Introduction to Quantum Algorithms via Linear Algebra, second edition

Name: Introduction to Quantum Algorithms via Linear Algebra, second edition
Brand: MIT Press
Price: 43.99 EUR
Availability: OnlineOnly

Richard J. Lipton Kenneth W. Regan(Autor*in)

MIT Press

Erschienen am 6. April 2021

280 Seiten

E-Book

ePUB mit Adobe-DRM

Systemvoraussetzungen

978-0-262-36215-3 (ISBN)

43,99 €inkl. 7% MwSt.

Systemvoraussetzungen

für ePUB mit Adobe-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Personen

Inhalt

Intro
Title Page
Copyright
Dedication
Table of Contents
Preface to the First Edition
Preface to the Second Edition
Acknowledgments
I. Essential Algorithms
1. Introduction
1.1. The Model
1.2. The Space and the States
1.3. The Operations
1.4. Where Is the Input?
1.5. What Exactly Is the Output?
1.6. Summary and Notes
2. Numbers and Strings
2.1. Asymptotic Notation
2.2. Problems
2.3. Selected Answers
2.4. Summary and Notes
3. Basic Linear Algebra
3.1. Hilbert Spaces
3.2. Products of Spaces and Tensor Products
3.3. Matrices
3.4. Complex Spaces and Inner Products
3.5. Tensor Products of Matrices
3.6. Matrices, Graphs, and Sums over Paths
3.7. Problems
3.8. Selected Answers
3.9. Summary and Notes
4. Boolean Functions, Quantum Bits, and Feasibility
4.1. Feasible Boolean Functions
4.2. An Example
4.3. Quantum Representation of Boolean Arguments
4.4. Quantum Feasibility
4.5. Examples of Quantum Circuits
4.6. Problems
4.7. Selected Answers
4.8. Summary and Notes
5. Special Matrices
5.1. Hadamard Matrices
5.2. Fourier Matrices
5.3. Reversible Computation and Permutation Matrices
5.4. Feasible Diagonal Matrices
5.5. Reflections
5.6. Problems
5.7. Selected Answers
5.8. Summary and Notes
6. Tricks
6.1. Start Vectors
6.2. Controlling and Copying Base States
6.3. The Copy-Uncompute Trick
6.4. Superposition Tricks
6.5. Flipping a Switch
6.6. Measurement Tricks
6.7. Partial Transforms
6.8. Problems
6.9. Selected Answers
6.10. Summary and Notes
7. Phil's Algorithm
7.1. The Algorithm
7.2. The Analysis
7.3. An Example
7.4. A Two-Qubit Example
7.5. Phil Measures Up
7.6. Quantum Mazes Versus Circuits Versus Matrices
7.7. Problems
7.8. Selected Answers
7.9. Summary and Notes
8. Deutsch's Algorithm
8.1. The Algorithm
8.2. The Analysis
8.3. Superdense Coding and Teleportation
8.4. Problems
8.5. Summary and Notes
9. The Deutsch-Jozsa Algorithm
9.1. The Algorithm
9.2. The Analysis
9.3. Problems
9.4. Summary and Notes
10. Simon's Algorithm
10.1. The Algorithm
10.2. The Analysis
10.3. Problems
10.4. Summary and Notes
11. Shor's Algorithm
11.1. Strategy
11.2. Good Numbers
11.3. The Quantum Part of the Algorithm
11.4. Analysis of the Quantum Part
11.5. Probability of a Good Number
11.6. Using a Good Number
11.7. Continued Fractions
11.8. Problems
11.9. Summary and Notes
12. Factoring Integers
12.1. Some Basic Number Theory
12.2. Periods Give the Order
12.3. Factoring
12.4. Problems
12.5. Summary and Notes
13. Grover's Algorithm
13.1. The Algorithm
13.2. The Analysis
13.3. The General Case, with k Unknown
13.4. Problems
13.5. Summary and Notes
II. Advanced Algorithms
14. Physics of Quantum Computing
14.1. Coherence and Cards
14.2. Dirac Notation
14.3. What Are Qubits?
14.4. Transformations and the Bloch Sphere
14.5. Measurements of Pure States
14.6. Mixed States and Decoherence
14.6.1. Trace and POVM
14.6.2. Partial Traces
14.6.3. Depolarizing and Dephasing
14.7. The CHSH Game
14.7.1. Classical Case
14.7.2. Quantum Case
14.7.3. Quantum Case Redux
14.8. Quantum Supremacy
14.9. Problems
14.10. Summary and Notes
15. Phase Estimation and Approximate Counting
15.1. Grover Approximate Counting
15.2. The Algorithm
15.3. The Analysis
15.4. Problems
15.5. Summary and Notes
16. Quantum Walks
16.1. Classical Random Walks
16.2. Random Walks and Matrices
16.3. An Encoding Nicety
16.4. Defining Quantum Walks
16.5. Interference and Diffusion
16.6. The Big Factor
16.7. Problems
16.8. Summary and Notes
17. Quantum Walk Search Algorithms
17.1. Search in Big Graphs
17.2. General Quantum Walk for Graph Search
17.3. Specifying the Generic Walk
17.4. Adding the Data
17.5. Tool Kit Theorem for Quantum Walk Search
17.5.1. The Generic Algorithm
17.5.2. The Generic Analysis
17.6. Grover Search as Generic Walk
17.7. Element Distinctness
17.8. Subgraph Triangle Incidence
17.9. Finding a Triangle
17.10. Evaluating Formulas and Playing Chess
17.11. Problems
17.12. Summary and Notes
18. Quantum Matrix Algorithms
18.1. Hermitian Matrices and Nature's Algorithm
18.2. The HHL Algorithm
18.3. Error Analysis
18.4. Improvements
18.5. Problems
18.6. Summary and Notes
19. Quantum Computation and BQP
19.1. The Class BQP
19.2. Equations, Solutions, and Complexity
19.3. A Circuit-Labeling Algorithm
19.4. Sums over Paths and Polynomial Roots
19.5. The Additive Polynomial Simulation
19.6. Bounding BQP
19.7. Logical Description of Quantum Systems
19.8. Problems
19.9. Summary and Notes
20. Beyond
20.1. Reviewing the Algorithms
20.2. Some Further Topics
20.3. The "Quantum" in the Algorithms
References
Index

Systemvoraussetzungen

Als PDF speichern Als Link merken