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

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory—a linear-scaling, massively parallel framework—as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models

Development of Algorithms for the Direct Multi-Configuration Self- Consistent Field (MCSCF) Method

In order to improve the performance of the current parallelized direct multi-configuration self-consistent field (MCSCF) implementations of the program package Gaussian [42], consisting of the complete active space (CAS) SCF method [43] and the restricted active space (RAS) SCF method [44], this thesis introduces a matrix multiplication scheme as part of the CI eigenvalue evaluation of these methods. Thus highly optimized linear algebra routines, which are able to use data in a sequential and predictable way, can be used in our method, resulting in a much better performance overall than the current methods. The side effect of this matrix multiplication scheme is that it requires some extra memory to store the additional intermediate matrices. Several chemical systems are used to demonstrate that the new CAS and RAS methods are faster than the current CAS and RAS methods respectively. This thesis is structured into four chapters. Chapter One is the general introduction, which describes the background of the CASSCF/RASSCF methods. Then the efficiency of the current CASSCF/RASSCF code is discussed, which serves as the motivation for this thesis, followed by a brief introduction to our method. Chapter Two describes applying the matrix multiplication scheme to accelerate the current direct CASSCF method, by reorganizing the summation order in the equation that generates non-zero Hamiltonian matrix elements. It is demonstrated that the new method can perform much faster than the current CASSCF method by carrying out single point energy calculations on pyracylene and pyrene molecules, and geometry optimization calculations on anthracene+ / phenanthrene+ molecules. However, in the RASSCF method, because an arbitrary number of doubly-occupied or unoccupied orbitals are introduced into the CASSCF reference space, many new orbital integral cases arise. Some cases are suitable for the matrix multiplication scheme, while others are not. Chapter Three applies the scheme to those suitable integral cases that are also the most time-consuming cases for the RASSCF calculation. The coronene molecule - with different sizes of orbital active space - has been used to demonstrate that the new RASSCF method can perform significantly faster than the current Gaussian method. Chapter Four describes an attempt to modify the other integral cases, based on a review of the method developed by Saunders and Van Lenthe [95]. Calculations on coronene molecule are used again to test whether this implementation can further improve the performance of the RASSCF method developed in Chapter Three

Research and Technology 1995

This report selectively summarizes the NASA Lewis Research Center's research and technology accomplishments for fiscal year 1995. It comprises over 150 short articles submitted by the staff members of the technical directorates. The report is organized into six major sections: aeronautics, aerospace technology, space flight systems, engineering support, Lewis Research Academy, and technology transfer. A table of contents, an author index, and a list of NASA Headquarters program offices have been included to assist the reader in finding articles of special interest. This report is not intended to be a comprehensive summary of all research and technology work done over the past fiscal year. Most of the work is reported in Lewis-published technical reports, journal articles, and presentations prepared by Lewis staff members and contractors (for abstracts of these Lewis-authored reports, visit the Lewis Technical Report Server (LETRS) on the World Wide Web-http://letrs.lerc.nasa.gov/LeTRS/). In addition, university grants have enabled faculty members and graduate students to engage in sponsored research that is reported at technical meetings or in journal articles. For each article in this report, a Lewis contact person has been identified, and where possible, reference documents are listed so that additional information can be easily obtained. The diversity of topics attests to the breadth of research and technology being pursued and to the skill mix of the staff that makes it possible. For more information about Lewis' research, visit us on the World Wide web-http://www.lerc.nasa.gov

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.Comment: 268 pages, 87 figures. Comments and feedback are very welcome. Figures and tex files are available at https://github.com/Shmoo137/Lecture-Note

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning

Pacific Northwest National Laboratory institutional plan FY 1997--2002

Pacific Northwest National Laboratory`s core mission is to deliver environmental science and technology in the service of the nation and humanity. Through basic research fundamental knowledge is created of natural, engineered, and social systems that is the basis for both effective environmental technology and sound public policy. Legacy environmental problems are solved by delivering technologies that remedy existing environmental hazards, today`s environmental needs are addressed with technologies that prevent pollution and minimize waste, and the technical foundation is being laid for tomorrow`s inherently clean energy and industrial processes. Pacific Northwest National Laboratory also applies its capabilities to meet selected national security, energy, and human health needs; strengthen the US economy; and support the education of future scientists and engineers. Brief summaries are given of the various tasks being carried out under these broad categories

Bibliography of Lewis Research Center technical publications announced in 1993

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1993. All the publications were announced in the 1993 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

WOFEX 2021 : 19th annual workshop, Ostrava, 1th September 2021 : proceedings of papers

The workshop WOFEX 2021 (PhD workshop of Faculty of Electrical Engineer-ing and Computer Science) was held on September 1st September 2021 at the VSB – Technical University of Ostrava. The workshop offers an opportunity for students to meet and share their research experiences, to discover commonalities in research and studentship, and to foster a collaborative environment for joint problem solving. PhD students are encouraged to attend in order to ensure a broad, unconfined discussion. In that view, this workshop is intended for students and researchers of this faculty offering opportunities to meet new colleagues.Ostrav