Download or read book Approximability of Optimization Problems through Adiabatic Quantum Computation written by William Cruz-Santos and published by Springer Nature. This book was released on 2022-05-31 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Solving Optimization Problems Using Adiabatic Quantum Computing written by Kai Liu and published by . This book was released on 2018 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The commercial D-Waves quantum annealer has given rise to plenty of interests due to the reported quantum speedup against classical annealing. In order to make use of this new technology, a problem must be formulated into a form of quadratic unconstrained binary optimization (QUBO) or Ising model. This thesis reports on case studies using a D-Wave quantum annealer to solve several optimization problems and providing results validation using classical exact approaches. In our thesis, we briefly introduce several classical techniques designed for QUBO problems and implement two exact approaches. With the proper tools, a D-Wave 2X computer consisted of 1098 active qubits is then evaluated for the Degree-Constrained Minimum Spanning Tree and the Steiner Tree problems, establishing their QUBO formulations are suitable for adiabatic quantum computers. Motivated by the remarkable performance, two more optimization problems are studied—the Bounded-Depth Steiner Tree problem and the Chromatic Sum problem. We propose a new formulation for each problem. The numbers of qubits (dimension of QUBO matrices) required by our formulations are O(|V|3) and O(|V|2) respectively, where |V| represents the number of vertices.

Download or read book Adiabatic Quantum Computation and Quantum Annealing written by Catherine C. McGeoch and published by Springer Nature. This book was released on 2022-06-01 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a novel computing platform designed to solve NP-hard optimization problems. Starting with a 16-qubit prototype announced in 2007, the company has launched and sold increasingly larger models: the 128-qubit D-Wave One system was announced in 2010 and the 512-qubit D-Wave Two system arrived on the scene in 2013. A 1,000-qubit model is expected to be available in 2014. This monograph presents an introductory overview of this unusual and rapidly developing approach to computation. We start with a survey of basic principles of quantum computation and what is known about the AQC model and the QA algorithm paradigm. Next we review the D-Wave technology stack and discuss some challenges to building and using quantum computing systems at a commercial scale. The last chapter reviews some experimental efforts to understand the properties and capabilities of these unusual platforms. The discussion throughout is aimed at an audience of computer scientists with little background in quantum computation or in physics. Table of Contents: Acknowledgments / Introduction / Adiabatic Quantum Computation / Quantum Annealing / The D-Wave Platform / Computational Experience / Bibliography / Author's Biography

Download or read book 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems MFI written by IEEE Staff and published by . This book was released on 2021-09-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference provides a medium to discuss advances and applications of fusion and integration methodologies The conference will include contributions in the areas of theory, sensors, algorithms, and applications

Download or read book Lagrangian Duality and Adiabatic Quantum Computation for Constrained Optimization Problems written by Einar Gabbassov and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Quantum Approximate Optimization Algorithm (QAOA) is a heuristic method for solving unconstrained binary optimization problems with a gate-based quantum computer. The QAOA consists of a particular quantum circuit architecture, together with a prescription for choosing the parameterization of the circuit. The first part of the thesis studies both the architecture and optimal parameterization of the QAOA circuit. After reviewing the necessary mathematical and physical background, we derive QAOA from scratch and discuss some of its properties. The second part of the thesis focuses on solving constrained combinatorial optimization problems in the setting of fault-tolerant quantum computation and presents a novel Lagrangian duality approach to Discretized Adiabatic Quantum Computation (DAQC). The proposed method allows for building highly resource-efficient and parallelizable quantum circuits. The thesis presents numerical evidence that demonstrates that the proposed approach gives the quadratic improvement in circuit complexity and evolution time over circuits derived from the traditional Quadratic Unconstrained Binary Optimization (QUBO) formalism. We illustrate our findings in the benchmark of the QUBO- and Lagrangian-based DAQC on the NP-complete 1D 0-1 knapsack problem.

Download or read book Graph Theory Adiabatic Quantum Computing Methods written by N.B. Singh and published by N.B. Singh. This book was released on with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Graph Theory: Adiabatic Quantum Computing Methods" explores the convergence of quantum computing and graph theory, offering a comprehensive examination of how quantum algorithms can tackle fundamental graph problems. From foundational concepts to advanced applications in fields like cryptography, machine learning, and network analysis, this book provides a clear pathway into the evolving landscape of quantum-enhanced graph algorithms. Designed for researchers, students, and professionals alike, it bridges theoretical insights with practical implementations, paving the way for innovative solutions in computational graph theory.

Download or read book Case Studies in Quantum Adiabatic Optimization written by David Nicholas Gosset and published by . This book was released on 2011 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum adiabatic optimization is a quantum algorithm for solving classical optimization problems (E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser. Quantum computation by adiabatic evolution, 2000. arXiv:quant-ph/0001106). The solution to an optimization problem is encoded in the ground state of a "problem Hamiltonian" Hp which acts on the Hilbert space of n spin 1/2 particles and is diagonal in the Pauli z basis. To produce this ground state, one first initializes the quantum system in the ground state of a different Hamiltonian and then adiabatically changes the Hamiltonian into Hp. Farhi et al suggest the interpolating Hamiltonian [mathematical formula] ... where the parameter s is slowly changed as a function of time between 0 and 1. The running time of this algorithm is related to the minimum spectral gap of H(s) for s E (0, 11. We study such transverse field spin Hamiltonians using both analytic and numerical techniques. Our approach is example-based, that is, we study some specific choices for the problem Hamiltonian Hp which illustrate the breadth of phenomena which can occur. We present I A random ensemble of 3SAT instances which this algorithm does not solve efficiently. For these instances H(s) has a small eigenvalue gap at a value s* which approaches 1 as n - oc. II Theorems concerning the interpolating Hamiltonian when Hp is "scrambled" by conjugating with a random permutation matrix. III Results pertaining to phase transitions that occur as a function of the transverse field. IV A new quantum monte carlo method which can be used to compute ground state properties of such quantum systems. We discuss the implications of our results for the performance of quantum adiabatic optimization algorithms.

Download or read book Adiabatic Quantum Computation and Quantum written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the native instruction set'' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a novel computing platform designed to solve NP-hard optimization problems. Starting with a 16-qubit prototype announced in 2007, the company has launched and sold increasingly larger models: the 128-qubit D-Wave One system was announced in 2010 and the 512-qubit D-Wave Two system arrived on the scene in 2013. A 1,000-qubit model is expected to be available in 2014. This monograph presents an introductory overview of this unusual and rapidly developing approach to computation. We start with a survey of basic principles of quantum computation and what is known about the AQC model and the QA algorithm paradigm. Next we review the D-Wave technology stack and discuss some challenges to building and using quantum computing systems at a commercial scale. The last chapter reviews some experimental efforts to understand the properties and capabilities of these unusual platforms. The discussion throughout is aimed at an audience of computer scientists with little background in quantum computation or in physics.

Download or read book A Practical Guide to Quantum Machine Learning and Quantum Optimization written by Elias F. Combarro and published by Packt Publishing Ltd. This book was released on 2023-03-31 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Quantum Spin Glasses Annealing and Computation written by Shu Tanaka and published by Cambridge University Press. This book was released on 2017-05-04 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum annealing is a new-generation tool of information technology, which helps in solving combinatorial optimization problems with high precision, based on the concepts of quantum statistical physics. Detailed discussion on quantum spin glasses and its application in solving combinatorial optimization problems is required for better understanding of quantum annealing concepts. Fulfilling this requirement, the book highlights recent development in quantum spin glasses including Nishimori line, replica method and quantum annealing methods along with the essential principles. Separate chapters on simulated annealing, quantum dynamics and classical spin models are provided for enhanced learning. Important topics including adiabatic quantum computers and quenching dynamics are discussed in detail. This text will be useful for students of quantum computation, quantum information, statistical physics and computer science.

Download or read book John Babikian Quantum Computing written by John Babikian and published by John Babikian. This book was released on 2016-02-25 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the realm of blockchain technology, John Babikian, a notable lawyer and computer engineer, has carved out a distinct identity for himself. With several years of involvement in the industry, he has not only garnered attention but has also made substantial investments in various blockchain projects. Delving into the essence of blockchain technology and John's profound interest in it, this article aims to unravel the dynamics of this rapidly expanding industry and the notable contributions made by John Babikian. John Babikian is also a renowned author, researcher, and speaker specializing in cutting-edge technology and its transformative impact on various aspects of life. With a passion for understanding and harnessing the power of innovation, John Babikian academic background in computer science and engineering along with law has provided him with a strong foundation for his work in quantum computing. Over the years, he has conducted research, developed applications, and collaborated with leading experts in the world.

Download or read book Advanced Information Networking and Applications written by Leonard Barolli and published by Springer Nature. This book was released on with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Information and Computation for Chemistry Volume 154 written by Sabre Kais and published by John Wiley & Sons. This book was released on 2014-01-31 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the intersection of quantum information and chemical physics The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics. This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science community. It examines topics in quantum computation and quantum information that are related to or intersect with key topics in chemical physics. The reviews address both what chemistry can contribute to quantum information and what quantum information can contribute to the study of chemical systems, surveying both theoretical and experimental quantum information research within the field of chemical physics. With contributions from an international team of leading experts, Volume 154 offers seventeen detailed reviews, including: Introduction to quantum information and computation for chemistry Quantum computing approach to non-relativistic and relativistic molecular energy calculations Quantum algorithms for continuous problems and their applications Photonic toolbox for quantum simulation Vibrational energy and information transfer through molecular chains Tensor networks for entanglement evolution Reviews published in Advances in Chemical Physics are typically longer than those published in journals, providing the space needed for readers to fully grasp the topic: the fundamentals as well as the latest discoveries, applications, and emerging avenues of research. Extensive cross-referencing enables readers to explore the primary research studies underlying each topic.

Download or read book Adiabatic Processes Noise and Stochastic Algorithms for Quantum Computing and Quantum Simulation written by Guanglei Xu and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid developments in experiments provide promising platforms for realising quantum computation and quantum simulation. This, in turn, opens new possibilities for developing useful quantum algorithms and explaining complex many-body physics. The advantages of quantum computation have been demonstrated in a small range of subjects, but the potential applications of quantum algorithms for solving complex classical problems are still under investigation. Deeper understanding of complex many-body systems can lead to realising quantum simulation to study systems which are inaccessible by other means.This thesis studies different topics of quantum computation and quantum simulation.The first one is improving a quantum algorithm in adiabatic quantum computing, which can be used to solve classical problems like combinatorial optimisation problems and simulated annealing. We are able to reach a new bound of time cost for the algorithm which has a potential to achieve a speed up over standard adiabatic quantum computing. The second topic is to understand the amplitude noise in optical lattices in the context of adiabatic state preparation and the thermalisation of the energy introduced to the system. We identify regimes where introducing certain type of noise in experiments would improve the final fidelity of adiabatic state preparation, and demonstrate the robustness of the state preparation to imperfect noise implementations. We also discuss the competition between heating and dephasing effects, the energy introduced by non-adiabaticity and heating, and the thermalisation of the system after an application of amplitude noise on the lattice. The third topic is to design quantum algorithms to solve classical problems of fluid dynamics. We develop a quantum algorithm based around phase estimation that can be tailored to specific fluid dynamics problems and demonstrate a quantum speed up over classical Monte Carlo methods. This generates new bridge between quantum physics and fluid dynamics engineering, can be used to estimate the potential impact of quantum computers and provides feedback on requirements for implementing quantum algorithms on quantum devices.

Download or read book Quantum Machine Learning written by Siddhartha Bhattacharyya and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum-enhanced machine learning refers to quantum algorithms that solve tasks in machine learning, thereby improving a classical machine learning method. Such algorithms typically require one to encode the given classical dataset into a quantum computer, so as to make it accessible for quantum information processing. After this, quantum information processing routines can be applied and the result of the quantum computation is read out by measuring the quantum system. While many proposals of quantum machine learning algorithms are still purely theoretical and require a full-scale universal quantum computer to be tested, others have been implemented on small-scale or special purpose quantum devices.

Download or read book Computational Drug Discovery written by Vasanthanathan Poongavanam and published by John Wiley & Sons. This book was released on 2024-01-19 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Drug Discovery A comprehensive resource that explains a wide array of computational technologies and methods driving innovation in drug discovery Computational Drug Discovery: Methods and Applications (2 volume set) covers a wide range of cutting-edge computational technologies and computational chemistry methods that are transforming drug discovery. The book delves into recent advances, particularly focusing on artificial intelligence (AI) and its application for protein structure prediction, AI-enabled virtual screening, and generative modeling for compound design. Additionally, it covers key technological advancements in computing such as quantum and cloud computing that are driving innovations in drug discovery. Furthermore, dedicated chapters that addresses the recent trends in the field of computer aided drug design, including ultra-large-scale virtual screening for hit identification, computational strategies for designing new therapeutic modalities like PROTACs and covalent inhibitors that target residues beyond cysteine are also presented. To offer the most up-to-date information on computational methods utilized in computational drug discovery, it covers chapters highlighting the use of molecular dynamics and other related methods, application of QM and QM/MM methods in computational drug design, and techniques for navigating and visualizing the chemical space, as well as leveraging big data to drive drug discovery efforts. The book is thoughtfully organized into eight thematic sections, each focusing on a specific computational method or technology applied to drug discovery. Authored by renowned experts from academia, pharmaceutical industry, and major drug discovery software providers, it offers an overview of the latest advances in computational drug discovery. Key topics covered in the book include: Application of molecular dynamics simulations and related approaches in drug discovery The application of QM, hybrid approaches such as QM/MM, and fragment molecular orbital framework for understanding protein-ligand interactions Adoption of artificial intelligence in pre-clinical drug discovery, encompassing protein structure prediction, generative modeling for de novo design, and virtual screening. Techniques for navigating and visualizing the chemical space, along with harnessing big data to drive drug discovery efforts. Methods for performing ultra-large-scale virtual screening for hit identification. Computational strategies for designing new therapeutic models, including PROTACs and molecular glues. In silico ADMET approaches for predicting a variety of pharmacokinetic and physicochemical endpoints. The role of computing technologies like quantum computing and cloud computing in accelerating drug discovery This book will provide readers an overview of the latest advancements in computational drug discovery and serve as a valuable resource for professionals engaged in drug discovery.

Download or read book Advances in Chemical Physics Volume 155 written by Stuart A. Rice and published by John Wiley & Sons. This book was released on 2014-03-18 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cutting edge of research in chemical physics Each volume of the Advances in Chemical Physics series discusses aspects of the state of diverse subjects in chemical physics and related fields, with chapters written by top researchers in the field. Reviews published in Advances in Chemical Physics are typically longer than those published in journals, providing the space needed for readers to fully grasp the topic, including fundamentals, latest discoveries, applications, and emerging avenues of research. Volume 155 explores: Modeling viral capsid assembly Charges at aqueous interfaces, including the development of computational approaches in direct contact with the experiment Theory and simulation advances in solute precipitate nucleation A computational viewpoint of water in the liquid state Construction of energy functions for lattice heteropolymer models, including efficient encodings for constraint satisfaction programming and quantum annealing Advances in Chemical Physics is ideal for introducing novices to topics in chemical physics and serves as the perfect supplement to any advanced graduate class devoted to its study. The series also provides the foundation needed for more experienced researchers to advance research studies.