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In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.

We introduce a quantum Lernmatrix based on the Monte Carlo Lernmatrix in which n units are stored in the quantum superposition of log2(n) units representing On2log(n)2 binary sparse coded patterns. During the retrieval phase, quantum counting of ones based on Euler’s formula is used for the pattern recovery as proposed by Trugenberger. We demonstrate the quantum Lernmatrix by experiments using qiskit. We indicate why the assumption proposed by Trugenberger, the lower the parameter temperature t; the better the identification of the correct answers; is not correct. Instead, we introduce a tree-like structure that increases the measured value of correct answers. We show that the cost of loading L sparse patterns into quantum states of a quantum Lernmatrix are much lower than storing individually the patterns in superposition. During the active phase, the quantum Lernmatrices are queried and the results are estimated efficiently. The required time is much lower compared with the conventional approach or the of Grover’s algorithm.

Quantum computing is aninterdisciplinary field that lies at the intersection of mathematics, quantum physics, and computer science, and finds applications in areas including optimization, machine learning, and simulation of chemical, physical, and biological systems. It has the potential to help solve problems that so far have no satisfying method solving them, and to provide significant speedup to solutions when compared with their best classical approaches. In turn, quantum computing may allow us to solve problems for inputs that so far are deemed practically intractable. With the computational power of quantum computers and the proliferation of quantum development kits, quantum computing is anticipated to become mainstream, and the demand for a skilled workforce in quantum computing is expected to increase significantly. Therefore, quantum computing education is ramping up. This article describes our experiences in designing and delivering quantum computing workshops for youth (Grades 9–12). We introduce students to the world of quantum computing in innovative ways, such as newly designed unplugged activities for teaching basic quantum computing concepts. We also take a programmatic approach and introduce students to the IBM Quantum Experience using Qiskit and Jupyter notebooks. Our contributions are as follows. First, we present creative ways to teach quantum computing to youth with little or no experience in science, technology, engineering, and mathematics areas; second, we discuss diversity and highlight various pathways into quantum computing from quantum software to quantum hardware; and third, we discuss the design and delivery of online and in-person motivational, introductory, and advanced workshops for youth.

This paper proposes a quantum computing approach for insurance capital modelling. Using an open-source software development kit, Qiskit, an algorithm for working on a superconducting type IBM quantum computer is developed and implemented to predict the capital of insurance companies in the classical surplus process. With the fundamental properties of quantum mechanics, Dirac notation and Feynman’s path calculation are shown. Furthermore, custom quantum insurance premium and claim gates are investigated in order to build a quantum circuit with respect to initial reserve, premium and claim amounts. Some numerical results are presented and discussed at the end of the paper.

Precise measurements of parameters in the PMNS framework might lead to new physics beyond the Standard Model. However, they are incredibly challenging to determine in neutrino oscillation experiments. Quantum simulations can be a powerful supplementary tool to study these phenomenologies. In today's noisy quantum hardware, encoding neutrinos in a multi-qubit system requires a redundant basis and tricky entangling gates. We encode a three-flavor neutrino in a superconducting qutrit and study its oscillations using PMNS theory with time evolution expressed in terms of single qutrit gates. The qutrit is engineered from the multi-level structure of IBM transmon devices. High-fidelity gate control and readout are fine-tuned using programming microwave pulses using a high-level language. Our quantum simulations on real hardware match well to analytical calculations in three oscillation cases: vacuum, interaction with matter, and CP-violation.

RESUMEN: Con el presente trabajo se buscan explorar los fundamentos de la computación cuántica, a la par que se muestre el camino que ha tomado esta ciencia incipiente en los últimos años. Además, se expondrá su utilidad mediante la implementación de un algoritmo cuántico al proceso de reconstrucción de trazas, definidas a partir de los hits en un detector de partículas. Al finalizar el texto, uno será capaz de comprobar que, más allá de ser una curiosidad teórica, la computación cuántica se alza como una nueva forma de afrontar problemas físicos y que algunas de sus ventajas pueden disfrutarse en la actualidad. ABSTRACT: With this work we aim to explore the basics of quantum computing, while showing the path this new technology is taking in the last few years. Furthermore, its utility will be showed by applying a quantum algorithm to the track reconstruction process in a particle detector. At the end of this work, one will be able to prove that, being more than just a simple theoretical curiosity, quantum computing has became a new framework for solving physics problems and that some of its advantages can be used in the present day. Grado en Física

From Pharmacology to Cryptography and from Geology to Astronomy are some of the scientific fields in which Quantum Computing potentially will take off and fly high. Big Quantum Computing vendors invest a large amount of money in improving the hardware and they claim that soon enough a quantum program will be hundreds of thousands of times faster than a typical one we know nowadays. But still the reliability of such systems is the main obstacle. In this work, the reliability of real quantum devices is tested and techniques of noise and error correction are presented while measurement error mitigation is explored. In addition, a well-known string matching algorithm (Bernstein-Vazirani) was applied to the real quantum computing device in order to measure its accuracy and reliability. Simulated environments were also used in order to evaluate the results. The results obtained, even if these were not 100% accurate, are very promising which proves that even these days a quantum computer working side by side with a typical one is reliable and especially when error mitigation techniques are applied.

We indicate the quantum tree search qiskit implementation by popular examples from symbolical artificial intelligence, the 3-puzzle, 8-puzzle and the ABC blocks world. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits and algorithms from IBM. The objects are represented by symbols and adjectives. Two principles are presented. Either the position description (adjective) is fixed and the class descriptors moves (is changed) or, in the reverse interpretation, the class descriptor is fixed and the position descriptor (adjective) moves (is changed). We indicate how to decompose the permutation operator that executes the rules by the two principles. We demonstrate that the the branching factor is reduced by Grover’s amplification to the square root of the average branching factor and not to the maximal branching factor as previously assumed.

Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover’s search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high probability for several cases and are illustrated for the cases involving two variables for both 3- and 4-bit numbers. Methods are defined for inequality comparisons, and these are combined according to the form of the satisfiability formula, to form the oracle for the algorithm. The circuit is constructed using IBM Qiskit and is verified on an IBM simulator. It is further executed on one of the noisy intermediate-scale quantum processors from IBM on the cloud. Noise levels in the processor at present are found to be too high for successful execution. Running the algorithm on the simulator with a custom noise model lets us identify the noise threshold for successful execution.

This work aims at testing a new quantum computing algorithm to reconstruct vertices in the con- text of High Energy Physics. In order to do this, a complete simulation suite of tracks and vertexing has been implemented. A tracker and the tracks have been generated, with a realistic parametriza- tion that allows for their manipulation and latter analysis. Afterwards, and making use of IBM framework, qiskit, the VQE (Variational Quantum Eigensolver) algorithm has been implemented in python. It has finally been tested and a metric of its efficiency depending on the distance between vertices and the number of evaluation shots has been made. The algorithm shows a great reliability in the reconstruction of vertices, when separated enough. It requires a decent amount of evaluation shots, this value being a minimum of around 500, where, for a reasonable distance, the efficiency gets to about 85%. For an even more reliable result, which might be interesting, especially for the shorter separations, the number of shots may be raised up to 1000. Tested with 1000 evaluations per step, and with distances between 0.0 and 0.1 cm, the algorithm returns an efficiency of almost 90% with distances from 0.3 cm. It was expected to achieve an even higher efficiency, especially for the larger separations, however, there seems to be a saturation issue that makes it so that the efficiency does not get to values close to 100%. This might be solved by increasing the number of evaluation shots in the future. In any case, this work shows the proof of concept that a quantum computing algorithm can be used to solve the problem of the vertex reconstruction opening a very interesting field where surely many parameters can be optimized to get better results. El objetivo de este trabajo es probar la viabilidad de diseñar un nuevo algoritmo de computación cuántica y utilizarlo para la reconstrucción de vértices en Física de Altas Energías. Para hacer esto, se ha realizado una simulación completa de un sistema formado por un tracker y unas trazas generadas y medidas en su interior. La parametrización de estos es realista, lo cual permite manipularlo y analizarlo con la posibilidad de extrapolarlo a casos reales. Más tarde se ha aplicado el algoritmo VQE (Variational Quantum Eigensolver) en el lenguaje python. Se ha comprobado su eficiencia en función de la separación de los vértices y el número de evaluaciones del algoritmo. El algoritmo devuelve unos resultados muy positivos en la reconstrucción de vértices para separaciones razonables. Requiere un número considerable de evaluaciones para obtener eficiencias suficientemente altas (superiores al 85%). Siendo este valor de alrededor de 500 “shots”. Para obtener eficiencias mayores, el número de evaluaciones puede subirse. Para 1000 evaluaciones por iteración, se obtienen eficiencias de casi el 90% de acierto para distancias entre vértices de 0.3 cm, e incluso mejores para una separación mayor. Sin embargo, parece haber un problema de saturación del algoritmo para distancias mayores a 0.1 cm. Esto quizás podría resolverse aumentando aun más el número de “shots”. Finalmente, con este trabajo queda demostrado que un algoritmo de computación cuántica puede ser utilizado para la reconstrucción de vértices. Se abren con ´el un campo con muchas opciones interesantes donde seguro que el proceso y los parámetros pueden optimizarse y llegar a obtenerse resultados mejores. Grado en Física

[CA] La computació quàntica pretén donar un gir a tota la computació tal i como la coneixem. En els últims anys s’han realitzat grans avanços que inclús han aconseguit el desenvolupament de llenguatges d’alt nivell per a aquestes revolucionàries computadores. Aquestes revolucionàries arquitectures faciliten la solució de determinats tipus de problemes com la factorització de nombres enters, el logaritme discret o el logaritme discret de curva elíptica, entre altres, que són la base dels algoritmes criptogràfics actuals. Llavors, a pesar de què encara no existeixen computadores quàntiques tan potents com per a trencar les claus generades pels algoritmes criptogràfics actuals, s’està treballant ja en la criptografia postquàntica per a assegurar que els futurs algoritmes criptogràfics siguen robustos per afrontar possibles atacs quàntics en el futur. D’altra banda, hi ha una forta postura que assegura que mai s’aconseguirà construir una computadora quàntica competent. No obstant, la major part del esforç dedicat a la computació quàntica s’invirteix en desenvolupar mètodes de tolerància quàntica a fallades. En aquest treball es donarà a conèixer les bases de la computació quàntica, es presentaran diversos llenguatges quàntics d’alt nivell i les plataformes de simul·lació existents, i es realitzaran experiments per a determinar la capacitat de les computadores quàntiques actuals per a trencar l’encriptació RSA mitjançant l’algoritme quàntic de factorització Shor, analitzant així quánt prop- o lluny -queda la revolució computacional en termes de seguretat, i debatint -en contraposició- si en volta de parlar de supremacia quàntica hauríem de parlar d’utopia quàntica., [ES] La computación cuántica pretende dar un giro a toda la computación tal y como la conocemos. En los últimos años se han realizado grandes avances que incluso han llevado al desarrollo de lenguajes de alto nivel para estas revolucionarias computadoras. Estas revolucionarias arquitecturas permitirán la solución de determinados tipos de problemas como la factorización de números enteros, el logaritmo discreto o el logaritmo discreto de curva elíptica, entre otros, que son la base de los algoritmos criptográficos actuales. Por ello, a pesar de que no existen todavía computadoras cuánticas lo suficientemente potentes como para romper las claves generadas por los algoritmos criptográficos actuales, se está trabajando ya en la criptografía postcuántica para asegurar que los futuros algoritmos criptográficos sean robustos frente a posibles ataques cuánticos en el futuro. Por otro lado, hay una fuerte postura que asegura que nunca se va a llegar a construir una computadora cuántica competente. Sin embargo, la mayor parte del esfuerzo dedicado a la computación cuántica se invierte en desarrollar métodos de tolerancia cuántica a fallos. En este trabajo se dará a conocer las bases de la computación cuántica, se presentarán diversos lenguajes cuánticos de alto nivel y las plataformas de simulación existentes, y se realizarán experimentos para determinar la capacidad de los computadores cuánticos actuales para romper la encriptación RSA mediante el algoritmo cuántico de factorización Shor, analizando así cuán cerca- o lejos -queda la revolución computacional en temas de seguridad, y debatiendo, en contraposición, si en vez de hablar de supremacía cuántica debemos hablar de utopía cuántica., [EN] Quantum computing aims to give a turn to all computing as we know it. In recent years, great advances have been made that have even led to the development of high-level languages for these revolutionary computers. These revolutionary architectures will allow the solution of certain types of problems such as the factorization of integers, the discrete logarithm or the discrete logarithm of elliptic curve, among others, which are the basis of current cryptographic algorithms. Therefore, despite the fact that there are still no quantum computers powerful enough to break the keys generated by current cryptographic algorithms, work is already under way on post-quantum cryptography to ensure that future cryptographic algorithms are robust against possible quantum attacks in the future. On the other hand, there is a strong position that ensures that a competent quantum computer will never be built. However, most of the effort dedicated to quantum computing is invested in developing quantum fault-tolerance methods. In this work, the bases of quantum computing, various high-level quantum languages and existing simulation platforms will be presented, and experiments will be carried out to determine the ability of current quantum computers to break RSA encryption using the quantum factorization Shor¿s algorithm, thus analyzing how close - or far - is the computational revolution in terms of security, and debating, in contrast, if instead of talking about quantum supremacy we should talk about quantum utopia.

[ES] La computación cuántica es un área de investigación que estudia los algoritmos y sistemas que usan las propiedades de la física cuántica para solucionar problemas matemáticos complejos o costosos. La principal ventaja de los computadores cuánticos es la capacidad de los cúbits de mantener una superposición de ambos estados {0,1}. Gracias a esto, se consigue evaluar y guardar todas las posibles soluciones simultáneamente cuya consecuencia es una mejora exponencial al obtener los resultados. El trabajo consiste en desarrollar un simulador de computación cuántica que permite ejecutar circuitos cuánticos con varias puertas lógicas y varios cúbits en un ordenador clásico. La aplicación del simulador es de escritorio, está acompañada de una interfaz gráfica, desarrollada con el lenguaje Python y tiene un carácter educativo, ilustrando los fenómenos de la cuántica. Puedes simular tus propios circuitos arrastrando las puertas lógicas, guardarlos en el ordenador o lanzarlos en hardware cuántico real de proveedores como IBM. Se comparan las características de los distintos sistemas cuánticos actuales de importantes empresas tecnológicas., [EN] Quantum computing is an area of research that studies algorithms and systems that use the properties of quantum physics to solve complex or hard mathematical problems. The main advantage of quantum computers is the ability of qubits to maintain a superposition of both {0,1} states. Thanks to this, it is possible to evaluate and store all possible solutions simultaneously, the consequence of which is an exponential improvement in obtaining the results. The work consists of developing a quantum computing simulator that allows running quantum circuits with several logic gates and several qubits on a classical computer. The desktop application of the simulator is accompanied by a graphical interface, developed with the Python language and has a teaching approach, illustrating the phenomena of quantum. You can simulate your own circuits by dragging the logic gates, save them in the computer or launch them on real quantum hardware from providers such as IBM. It compares the characteristics of different current quantum systems from major technology companies., [CA] La computació quàntica és un àrea d’investigació que estudia els algorismes i sistemes que usen les propietats de la física cuàntica per a solucionar problemes matemàtics complexos o costosos. El principal avantatge dels computadors quàntics és la capacitat dels qubits de mantindre una superposición de tots dos estats {0,1}. Gràcies a això, s’aconsegueix avaluar i guardar totes les possibles solucions simultàniament que dona com a consequència una millora exponencial en l’obtenció dels resultats. El treball consisteix a desenvolupar un simulador de computació quàntica que permet executar circuits quàntics amb diverses portes lògiques i diversos qubits en un ordinador clàssic. L’aplicació del simulador és d’escriptori, està acompanyada d’una interfície gràfica, desenvolupada amb el llenguatge Python i té un caràcter educatiu, il·lustrant els fenòmens de la quàntica. Pots simular els teus propis circuits arrossegant les portes lògiques, guardar-los en l’ordinador o llançar-los en maquinari quàntic real de proveïdors com IBM. Es comparen les característiques dels diferents sistemes quàntics actuals d’importants empreses tecnològiques.

Dissertação de mestrado integrado em Engenharia Física, Quantum computing is an emergent field that brings together Quantum Mechanics, Computer Science and Information Theory, which promises improvements to classical algorithms such as simulation of quantum systems, cryptography, data base searching and many others. Among these algorithms, quantum walks may provide a quadratic speed up when compared to their classical counterparts, allowing improvements to applications such as element distinctness, searching problems, matrix product verification and hitting times in graphs. The present work offers a general theoretical overview, simulation and circuit implementation of the coined, staggered and continuous-time quantum walk models. The first two chapters of this thesis are dedicated to the definition of the theoretical framework, simulation in Python and comparison of the aforementioned quantum walk models for the simple case of the dynamics in a line graph and for the search algorithm in a complete graph. This is then used as a benchmark for the final chapter, devoted to building and testing the circuits corresponding to models mentioned above in IBM’s Qiskit. A main contribution of this dissertation concerns the circulant graph approach to diagonal operators for continuous-time quantum walks., A computação quântica é uma área emergente, que junta os campos de Mecânica Quântica, Ciências da Computação e Teoria da Informação, com a promessa de melhoramentos a algoritmos clássicos tais como a simulação de sistemas quânticos, criptografia, busca em base de dados, e outros. Entre estes algoritmos, as caminhadas quânticas surgem com um ganho quadrático de complexidade em comparação às caminhadas clássicas, possibilitando melhor desempenho em aplicações como distinção de elementos, problemas de busca, verificação de produtos de matrizes e tempos de alcance em grafos. O trabalho atual oferece uma visão geral de um ponto de vista teórico, de simulação e de implementação de circuitos, relativos aos modelos de caminhadas quânticas com moeda, escalonadas e contínuas no tempo. Os primeiros dois capítulos desta tese são dedicados à definição da estrutura teórica, simulação em Python e comparação dos modelos supracitados, para o caso simples da dinâmica na linha, e para o problema de busca num grafo completo. Isto será então utilizado como referência para o capítulo final, dedicado à construção e teste dos circuitos correspondentes aos modelos supracitados. Uma contribuição principal desta dissertação diz respeito à abordagem de grafos circulantes para realização de caminhadas quânticas continuas no tempo., Finally, this dissertation was financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalization - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI- 01-0145-FEDER-030947.

Booleove funkcije i S-kutijeˇcesto se koriste kao kriptografske primitive. Krip-tografske primitive moraju pokazivati odre ̄dena matematiˇcka svojstva kako bi moglaodoljevati napadima. Generiranje kriptografski signifikatnih Booleovih funkcija i S-kutija je složen i zahtjevan posao koji se pokušava riješiti principima kvatnog raˇcunar-stva. Osim generiranja kvatno se raˇcunarstvo može koristiti i za ispitivanje svojstavate samo implementaciju primitiva. Boolean functions and S-boxes are often used as cryptographic primitives. Cryp-tographic primitives must show certain mathematical properties in order to withstandattacks. Generating cryptographically significant Boolean functions and S-boxes isa complex and demanding job that is being solved with the principles of quantumcomputing. In addition to generating, quantum computing can also be used to testproperties and implement primitives.

Cilj ovog rada je ispitati mogućnost primjene automatskog genetskog programiranja za razvoj kvantnih algoritama. U radu je objašnjena paradigma kvantnog računanja i opisana su dva postojeća kvantna algoritma (Deutsch-Jozsa algoritam i Simonov algoritam). Ostvaren je programski sustav koji uporabom genetskog programiranja razvija algoritme prilagođene kvantnom računalu. Ispitana je učinkovitost sustava u reproduciranju opisanih kvantnih algoritama te su navedeni dobiveni rezultati. The aim of this paper is to examine the possibility of applying automatic genetic programming for the development of quantum algorithms. The paper explains the paradigm of quantum computing and describes two existing quantum algorithms (Deutsch-Jozsa algorithm and Simon's algorithm). A software system has been created that uses genetic programming to develop algorithms adapted to the quantum computer. The efficiency of the system in reproducing the described quantum algorithms was examined and the obtained results were stated.

LOGOS > VOL. II NO. I > INVESTIGACIONES La investigación se realiza con el objetivo de relacionar la computación clásica y la computación cuántica, así como determinar cuáles serán las implicaciones que podríamos ver en un futuro. Como consecuencia, surgen las preguntas: ¿Será la computación clásica eventualmente reemplazada por su contraparte cuántica? ¿Vendrá esta tecnología a revolucionar totalmente el viejo paradigma de las computadoras clásicas o tendrá una aplicación específica en ciertas industrias y se complementará con las computadoras actuales? En este artículo responderemos a ambas preguntas por medio de la ejecución de varios algoritmos de prueba cuyos resultados son la base de nuestro análisis. Cabe destacar que este artículo no se basa en simulaciones, sino en ejecuciones reales de algoritmos cuánticos en una computadora cuántica de 15-qubits. Con el patrocinio de Fondo California 49 https://www.california49.org

En este Trabajo de Fin de Grado se estudia la posible disminución en el tiempo de computación que originaría el desarrollo de un algoritmo de búsqueda similar al dado por el algoritmo de Grover [1] para realizar el test de dominancia en los algoritmos de Optimización Combinatoria Multiobjetivo. Para ello, en primer lugar, se hará una introducción tanto al estado actual de la Computación Cuántica como a los conceptos de este paradigma necesarios para comprender el algoritmo de Grover. Tras esta introducción, se procede a hablar del propio algoritmo de Grover, se realiza una demostración empírica de este algoritmo y se finaliza explicando posibles vías futuras para continuar este desarrollo. This end of degree project aims to perform a similar Grover [1] search algorithm to accelerate the computational time of the Combinatorial Multiobjective Optimization dominance test. To achieve this, an introduction to Quantum Computation actual state and concepts are shown first, followed by Grover algorithm explanation and an empirical demonstration of this algorithm. This document finishes with possible future ways to continue with this development.

International audience

У роботi представлено ефективний алгоритм множення елементiв поля GF(28), яке використовується в шифрах нацiональних стандартiв блокового та потокового шифрування України. Запропонований алгоритм можна ефективно реалiзувати у квантовiй моделi обчислень без залучення додаткових кубiтiв, що робить його надзвичайно цiнним при оцiнцi вентильної складностi квантових атак на вказанi шифри.

Neste artigo, apresentamos a ferramenta Quantum Information Software Development Kit – Qiskit para o ensino de computação quântica para estudantes de graduação com conhecimento básico dos postulados da mecânica quântica. Nos concentramos na apresentação da construção dos programas em qualquer laptop ou desktop comum e a sua execução em processadores quânticos reais através do acesso remoto aos hardwares disponibilizados na plataforma IBM Quantum Experience. Os códigos são disponibilizados ao longo do texto para que os leitores, mesmo com pouca experiência em computação científica, possam reproduzi-los e adotar os métodos discutidos neste artigo para abordar seus próprios projetos de computação quântica. Os resultados apresentados estão de acordo com as previsões teóricas, mostrando a eficácia do pacote Qiskit como uma ferramenta de trabalho em sala de aula para a introdução de conceitos aplicados de computação e informação quântica. In this paper, we present the Quantum Information Software Development Kit – Qiskit for teaching quantum computing to undergraduate students, with basic knowledge of quantum mechanics postulates. We focus on presenting the construction of the programs on any common laptop or desktop computer and their execution on real quantum processors through the remote access to the quantum hardware available on the IBM Quantum Experience platform. The codes are made available throughout the text so that readers, even with little experience in scientific computing, can reproduce them and adopt the methods discussed in this paper to address their own quantum computing projects. The results presented are in agreement with theoretical predictions and show the effectiveness of the Qiskit package as a robust classroom working tool for the introduction of applied concepts of quantum computing and quantum information theory.

Shor���s Algorithmen f��r die Primfaktorzerlegung und f��r das Problem des diskreten Logarithmus z��hlen zu den bahnbrechendsten Entwicklungen im Bereich der Quanteninformatik. Sie l��sen Probleme in polynomieller Zeit mithilfe eines Quantencomputers, f��r welche keine effizienten klassischen Algorithmen bekannt sind. Diese Tatsache unterstreicht den Nutzen von Quantencomputern im Allgemeinen. Heutzutage existieren Bibliotheken und Simulatoren, die es erm��glichen, Quantenalgorithmen zu implementieren und zu analysieren. Eine dieser Bibliotheken, welche au��erdem noch die M��glichkeit bietet, die Algorithmen auf echten Maschinen auszuf��hren, ist Qiskit. Qiskit beinhaltet zurzeit jedoch keine Referenzimplementierung f��r Shor���s Algorithmus f��r den diskreten Logarithmus. F��r eine Implementierung m��ssen zus��tzlich zur allgemeinen Beschreibung des Algorithmus noch Prozeduren f��r modulare Arithmetik bereitgestellt werden. F��r diese Berechnungen gibt es viele unterschiedliche Algorithmen, wobei manche sehr klassischen Prozeduren ��hneln und andere wiederum die Eigenheiten von Quantencomputern ausnutzen. Diese Arbeit liefert eine Referenzimplementierung von Shor���s Algorithmus f��r das Problem des diskreten Logarithmus. Dabei werden drei verschiedene Versionen der ben��tigten Routinen f��r modulare Arithmetik verwendet. Da aktuelle Quantencomputer immer noch relativ wenige Quantenbits, oder Qubits, f��r die Berechnung zur Verf��gung stellen, liegt der Hauptfokus der Arbeit auf M��glichkeiten der Implementierung, die eine minimale Anzahl an Qubits ben��tigen. Mithilfe der Simulationsfunktionen von Qiskit wird zus��tzlich zum Vergleich der Implementierungen bez��glich der asymptotischen Zeitkomplexit��t ein Vergleich der verschiedenen Versionen anhand der konkreten Anzahl an elementaren Operationen f��r kleine Probleminstanzen vorgenommen. Au��erdem wird diese Analyse um eine genaue Untersuchung der Erfolgswahrscheinlichkeit erg��nzt, da diese f��r die Laufzeit insgesamt ausschlaggebend ist., One of the groundbreaking results in the field of quantum computing is Shor���s work describing algorithms for prime factorization and for the discrete logarithm problem. These algorithms solve problems in polynomial time on a quantum computer, for which no efficient solution is known on a classical computer, which highlights the utility of quantum computers. Today there are libraries and simulators available that enable the implementation and analysis of quantum algorithms. One of these development environments is Qiskit, which furthermore enables its users to execute quantum algorithms on real devices. However, this library currently does not contain a reference implementation of Shor���s algorithm for the discrete logarithm problem. For such an implementation, not only the structure of the overall algorithm but also procedures for performing modular arithmetic on a quantum computer have to be provided. There are various ways of performing these calculations. Some are very similar to classical procedures and some utilize the peculiarities of quantum systems. This work provides a reference implementation of Shor���s algorithm for the discrete logarithm problem. This quantum program makes use of three different implementations of the required modular arithmetic procedures. Since current quantum computers are still small in the number of qubits available for computation, this thesis focuses on implementation proposals that optimize the space complexity of the algorithm for the discrete logarithm problem. The presented implementations are compared using their asymptotic complexity bounds. Additionally, using Qiskit���s simulation capabilities, a comparison of the different versions using concrete values for the number of elementary instructions for small problem instances is presented. Furthermore, this analysis is extended to also investigate the actual success probability of the algorithm as this value is crucial for the overall runtime.

In the past few years, IBM has expanded their Quantum Experience to include a high-level Python module called Qiskit as well as a 15-qubit machine (ibmq_16_melbourne). In order to evaluate IBM’s progress, we create an overview of the processes involved in developing and running an algorithm on IBM’s quantum machines. This includes exploring the new resources that IBM has made available recently including the Qiskit Python module. Then, we test textbook algorithms such as the Deutsch-Jozsa algorithm, Grover’s search algorithm, and Quantum Fourier Transform on ibmq_16_melbourne and compare the results with the output of a simulator. Constraints imposed by IBM’s Quantum Experience and significant differences between algorithm performance on IBM's quantum hardware and the simulator will be used to assess IBM’s quantum computing capabilities. Ensign, United States Navy Approved for public release. distribution is unlimited

International audience

The goal of this research report was to draw the state of the art of the advancement in quantum computing as part of a project of the International Master Research of the ISIMA engineering school. To do so, we first studied the principles of quantum physics required to understand quantum computing, namely, quantum superposition, quantum entanglement and wave-function collapse. These principles define a qubit which represents thequantum information. Qubits are, however, limited by decoherence, which prevents them to stay in a superposed state for a long period of time, and the no-cloning theorem, which prevents the copy of the superposed state of a qubit. We can interact with qubits thanks to quantum gates which composed quantum circuits. Throughout this project, we analysed Grover’s algorithm which is a quantum search algorithm. Then, we implemented it with Qiskit, a Python’s library developed by IBM. Eventually, we executed it on a real quantum computer available on IBM Q Experience and we found reproducibility issues. Today, quantum computers cannot handle many qubits nor apply many quantum gates, but it was enough for Google to claim to have reached quantum supremacy in October 2019.; Le but de ce rapport de recherche était de dresser un état de l’art de l’avancement en informatique quantique dans le cadre d’un projet du Master de recherche international de l’école d’ingénieur ISIMA. Pour cela, nous avons d’abord étudié les principes de la physique quantique nécessaires à la compréhension de l’informatique quantique, à savoir, la superposition quantique, l’intrication quantique et la réduction du paquet d’onde. Ces principes permettent de définir le concept de qubit qui est le support de l’information quantique. Le qubit est limité par le phénomène de décohérence qui empêche les qubits de rester longtemps dans un état superposé. De plus, il est impossible de copier l’état d’un qubit à cause du théorème de non-clonage. Les qubits peuvent être manipulés avec des portes quantiques qui forment alors des circuits quantiques.Au cours de ce projet, nous avons analysé l’algorithme de Grover qui est un algorithme quantique de recherche. Puis, nous l’avons implémenté à l’aide de la bibliothèque Python Qiskit développée par IBM. Enfin, nous avons exécuté cet algorithme sur un véritable ordinateur quantique mis à disposition via la plateforme IBM Q Experience et nous avons constaté des problèmes de reproductibilité.A ce jour, les ordinateurs quantiques ne sont capables de manipuler qu’un nombre restreint de qubits et de leurs appliquer un nombre restreint de portes quantiques mais cela a été suffisant pour que Google affirme avoir atteint la suprématie quantique en octobre 2019.

La computación clásica forma parte de nuestro día a día y ha sido uno de los pilares que ha impulsado la innovación en las últimas décadas. Sin embargo, hay problemas que esta tecnología no es capaz de resolver o es muy poco eficiente hacerlo de esta manera. Aquí es donde entra en juego la computación cuántica, campo en el cual se están alcanzando progresos significativos. La principal diferencia entre la computación clásica y la cuántica es que en esta última se hace uso de fenómenos cuánticos, tales como la superposición y el entrelazamiento. Para ello la computación cuántica se basa en el uso de qubits o bits cuánticos, dejando de lado los bits clásicos y los sistemas lógicos empleados por los sistemas informáticos convencionales. Esta tecnología resulta de gran interés actualmente por su enorme potencial, que supone la posibilidad de revolucionar el mundo de la computación. Una misma tarea puede tener diferente complejidad en computación clásica y en computación cuántica, lo que ha dado lugar a una gran expectación. También permite la resolución de problemas intratables anteriormente. En general, los ordenadores cuánticos, debido a su gran capacidad de manejo de datos, nos ofrecen la posibilidad de impulsar grandes avances en diversos campos, desde la ingeniería hasta la investigación farmacéutica, por ejemplo. En este trabajo se aborda el estudio del algoritmo cuántico de Grover, que resuelve el problema de encontrar una entrada en una base de datos desestructurada. En primer lugar se introducen los conceptos básicos para la comprensión del algoritmo, tales como el oráculo y la amplificación de amplitud. Posteriormente se tratan las mejoras respecto de los algoritmos de búsqueda clásicos y el hecho de que el algoritmo de Grover es óptimo. Esto completa la parte de desarrollo teórico. Posteriormente se presenta una componente de simulación en la plataforma IBM Quantum Experience para las diferentes situaciones propuestas. Más tarde se lleva a cabo la implementación real del algoritmo en los ordenadores cuánticos de IBM así como la implementación mitigando en cierta medida el error propio de los ordenadores cuánticos. Finalmente, se comentan algunas aplicaciones dentro del gran abanico de aplicaciones existentes a día de hoy.

This paper introduces the first functional model of a quantum parliament that is dominated by two parties or coalitions, and may or may not contain independent legislators. We identify a single crucial parameter, aptly named free will radius, which can be used as a practical measure of the quantumness of the parties and the parliament as a whole. The free will radius used by the two parties determines the degree of independence that is afforded to the representatives of the parties. Setting the free will radius to zero degrades the quantum parliament to a classical one. On the other hand, setting the free will radius to its maximum value 1 makes the representatives totally independent. Moreover, we present a quantum circuit in Qiskit with which we simulate the operation of the quantum parliament under various scenarios. The experimental results allow us to arrive at some novel and fundamental conclusions that, we believe, provide new insights into the operation and the traits of a possible future quantum parliament. Finally, we propose the game “Passing the Bill,” which captures the operation of the quantum parliament and basic options available to the leadership of the two parties.

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.