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Quantum Walks And Search Algorithms

Author: Renato Portugal
Publisher: Springer Science & Business Media
ISBN: 146146336X
Size: 28.14 MB
Format: PDF, Docs
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This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operator Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting distribution and mixing time Spatial search algorithms, with emphasis on the abstract search algorithm (the two-dimensional lattice is used as an example) Szedgedy's quantum-walk model and a natural definition of quantum hitting time (the complete graph is used as an example) The reader will benefit from the pedagogical aspects of the book, learning faster and with more ease than would be possible from the primary research literature. Exercises and references further deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks are also provided.

Physical Implementation Of Quantum Walks

Author: Kia Manouchehri
Publisher: Springer Science & Business Media
ISBN: 3642360149
Size: 20.32 MB
Format: PDF
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Given the extensive application of random walks in virtually every science related discipline, we may be at the threshold of yet another problem solving paradigm with the advent of quantum walks. Over the past decade, quantum walks have been explored for their non-intuitive dynamics, which may hold the key to radically new quantum algorithms. This growing interest has been paralleled by a flurry of research into how one can implement quantum walks in laboratories. This book presents numerous proposals as well as actual experiments for such a physical realization, underpinned by a wide range of quantum, classical and hybrid technologies.

Search Algorithms And Applications

Author: Nashat Mansour
Publisher: BoD – Books on Demand
ISBN: 9533071567
Size: 37.88 MB
Format: PDF, ePub, Docs
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Search algorithms aim to find solutions or objects with specified properties and constraints in a large solution search space or among a collection of objects. A solution can be a set of value assignments to variables that will satisfy the constraints or a sub-structure of a given discrete structure. In addition, there are search algorithms, mostly probabilistic, that are designed for the prospective quantum computer. This book demonstrates the wide applicability of search algorithms for the purpose of developing useful and practical solutions to problems that arise in a variety of problem domains. Although it is targeted to a wide group of readers: researchers, graduate students, and practitioners, it does not offer an exhaustive coverage of search algorithms and applications. The chapters are organized into three parts: Population-based and quantum search algorithms, Search algorithms for image and video processing, and Search algorithms for engineering applications.

Computer Science Theory And Applications

Author: Farid M. Ablaev
Publisher: Springer
ISBN: 3642131824
Size: 10.20 MB
Format: PDF, Mobi
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Annotation This book constitutes the proceedings of the 5th International Computer Science Symposium in Russia, CSR 2010, held in Kazan, Russia, in June 2010. The 30 papers presented were carefully reviewed and selected from 62 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.

Quantum Algorithms Via Linear Algebra

Author: Richard J. Lipton
Publisher: MIT Press
ISBN: 0262028395
Size: 12.61 MB
Format: PDF, ePub
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Quantum computing explained in terms of elementary linear algebra, emphasizing computation and algorithms and requiring no background in physics.

Solid State Quantum Computing

Author: Hsi-Sheng Goan
Publisher: American Inst. of Physics
ISBN: 9780735406056
Size: 15.44 MB
Format: PDF
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The IWSSQC 2008 covered all aspects of solid-state implementations for quantum information processing, and topics that were addressed included both theoretical and experimental attempts. The specific topics covered in these proceedings include superconducting circuit QED, quantum measurement of solid-state qubits, entanglement in solid-state devices, semiconductor donor spin quantum computing, decoherence and disentanglement in quantum open systems, and mesoscopic electron transport. It provides a unique opportunity for experts and beginners to gain insight into the rapidly growing field of Quantum Information Science. It is also useful as a reference book for graduate students and researchers in physics and engineering.

A Primer On Quantum Computing

Author: Franklin de Lima Marquezino
Publisher: Springer
ISBN: 9783030190651
Size: 34.47 MB
Format: PDF, Mobi
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This book is about quantum computing and quantum algorithms. The book starts with a chapter introducing the basic rules of quantum mechanics and how they can be used to build quantum circuits and perform computations. Further, Grover's algorithm is presented for unstructured search discussing its consequences and applications. Next, important techniques are discussed such as Quantum Fourier Transform and quantum phase estimation. Finally, Shor's algorithm for integer factorization is explained. At last, quantum walks are explained in detail covering both the discrete and continuous time models,and applications of this techniques are described for the design and analyses of quantum algorithms.