Quantum Walks and Search Algorithms
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Beschreibung
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 operater
- 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.
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.
Serves as the first textbook on Quantum Walks, which is an active area of research with growing interest Features exercises and guidelines in each chapter to use or develop computer programs for simulation of quantum walks Contains topics that students will learn faster and with more ease than would be possible from the primary research literature Includes supplementary material: sn.pub/extras
Autor*in
Renato Portugal
Themen in »Quantum Walks and Search Algorithms«
Abstract Search Algorithms Continuous-time Algorithms Discrete-time Quantum Walks Grover’s Algorithm Quantum Algorithms Quantum Hitting Times Quantum Markov Chains Quantum Mixing Times Quantum Search Algorithms Quantum Walks on Graphs Szegedy’s Quantum-walk Model
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From the reviews:
“The reviewed book is a pedagogically oriented survey of the main results regarding quantum walks and quantum search algorithms. … The book is nicely written, the concepts are introduced naturally, and many meaningful connections between them are highlighted. The author proposes a series of exercises that help the reader get some working experience with the presented concepts, facilitating a better understanding. Each chapter ends with a discussion of further references, pointing the reader to major results on the topics presented in the respective chapter.” (Florin Manea, zbMATH, Vol. 1275, 2014)()