Download or read book Adiabatic Quantum Computing with QUBO Formulations written by Richard Hua and published by . This book was released on 2016 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study two types of problems in this thesis, graph covering problems including the Dominating Set and Edge Cover which are classic combinatorial problems and the Graph Isomorphism Problem with several of its variations. For each of the problems, we provide efficient quadratic unconstrained binary optimization (QUBO) formulations suitable for adiabatic quantum computers, which are viewed as a real-world enhanced model of simulated annealing. The number of qubits (dimension of QUBO matrices) required to solve the graph covering problems are O(n + n lg n) and O(m + n lg n) respectively, where n is the number of vertices and m is the number of edges. We also extend our formulations for the Minimum Vertex- Weighted Dominating Set problem and Minimum Edge-Weighted Edge Cover problem. For the Graph Isomorphism Problem, we provide two QUBO formulation through two approaches both requiring O(n2) variables. We also provide several different formulations for two extensions of the Graph Isomorphism Problems each requiring a different number of variables ranging from O(n1n2) to O((n1 + 1)n2). We also provide some experimental results using a D-Wave 2X quantum computer with 1098 active qubit-coupled processors on the problems studied here for a selection of known common graphs.

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 Formulating Mixed Dominating Set Problems for Adiabatic Quantum Computers written by M. J. Dinneen and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this paper, we present efficient quadratic unconstrained binary optimization(QUBO) formulations for the mixed dominating set and the weighted mixed dominating set problems, which are both NP-hard. By using a D-Wave 2X quantum computerwith 1098 active qubits, the QUBO formulation of the unweighted mixed dominatingset is tested on several small graphs. In every test graph, 30K samples were takenon the D-Wave computer in two different execution modes (with and without postprocessing optimization). The experimental results achieved optimal answers in themajority of the cases. The correctness of the formulations are proven, establishingempirical evidence that our formulation and their implementations are correct. Keywords: Adiabatic quantum computing; Quadratic Unconstrained Binary Optimization; Ising/QUBO formulation; Mixed dominating set; Weighted mixed dominating set"--Page 1.

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 Adiabatic Quantum Computation and Quantum Annealing written by Catherine C. McGeoch and published by Morgan & Claypool Publishers. This book was released on 2014-07-01 with total page 95 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.

Download or read book Solving the Bounded Depth Steiner Tree Problem Using an Adiabatic Quantum Computer written by Kai Liu and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book QUBO Formulations for the Graph Isomorphism Problem and Related Problems written by Cristian Calude and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "We present and compare various methods to construct efficient QUBO formulations for the Graph Isomorphism Problem—one of a very few problems in NP that is neither known to be solvable in polynomial time nor NP-complete—and two related Subgraph Isomorphism Problems that are NP-hard. Experimental results on two QUBO formulations of the Graph Isomorphism Problem suggest that our direct formulation is more practical than the others with respect to running on the D-Wave architecture.Keywords: Adiabatic quantum computing, Quadratic Unconstrained Binary Optimization, Chimera graph, Graph Isomorphism Problem, Subgraph Isomorphism Problem."--Page 1.

Download or read book Solving the Hamiltonian Cycle Problem Using a Quantum Computer written by M. J. Dinneen and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "We review existing quantum computational methods for solving the Hamiltonian cycle problem in different computational frameworks such as quantum circuits, quantum walks and adiabatic quantum computation. Then we present a QUBO (quadratic unconstrained binary optimization) formulation, which is suitable for the adiabatic quantum computation for a D-Wave architecture. Further, we derive a physical Hamiltonian from the QUBO formulation and discuss its adequateness in the adiabatic frame-work. Finally, we discuss the complexity of running the Hamiltonian cycle QUBO on a D-Wave quantum computer, and compare it with existing quantum computational methods."--Page 1.

Download or read book Improved QUBO Formulations for D Wave Quantum Computing written by Alexander Fowler and published by . This book was released on 2017 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Computing is one of the most exciting and potentially societychanging elds in contemporary science and engineering research. While the potential power of quantum computers has been known since 1981, scepticism in their long-term practical capabilities has been rife due to limited success in physically building scalable quantum computers. Recent breakthroughs have increased hope however; chief among these was the development of a series of quantum computers by D-Wave Systems | a Canadian specialist quantum computing company. To solve a problem on a D-Wave device, it must be formulated in QUBO or Ising model form. The key determinants of a formulation's e cacy are the number of variables it uses, and its density. The smaller these are the better. In this thesis, we signi cantly improve the QUBO formulations for ve NPhard graph problems in this regard. For four of these problems featuring a graph with jV j vertices, O(jV j2)-variable and O(jV j3)-density formulations are given in place of preceding formulations which at-best used O(jV j3) variables and O(jV j4) density. We improve one other problem's formulation so it uses O(jV j3) variables and O(jV j5) density; its previous-best used O(jV j3 log(jV j)2)) variables and O(jV j6 log(jV j)4) density.

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 Quantum Technology and Optimization Problems written by Sebastian Feld and published by Springer. This book was released on 2019-03-13 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Multiprocessor Scheduling for Real Time Systems written by Sanjoy Baruah and published by Springer. This book was released on 2015-01-02 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of both theoretical and pragmatic aspects of resource-allocation and scheduling in multiprocessor and multicore hard-real-time systems. The authors derive new, abstract models of real-time tasks that capture accurately the salient features of real application systems that are to be implemented on multiprocessor platforms, and identify rules for mapping application systems onto the most appropriate models. New run-time multiprocessor scheduling algorithms are presented, which are demonstrably better than those currently used, both in terms of run-time efficiency and tractability of off-line analysis. Readers will benefit from a new design and analysis framework for multiprocessor real-time systems, which will translate into a significantly enhanced ability to provide formally verified, safety-critical real-time systems at a significantly lower cost.

Download or read book Quantum Information Processing and Quantum Error Correction written by Ivan Djordjevic and published by Academic Press. This book was released on 2012-04-16 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice. This book is ideal for the electronics, photonics and computer engineer who requires an easy- to-understand foundation on the principles of quantum information processing and quantum error correction, together with insight into how to develop quantum electronic and photonic circuits. Readers of this book will be ready for further study in this area, and will be prepared to perform independent research. The reader completed the book will be able design the information processing circuits, stabilizer codes, Calderbank-Shor-Steane (CSS) codes, subsystem codes, topological codes and entanglement-assisted quantum error correction codes; and propose corresponding physical implementation. The reader completed the book will be proficient in quantum fault-tolerant design as well. Unique Features Unique in covering both quantum information processing and quantum error correction - everything in one book that an engineer needs to understand and implement quantum-level circuits. Gives an intuitive understanding by not assuming knowledge of quantum mechanics, thereby avoiding heavy mathematics. In-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits. Provides the right balance among the quantum mechanics, quantum error correction, quantum computing and quantum communication. Dr. Djordjevic is an Assistant Professor in the Department of Electrical and Computer Engineering of College of Engineering, University of Arizona, with a joint appointment in the College of Optical Sciences. Prior to this appointment in August 2006, he was with University of Arizona, Tucson, USA (as a Research Assistant Professor); University of the West of England, Bristol, UK; University of Bristol, Bristol, UK; Tyco Telecommunications, Eatontown, USA; and National Technical University of Athens, Athens, Greece. His current research interests include optical networks, error control coding, constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum error correction. He presently directs the Optical Communications Systems Laboratory (OCSL) within the ECE Department at the University of Arizona. Provides everything an engineer needs in one tutorial-based introduction to understand and implement quantum-level circuits Avoids the heavy use of mathematics by not assuming the previous knowledge of quantum mechanics Provides in-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits

Download or read book Innovations for Community Services written by Udo R. Krieger and published by Springer Nature. This book was released on 2023-08-31 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 23rd International Conference on Innovations for Community Services, I4CS 2023, held in Bamberg, Germany, in September 2023. The 15 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 38 submissions. One invited talk in full-paper length is included in the volume. The papers focus on topics such as distributed architectures and frameworks for community services, advanced applications regarding digital communities on the move, new trends of socialization covering the ambient work and living of digital societies.

Download or read book Quantum Computing and Quantum Bits in Mesoscopic Systems written by Anthony Leggett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information science is a new field of science and technology which requires the collaboration of researchers coming from different fields of physics, mathematics, and engineering: both theoretical and applied. Quantum Computing and Quantum Bits in Mesoscopic Systems addresses fundamental aspects of quantum physics, enhancing the connection between the quantum behavior of macroscopic systems and information theory. In addition to theoretical quantum physics, the book comprehensively explores practical implementation of quantum computing and information processing devices. On the experimental side, this book reports on recent and previous observations of quantum behavior in several physical systems, coherently coupled Bose-Einstein condensates, quantum dots, superconducting quantum interference devices, Cooper pair boxes, and electron pumps in the context of the Josephson effect. In these systems, the book discusses all required steps, from fabrication through characterization to the final basic implementation for quantum computing.

Download or read book Quantum Computing and Information written by Dr. Peter Y. Lee and published by Polaris QCI Publishing. This book was released on 2024-03-14 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlock the Potential of Quantum Computing This expertly crafted guide demystifies the complexities of quantum computing through a progressive teaching method, making it accessible to students and newcomers alike. Features Explores quantum systems, gates and circuits, entanglement, algorithms, and more. Unique 'scaffolding approach' for easy understanding. Ideal for educators, students, and self-learners. Authors Dr. Peter Y. Lee (Ph.D., Princeton University) – Expert in quantum nanostructures, extensive teaching experience. Dr. Huiwen Ji (Ph.D., Princeton University) – Solid background in quantum chemistry, award-winning researcher. Dr. Ran Cheng (Ph.D., University of Texas at Austin) – Specializes in condensed matter theory, award-winning physicist.

Download or read book Experience with Quantum Annealing Computation written by Catherine McGeoch and published by Frontiers Media SA. This book was released on 2024-09-18 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen four generations of quantum annealing processors, with qubit counts increasing from 512 on the D-Wave Two (released in 2013), to over 5000 on Advantage processors available in 2023. During this time, expanding access for researchers has sparked enormous growth in publications and in the body of knowledge surrounding capabilities, applications, and best practices in use of these novel computing systems. This Research Topic will invite submissions on all aspects of empirical experience with annealing-based quantum computers. The intention is to present a broad survey of the current state of knowledge about quantum annealing hardware, performance, software infrastructures, and applications.