Quantum-based Distributed Algorithms for Edge Node Placement and Workload Allocation

Edge computing is a promising technology that offers a superior user experience and enables various innovative Internet of Things applications. In this paper, we present a mixed-integer linear programming (MILP) model for optimal edge server placement and workload allocation, which is known to be NP-hard. To this end, we explore the possibility of addressing this computationally challenging problem using quantum computing. However, existing quantum solvers are limited to solving unconstrained binary programming problems. To overcome this obstacle, we propose a hybrid quantum-classical solution that decomposes the original problem into a quadratic unconstrained binary optimization (QUBO) problem and a linear program (LP) subproblem. The QUBO problem can be solved by a quantum solver, while the LP subproblem can be solved using traditional LP solvers. Our numerical experiments demonstrate the practicality of leveraging quantum supremacy to solve complex optimization problems in edge computing

Quantum Computing in the NISQ era and beyond

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away --- we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.Comment: 20 pages. Based on a Keynote Address at Quantum Computing for Business, 5 December 2017. (v3) Formatted for publication in Quantum, minor revision

Quantum Algorithms for Solving Hard Constrained Optimization Problems

En aquesta investigació, s'han examinat tècniques d'optimització per resoldre problemes de restriccions i s'ha fet un estudi de l'era quàntica i de les empreses líders del mercat, com ara IBM, D-Wave, Google, Xanadu, AWS-Braket i Microsoft. S'ha après sobre la comunitat, les plataformes, l'estat de les investigacions i s'han estudiat els postulats de la mecànica quàntica que serveixen per crear els sistemes i algorismes quàntics més eficients. Per tal de saber si és possible resoldre problemes de Problema de cerca de restriccions (CSP) de manera més eficient amb la computació quàntica, es va definir un escenari perquè tant la computació clàssica com la quàntica tinguessin un bon punt de referència. En primer lloc, la prova de concepte es centra en el problema de programació dels treballadors socials i més tard en el tema de la preparació per lots i la selecció de comandes com a generalització del Problema dels treballadors socials (SWP). El problema de programació dels treballadors socials és una mena de problema d'optimització combinatòria que, en el millor dels casos, es pot resoldre en temps exponencial; veient que el SWP és NP-Hard, proposa fer servir un altre enfoc més enllà de la computació clàssica per a la seva resolució. Avui dia, el focus a la computació quàntica ja no és només per la seva enorme capacitat informàtica sinó també, per l'ús de la seva imperfecció en aquesta era Noisy Intermediate-Scale Quantum (NISQ) per crear un poderós dispositiu d'aprenentatge automàtic que utilitza el principi variacional per resoldre problemes d'optimització en reduir la classe de complexitat. A la tesi es proposa una formulació (quadràtica) per resoldre el problema de l'horari dels treballadors socials de manera eficient utilitzant Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), Minimal Eigen Optimizer i ADMM optimizer. La viabilitat quàntica de l'algorisme s'ha modelat en forma QUBO, amb Docplex simulat Cirq, Or-Tools i provat a ordinadors IBMQ. Després d'analitzar els resultats de l'enfocament anterior, es va dissenyar un escenari per resoldre el SWP com a raonament basat en casos (qCBR), tant quànticament com clàssicament. I així poder contribuir amb un algorisme quàntic centrat en la intel·ligència artificial i l'aprenentatge automàtic. El qCBR és una tècnica d’aprenentatge automàtic basada en la resolució de nous problemes que utilitza l’experiència, com ho fan els humans. L'experiència es representa com una memòria de casos que conté qüestions prèviament resoltes i utilitza una tècnica de síntesi per adaptar millor l'experiència al problema nou. A la definició de SWP, si en lloc de pacients es tenen lots de comandes i en lloc de treballadors socials robots mòbils, es generalitza la funció objectiu i les restriccions. Per això, s'ha proposat una prova de concepte i una nova formulació per resoldre els problemes de picking i batching anomenat qRobot. Es va fer una prova de concepte en aquesta part del projecte mitjançant una Raspberry Pi 4 i es va provar la capacitat d'integració de la computació quàntica dins de la robòtica mòbil, amb un dels problemes més demandats en aquest sector industrial: problemes de picking i batching. Es va provar en diferents tecnologies i els resultats van ser prometedors. A més, en cas de necessitat computacional, el robot paral·lelitza part de les operacions en computació híbrida (quàntica + clàssica), accedint a CPU i QPU distribuïts en un núvol públic o privat. A més, s’ha desenvolupat un entorn estable (ARM64) dins del robot (Raspberry) per executar operacions de gradient i altres algorismes quàntics a IBMQ, Amazon Braket (D-Wave) i Pennylane de forma local o remota. Per millorar el temps d’execució dels algorismes variacionals en aquesta era NISQ i la següent, s’ha proposat EVA: un algorisme d’aproximació de Valor Exponencial quàntic. Fins ara, el VQE és el vaixell insígnia de la computació quàntica. Avui dia, a les plataformes líders del mercat de computació quàntica al núvol, el cost de l'experimentació dels circuits quàntics és proporcional al nombre de circuits que s'executen en aquestes plataformes. És a dir, amb més circuits més cost. Una de les coses que aconsegueix el VQE, el vaixell insígnia d'aquesta era de pocs qubits, és la poca profunditat en dividir el Hamiltonià en una llista de molts petits circuits (matrius de Pauli). Però aquest mateix fet, fa que simular amb el VQE sigui molt car al núvol. Per aquesta mateixa raó, es va dissenyar EVA per poder calcular el valor esperat amb un únic circuit. Tot i haver respost a la hipòtesi d'aquesta tesis amb tots els estudis realitzats, encara es pot continuar investigant per proposar nous algorismes quàntics per millorar problemes d'optimització.En esta investigación, se han examinado técnicas de optimización para resolver problemas de restricciones y se ha realizado un estudio de la era cuántica y de las empresas lideres del mercado, como IBM, D-Wave, Google, Xanadu, AWS-Braket y Microsoft. Se ha aprendido sobre su comunidad, sus plataformas, el estado de sus investigaciones y se han estudiado los postulados de la mecánica cuántica que sirven para crear los sistemas y algoritmos cuánticos más eficientes. Por tal de saber si es posible resolver problemas de Problema de búsqueda de restricciones (CSP) de manera más eficiente con la computación cuántica, se definió un escenario para que tanto la computación clásica como la cuántica tuvieran un buen punto de referencia. En primer lugar, la prueba de concepto se centra en el problema de programación de los trabajadores sociales y más tarde en el tema de la preparación por lotes y la selección de pedidos como una generalización del Problema de los trabajadores sociales (SWP). El problema de programación de los trabajadores sociales es una clase de problema de optimización combinatoria que, en el mejor de los casos, puede resolverse en tiempo exponencial; viendo que el SWP es NP-Hard, propone usar otro enfoque mas allá de la computación clásica para su resolución. Hoy en día, el foco en la computación cuántica ya no es sólo por su enorme capacidad informática sino también, por el uso de su imperfección en esta era Noisy Intermediate-Scale Quantum (NISQ) para crear un poderoso dispositivo de aprendizaje automático que usa el principio variacional para resolver problemas de optimización al reducir su clase de complejidad. En la tesis se propone una formulación (cuadrática) para resolver el problema del horario de los trabajadores sociales de manera eficiente usando Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), Minimal Eigen Optimizer y ADMM optimizer. La viabilidad cuántica del algoritmo se ha modelado en forma QUBO, con Docplex simulado Cirq, Or-Tools y probado en computadoras IBMQ. Después de analizar los resultados del enfoque anterior, se diseñó un escenario para resolver el SWP como razonamiento basado en casos (qCBR), tanto cuántica como clásicamente. Y así, poder contribuir con un algoritmo cuántico centrado en la inteligencia artificial y el aprendizaje automático. El qCBR es una técnica de aprendizaje automático basada en la resolución de nuevos problemas que utiliza la experiencia, como lo hacen los humanos. La experiencia se representa como una memoria de casos que contiene cuestiones previamente resueltas y usa una técnica de síntesis para adaptar mejor la experiencia al nuevo problema. En la definición de SWP, si en lugar de pacientes se tienen lotes de pedidos y en lugar de trabajadores sociales robots móviles, se generaliza la función objetivo y las restricciones. Para ello, se ha propuesto una prueba de concepto y una nueva formulación para resolver los problemas de picking y batching llamado qRobot. Se hizo una prueba de concepto en esta parte del proyecto a través de una Raspberry Pi 4 y se probó la capacidad de integración de la computación cuántica dentro de la robótica móvil, con uno de los problemas más demandados en este sector industrial: problemas de picking y batching. Se probó en distintas tecnologías y los resultados fueron prometedores. Además, en caso de necesidad computacional, el robot paraleliza parte de las operaciones en computación híbrida (cuántica + clásica), accediendo a CPU y QPU distribuidos en una nube pública o privada. Además, desarrollamos un entorno estable (ARM64) dentro del robot (Raspberry) para ejecutar operaciones de gradiente y otros algoritmos cuánticos en IBMQ, Amazon Braket (D-Wave) y Pennylane de forma local o remota. Para mejorar el tiempo de ejecución de los algoritmos variacionales en esta era NISQ y la siguiente, se ha propuesto EVA: un algoritmo de Aproximación de Valor Exponencial cuántico. Hasta la fecha, el VQE es el buque insignia de la computación cuántica. Hoy en día, en las plataformas de computación cuántica en la nube líderes de mercado, el coste de la experimentación de los circuitos cuánticos es proporcional al número de circuitos que se ejecutan en dichas plataformas. Es decir, con más circuitos mayor coste. Una de las cosas que consigue el VQE, el buque insignia de esta era de pocos qubits, es la poca profundidad al dividir el Hamiltoniano en una lista de muchos pequeños circuitos (matrices de Pauli). Pero este mismo hecho, hace que simular con el VQE sea muy caro en la nube. Por esta misma razón, se diseñó EVA para poder calcular el valor esperado con un único circuito. Aún habiendo respuesto a la hipótesis de este trabajo con todos los estudios realizados, todavía se puede seguir investigando para proponer nuevos algoritmos cuánticos para mejorar problemas de optimización combinatoria.In this research, Combinatorial optimization techniques to solve constraint problems have been examined. A study of the quantum era and market leaders such as IBM, D-Wave, Google, Xanadu, AWS-Braket and Microsoft has been carried out. We have learned about their community, their platforms, the status of their research, and the postulates of quantum mechanics that create the most efficient quantum systems and algorithms. To know if it is possible to solve Constraint Search Problem (CSP) problems more efficiently with quantum computing, a scenario was defined so that both classical and quantum computing would have a good point of reference. First, the proof of concept focuses on the social worker scheduling problem and later on the issue of batch picking and order picking as a generalization of the Social Workers Problem (SWP). The social workers programming problem is a combinatorial optimization problem that can be solved exponentially at best; seeing that the SWP is NP-Hard, it claims using another approach beyond classical computation for its resolution. Today, the focus on quantum computing is no longer only on its enormous computing power but also on the use of its imperfection in this era Noisy Intermediate-Scale Quantum (NISQ) to create a powerful machine learning device that uses the variational principle to solve optimization problems by reducing their complexity class. In the thesis, a (quadratic) formulation is proposed to solve the problem of social workers' schedules efficiently using Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), Minimal Eigen Optimizer and ADMM optimizer. The quantum feasibility of the algorithm has been modelled in QUBO form, with Cirq simulated, Or-Tools and tested on IBMQ computers. After analyzing the results of the above approach, a scenario was designed to solve the SWP as quantum case-based reasoning (qCBR), both quantum and classically. And thus, to be able to contribute with a quantum algorithm focused on artificial intelligence and machine learning. The qCBR is a machine learning technique based on solving new problems that use experience, as humans do. The experience is represented as a memory of cases containing previously resolved questions and uses a synthesis technique to adapt the background to the new problem better. In the definition of SWP, if instead of patients there are batches of orders and instead of social workers mobile robots, the objective function and the restrictions are generalized. To do this, a proof of concept and a new formulation has been proposed to solve the problems of picking and batching called qRobot. A proof of concept was carried out in this part of the project through a Raspberry Pi 4 and the integration capacity of quantum computing within mobile robotics was tested, with one of the most demanded problems in this industrial sector: picking and batching problems. It was tested on different technologies, and the results were promising. Furthermore, in case of computational need, the robot parallelizes part of the operations in hybrid computing (quantum + classical), accessing CPU and QPU distributed in a public or private cloud. Furthermore, we developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave) and Pennylane locally or remotely. To improve the execution time of variational algorithms in this NISQ era and the next, EVA has been proposed: A quantum Exponential Value Approximation algorithm. To date, the VQE is the flagship of quantum computing. Today, in the market-leading quantum cloud computing platforms, the cost of experimenting with quantum circuits is proportional to the number of circuits running on those platforms. That is, with more circuits, higher cost. One of the things that the VQE, the flagship of this low-qubit era, achieves is shallow depth by dividing the Hamiltonian into a list of many small circuits (Pauli matrices). But this very fact makes simulating with VQE very expensive in the cloud. For this same reason, EVA was designed to calculate the expected value with a single circuit. Even having answered the hypothesis of this work with all the studies carried out, it is still possible to continue research to propose new quantum algorithms to improve combinatorial optimization

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Benchmarks and Controls for Optimization with Quantum Annealing

Quantum annealing (QA) is a metaheuristic specialized for solving optimization problems which uses principles of adiabatic quantum computing, namely the adiabatic theorem. Some devices implement QA using quantum mechanical phenomena. These QA devices do not perfectly adhere to the adiabatic theorem because they are subject to thermal and magnetic noise. Thus, QA devices return statistical solutions with some probability of success where this probability is affected by the level of noise of the system. As these devices improve, it is believed that they will become less noisy and more accurate. However, some tuning strategies may further improve that probability of finding the correct solution and reduce the effects of noise on solution outcome. In this dissertation, these tuning strategies are explored in depth to determine the effect of preprocessing, annealing, and post-processing controls on performance. In particular, these tuning strategies were applied to a real-world NP (nondeterministic polynomial time)-hard optimization problem and portfolio optimization. Although the performance improved very little from tuning the spin reversal transforms, anneal time, and embedding, the results revealed that reverse annealing controls improved the probability of success by an order of magnitude over forward annealing alone. The chain strength experiments revealed that increasing the strength of the intra-chain coupling improves the probability of success until the intra-chain coupling strengths begin to overpower the inter-chain couplings. By taking a closer look at each physical qubit in the embedded chains, the probability for each qubit to be faulty was visualized and was used to develop a post-processing strategy that outperformed the standard, which chooses a logical qubit value from a broken chain. The results of these findings provide a guide for researchers to find the optimal set of controls for their unique real-world optimization problem to determine whether QA provides some benefit over classical computing, lay the groundwork for developing new tuning strategies that could further improve performance, and characterize the current hardware for benchmarking future generations of QA hardware

A Quantum Computational Approach to Correspondence Problems on Point Sets

Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review modern AQC and derive the first algorithm for transformation estimation and point set alignment suitable for AQC. Our algorithm has a subquadratic computational complexity of state preparation. We perform a systematic experimental analysis of the proposed approach and show several examples of successful point set alignment by simulated sampling. With this paper, we hope to boost the research on AQC for computer vision

Green Parallel Metaheuristics: Design, Implementation, and Evaluation

Fecha de lectura de Tesis Doctoral 14 mayo 2020Green parallel metaheuristics (GPM) is a new concept we want to introduce in this thesis. It is an idea inspired by two facts: (i) parallel metaheuristics could help as unique tools to solve optimization problems in energy savings applications and sustainability, and (ii) these algorithms themselves run on multiprocessors, clusters, and grids of computers and then consume energy, so they need an energy analysis study for their different implementations over multiprocessors. The context for this thesis is to make a modern and competitive effort to extend the capability of present intelligent search optimization techniques. Analyzing the different sequential and parallel metaheuristics considering its energy consumption requires a deep investigation of the numerical performance, the execution time for efficient future designing to these algorithms. We present a study of the speed-up of the different parallel implementations over a different number of computing units. Moreover, we analyze and compare the energy consumption and numerical performance of the sequential/parallel algorithms and their components: a jump in the efficiency of the algorithms that would probably have a wide impact on the domains involved.El Instituto Egipcio en Madrid, dependiente del Gobierno de Egipto