Introduction to Quantum Computing

ISBN-10: 019857049X
ISBN-13: 9780198570493
Edition: 2006
List price: $65.00 Buy it from $19.22
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Description: This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning  More...

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Book details

List price: $65.00
Copyright year: 2006
Publisher: Oxford University Press, Incorporated
Publication date: 1/18/2007
Binding: Paperback
Pages: 288
Size: 6.25" wide x 9.25" long x 0.50" tall
Weight: 0.792
Language: English

This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the necessary material is reviewed in the text.

Preface
Acknowledgements
Introduction and Background
Overview
Computers and the Strong Church-Turing Thesis
The Circuit Model of Computation
A Linear Algebra Formulation of the Circuit Model
Reversible Computation
A Preview of Quantum Physics
Quantum Physics and Computation
Linear Algebra and the Dirac Notation
The Dirac Notation and Hilbert Spaces
Dual Vectors
Operators
The Spectral Theorem
Functions of Operators
Tensor Products
The Schmidt Decomposition Theorem
Some Comments on the Dirac Notation
Qubits and the Framework of Quantum Mechanics
The State of a Quantum System
Time-Evolution of a Closed System
Composite Systems
Measurement
Mixed States and General Quantum Operations
Mixed States
Partial Trace
General Quantum Operations
A Quantum Model of Computation
The Quantum Circuit Model
Quantum Gates
1-Qubit Gates
Controlled-U Gates
Universal Sets of Quantum Gates
Efficiency of Approximating Unitary Transformations
Implementing Measurements with Quantum Circuits
Superdense Coding and Quantum Teleportation
Superdense Coding
Quantum Teleportation
An Application of Quantum Teleportation
Introductory Quantum Algorithms
Probabilistic Versus Quantum Algorithms
Phase Kick-Back
The Deutsch Algorithm
The Deutsch-Jozsa Algorithm
Simon's Algorithm
Algorithms with Superpolynomial Speed-Up
Quantum Phase Estimation and the Quantum Fourier Transform
Error Analysis for Estimating Arbitrary Phases
Periodic States
GCD, LCM, the Extended Euclidean Algorithm
Eigenvalue Estimation
Finding-Orders
The Order-Finding Problem
Some Mathematical Preliminaries
The Eigenvalue Estimation Approach to Order Finding
Shor's Approach to Order Finding
Finding Discrete Logarithms
Hidden Subgroups
More on Quantum Fourier Transforms
Algorithm for the Finite Abelian Hidden Subgroup Problem
Related Algorithms and Techniques
Algorithms Based on Amplitude Amplification
Grover's Quantum Search Algorithm
Amplitude Amplification
Quantum Amplitude Estimation and Quantum Counting
Searching Without Knowing the Success Probability
Related Algorithms and Techniques
Quantum Computational Complexity Theory and Lower Bounds
Computational Complexity
Language Recognition Problems and Complexity Classes
The Black-Box Model
State Distinguishability
Lower Bounds for Searching in the Black-Box Model: Hybrid Method
General Black-Box Lower Bounds
Polynomial Method
Applications to Lower Bounds
Examples of Polynomial Method Lower Bounds
Block Sensitivity
Examples of Block Sensitivity Lower Bounds
Adversary Methods
Examples of Adversary Lower Bounds
Generalizations
Quantum Error Correction
Classical Error Correction
The Error Model
Encoding
Error Recovery
The Classical Three-Bit Code
Fault Tolerance
Quantum Error Correction
Error Models for Quantum Computing
Encoding
Error Recovery
Three- and Nine-Qubit Quantum Codes
The Three-Qubit Code for Bit-Flip Errors
The Three-Qubit Code for Phase-Flip Errors
Quantum Error Correction Without Decoding
The Nine-Qubit Shor Code
Fault-Tolerant Quantum Computation
Concatenation of Codes and the Threshold Theorem
Tools for Analysing Probabilistic Algorithms
Solving the Discrete Logarithm Problem When the Order of a Is Composite
How Many Random Samples Are Needed to Generate a Group?
Finding r Given k/r for Random k
Adversary Method Lemma
Black-Boxes for Group Computations
Computing Schmidt Decompositions
General Measurements
Optimal Distinguishing of Two States
A Simple Procedure
Optimality of This Simple Procedure
Bibliography
Index

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