Quantum Technology And Optimization Problems

This book constitutes the refereed proceedings of the First International Workshop on Quantum Technology and Optimization Problems, QTOP 2019, held in Munich, Germany, in March 2019.The 18 full papers presented together with 1 keynote paper in this volume were carefully reviewed and selected from 21 submissions. The papers are grouped in the following topical sections: analysis of optimization problems; quantum gate algorithms; applications of quantum annealing; and foundations and quantum technologies.

Work with fully explained algorithms and ready-to-use examples that can be run on quantum simulators and actual quantum computers with this comprehensive guide Key FeaturesGet a solid grasp of the principles behind quantum algorithms and optimization with minimal mathematical prerequisitesLearn the process of implementing the algorithms on simulators and actual quantum computersSolve real-world problems using practical examples of methodsBook Description This book provides deep coverage of modern quantum algorithms that can be used to solve real-world problems. You'll be introduced to quantum computing using a hands-on approach with minimal prerequisites. You'll discover many algorithms, tools, and methods to model optimization problems with the QUBO and Ising formalisms, and you will find out how to solve optimization problems with quantum annealing, QAOA, Grover Adaptive Search (GAS), and VQE. This book also shows you how to train quantum machine learning models, such as quantum support vector machines, quantum neural networks, and quantum generative adversarial networks. The book takes a straightforward path to help you learn about quantum algorithms, illustrating them with code that's ready to be run on quantum simulators and actual quantum computers. You'll also learn how to utilize programming frameworks such as IBM's Qiskit, Xanadu's PennyLane, and D-Wave's Leap. Through reading this book, you will not only build a solid foundation of the fundamentals of quantum computing, but you will also become familiar with a wide variety of modern quantum algorithms. Moreover, this book will give you the programming skills that will enable you to start applying quantum methods to solve practical problems right away. What you will learnReview the basics of quantum computingGain a solid understanding of modern quantum algorithmsUnderstand how to formulate optimization problems with QUBOSolve optimization problems with quantum annealing, QAOA, GAS, and VQEFind out how to create quantum machine learning modelsExplore how quantum support vector machines and quantum neural networks work using Qiskit and PennyLaneDiscover how to implement hybrid architectures using Qiskit and PennyLane and its PyTorch interfaceWho this book is for This book is for professionals from a wide variety of backgrounds, including computer scientists and programmers, engineers, physicists, chemists, and mathematicians. Basic knowledge of linear algebra and some programming skills (for instance, in Python) are assumed, although all mathematical prerequisites will be covered in the appendices.

The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is large enough, then the system remains close to its ground state. An AQC algorithm uses the adiabatic theorem to approximate the ground state of the final Hamiltonian that corresponds to the solution of the given optimization problem. In this book, we investigate the computational simulation of AQC algorithms applied to the MAX-SAT problem. A symbolic analysis of the AQC solution is given in order to understand the involved computational complexity of AQC algorithms. This approach can be extended to other combinatorial optimization problems and can be used for the classical simulation of an AQC algorithm where a Hamiltonian problem is constructed. This construction requires the computation of a sparse matrix of dimension 2n × 2n, by means of tensor products, where n is the dimension of the quantum system. Also, a general scheme to design AQC algorithms is proposed, based on a natural correspondence between optimization Boolean variables and quantum bits. Combinatorial graph problems are in correspondence with pseudo-Boolean maps that are reduced in polynomial time to quadratic maps. Finally, the relation among NP-hard problems is investigated, as well as its logical representability, and is applied to the design of AQC algorithms. It is shown that every monadic second-order logic (MSOL) expression has associated pseudo-Boolean maps that can be obtained by expanding the given expression, and also can be reduced to quadratic forms. Table of Contents: Preface / Acknowledgments / Introduction / Approximability of NP-hard Problems / Adiabatic Quantum Computing / Efficient Hamiltonian Construction / AQC for Pseudo-Boolean Optimization / A General Strategy to Solve NP-Hard Problems / Conclusions / Bibliography / Authors' Biographies

Quantum technology has arrived as one of the most important new topics of research, as it is the newest way to create computing power, harness secure communications, and use sensitive measurement methods that surpass the capabilities of modern supercomputers. If successfully developed, quantum computers and technology will be able to perform algorithms at impressively quick rates and solve problems that were previously deemed impossible. This technology will disrupt what is already known about computing and will be able to reach new heights, speeds, and problem-solving capabilities not yet seen. Beyond its inherent benefits comes the fact that quantum technology will create improvements in many everyday gadgets as well, spanning many industries. The Research Anthology on Advancements in Quantum Technology presents the latest discoveries in quantum technology itself along with providing its essential uses, applications, and technologies that will impact computing in modern times and far into the future. Along with this overview comes a look at quantum technology in many different fields such as healthcare, communications, aviation, automotive, forecasting, and more. These industries will be looked at from the perspective of data analytics, pattern matching, cryptography, algorithms, and more. This book is essential for computer scientists, engineers, professionals, researchers, students, and practitioners interested in the latest information on quantum technology.

Work with fully explained algorithms and ready-to-use examples that can be run on quantum simulators and actual quantum computers with this comprehensive guide Key Features: Get a solid grasp of the principles behind quantum algorithms and optimization with minimal mathematical prerequisites Learn the process of implementing the algorithms on simulators and actual quantum computers Solve real-world problems using practical examples of methods Book Description: This book provides deep coverage of modern quantum algorithms that can be used to solve real-world problems. You'll be introduced to quantum computing using a hands-on approach with minimal prerequisites. You'll discover many algorithms, tools, and methods to model optimization problems with the QUBO and Ising formalisms, and you will find out how to solve optimization problems with quantum annealing, QAOA, Grover Adaptive Search (GAS), and VQE. This book also shows you how to train quantum machine learning models, such as quantum support vector machines, quantum neural networks, and quantum generative adversarial networks. The book takes a straightforward path to help you learn about quantum algorithms, illustrating them with code that's ready to be run on quantum simulators and actual quantum computers. You'll also learn how to utilize programming frameworks such as IBM's Qiskit, Xanadu's PennyLane, and D-Wave's Leap. Through reading this book, you will not only build a solid foundation of the fundamentals of quantum computing, but you will also become familiar with a wide variety of modern quantum algorithms. Moreover, this book will give you the programming skills that will enable you to start applying quantum methods to solve practical problems right away. What You Will Learn: Review the basics of quantum computing Gain a solid understanding of modern quantum algorithms Understand how to formulate optimization problems with QUBO Solve optimization problems with quantum annealing, QAOA, GAS, and VQE Find out how to create quantum machine learning models Explore how quantum support vector machines and quantum neural networks work using Qiskit and PennyLane Discover how to implement hybrid architectures using Qiskit and PennyLane and its PyTorch interface Who this book is for: This book is for professionals from a wide variety of backgrounds, including computer scientists and programmers, engineers, physicists, chemists, and mathematicians. Basic knowledge of linear algebra and some programming skills (for instance, in Python) are assumed, although all mathematical prerequisites will be covered in the appendices.

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This volume presents papers on the topics covered at the National Academy of Engineering's 2018 US Frontiers of Engineering Symposium. Every year the symposium brings together 100 outstanding young leaders in engineering to share their cutting-edge research and innovations in selected areas. The 2018 symposium was held September 5-7 and hosted by MIT Lincoln Laboratory in Lexington, Massachusetts. The intent of this book is to convey the excitement of this unique meeting and to highlight innovative developments in engineering research and technical work.

"Discusses the recent developments in quantum statistical physics of spin glasses and quantum computations"--Provided by publisher.