguistics, 2004. http://dx.doi.org/10.3115/1613984.1614024.

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Reports on the topic "Shor Algorithm"

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Cao, Zhengjun, Lihua Liu, and Andreas Christoforides. A Note on One Realization of a Scalable Shor Algorithm. Web of Open Science, December 2020. http://dx.doi.org/10.37686/qrl.v1i2.81.

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Very recently, Monz, et al. have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. In this note, we remark that the report is somewhat misleading because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles behind the demonstration have not been explained properly, including its correctness and complexity.
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Guliashki, Vassil, and Leoneed Kirilov. Algorithm Generating Initial Population of Schedules for Population-based Algorithms Solving Flexible Job Shop Problems. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, June 2019. http://dx.doi.org/10.7546/crabs.2019.06.01.

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Asquith, Paul, Rebecca Oman, and Christopher Safaya. Short Sales and Trade Classification Algorithms. Cambridge, MA: National Bureau of Economic Research, July 2008. http://dx.doi.org/10.3386/w14158.

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Jones, Peter W., Andrei Osipov, and Vladimir Rokhlin. A Randomized Approximate Nearest Neighbors Algorithm - A Short Version. Fort Belvoir, VA: Defense Technical Information Center, January 2011. http://dx.doi.org/10.21236/ada639824.

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Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. Office of Scientific and Technical Information (OSTI), May 1993. http://dx.doi.org/10.2172/10176421.

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Allende López, Marcos, Diego López, Sergio Cerón, Antonio Leal, Adrián Pareja, Marcelo Da Silva, Alejandro Pardo, et al. Quantum-Resistance in Blockchain Networks. Inter-American Development Bank, June 2021. http://dx.doi.org/10.18235/0003313.

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This paper describes the work carried out by the Inter-American Development Bank, the IDB Lab, LACChain, Cambridge Quantum Computing (CQC), and Tecnológico de Monterrey to identify and eliminate quantum threats in blockchain networks. The advent of quantum computing threatens internet protocols and blockchain networks because they utilize non-quantum resistant cryptographic algorithms. When quantum computers become robust enough to run Shor's algorithm on a large scale, the most used asymmetric algorithms, utilized for digital signatures and message encryption, such as RSA, (EC)DSA, and (EC)DH, will be no longer secure. Quantum computers will be able to break them within a short period of time. Similarly, Grover's algorithm concedes a quadratic advantage for mining blocks in certain consensus protocols such as proof of work. Today, there are hundreds of billions of dollars denominated in cryptocurrencies that rely on blockchain ledgers as well as the thousands of blockchain-based applications storing value in blockchain networks. Cryptocurrencies and blockchain-based applications require solutions that guarantee quantum resistance in order to preserve the integrity of data and assets in their public and immutable ledgers. We have designed and developed a layer-two solution to secure the exchange of information between blockchain nodes over the internet and introduced a second signature in transactions using post-quantum keys. Our versatile solution can be applied to any blockchain network. In our implementation, quantum entropy was provided via the IronBridge Platform from CQC and we used LACChain Besu as the blockchain network.
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Cable, S., T. Tajima, and K. Umegaki. Particle simulation algorithms with short-range forces in MHD and fluid flow. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/6970874.

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Cable, S., T. Tajima, and K. Umegaki. Particle simulation algorithms with short-range forces in MHD and fluid flow. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/10181739.

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Downard, Alicia, Stephen Semmens, and Bryant Robbins. Automated characterization of ridge-swale patterns along the Mississippi River. Engineer Research and Development Center (U.S.), April 2021. http://dx.doi.org/10.21079/11681/40439.

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The orientation of constructed levee embankments relative to alluvial swales is a useful measure for identifying regions susceptible to backward erosion piping (BEP). This research was conducted to create an automated, efficient process to classify patterns and orientations of swales within the Lower Mississippi Valley (LMV) to support levee risk assessments. Two machine learning algorithms are used to train the classification models: a convolutional neural network and a U-net. The resulting workflow can identify linear topographic features but is unable to reliably differentiate swales from other features, such as the levee structure and riverbanks. Further tuning of training data or manual identification of regions of interest could yield significantly better results. The workflow also provides an orientation to each linear feature to support subsequent analyses of position relative to levee alignments. While the individual models fall short of immediate applicability, the procedure provides a feasible, automated scheme to assist in swale classification and characterization within mature alluvial valley systems similar to LMV.
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Allen, Luke, Joon Lim, Robert Haehnel, and Ian Dettwiller. Helicopter rotor blade multiple-section optimization with performance. Engineer Research and Development Center (U.S.), June 2021. http://dx.doi.org/10.21079/11681/41031.

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This paper presents advancements in a surrogate-based, rotor blade design optimization framework for improved helicopter performance. The framework builds on previous successes by allowing multiple airfoil sections to designed simultaneously to minimize required rotor power in multiple flight conditions. Rotor power in hover and forward flight, at advance ratio 𝜇 = 0.3, are used as objective functions in a multi-objective genetic algorithm. The framework is constructed using Galaxy Simulation Builder with optimization provided through integration with Dakota. Three independent airfoil sections are morphed using ParFoil and aerodynamic coefficients for the updated airfoil shapes (i.e., lift, drag, moment) are calculated using linear interpolation from a database generated using C81Gen/ARC2D. Final rotor performance is then calculated using RCAS. Several demonstrative optimization case studies were conducted using the UH-60A main rotor. The degrees of freedom for this case are limited to the airfoil camber, camber crest position, thickness, and thickness crest position for each of the sections. The results of the three-segment case study show improvements in rotor power of 4.3% and 0.8% in forward flight and hover, respectively. This configuration also yields greater reductions in rotor power for high advance ratios, e.g., 6.0% reduction at 𝜇 = 0.35, and 8.8% reduction at 𝜇 = 0.4.
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