Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Complex Numbers
- 2 Complex Vector Spaces
- 3 The Leap from Classical to Quantum
- 4 Basic Quantum Theory
- 5 Architecture
- 6 Algorithms
- 7 Programming Languages
- 8 Theoretical Computer Science
- 9 Cryptography
- 10 Information Theory
- 11 Hardware
- Appendix A Historical Bibliography of Quantum Computing
- Appendix B Answers to Selected Exercises
- Appendix C Quantum Computing Experiments with MATLAB
- Appendix D Keeping Abreast of Quantum News: Quantum Computing on the Web and in the Literature
- Appendix E Selected Topics for Student Presentations
- Bibliography
- Index
2 - Complex Vector Spaces
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Complex Numbers
- 2 Complex Vector Spaces
- 3 The Leap from Classical to Quantum
- 4 Basic Quantum Theory
- 5 Architecture
- 6 Algorithms
- 7 Programming Languages
- 8 Theoretical Computer Science
- 9 Cryptography
- 10 Information Theory
- 11 Hardware
- Appendix A Historical Bibliography of Quantum Computing
- Appendix B Answers to Selected Exercises
- Appendix C Quantum Computing Experiments with MATLAB
- Appendix D Keeping Abreast of Quantum News: Quantum Computing on the Web and in the Literature
- Appendix E Selected Topics for Student Presentations
- Bibliography
- Index
Summary
Philosophy is written in that great book which continually lies open before us (I mean the Universe). But one cannot understand this book until one has learned to understand the language and to know the letters in which it is written. It is written in the language of mathematics, and the letters are triangles, circles and other geometric figures. Without these means it is impossible for mankind to understand a single word; without these means there is only vain stumbling in a dark labyrinth.
Galileo GalileiQuantum theory is cast in the language of complex vector spaces. These are mathematical structures that are based on complex numbers. We learned all that we need about such numbers in Chapter 1. Armed with this knowledge, we can now tackle complex vector spaces themselves.
Section 2.1 goes through the main example of a (finite-dimensional) complex vector space at tutorial pace. Section 2.2 provides formal definitions, basic properties, and more examples. Each of Section 2.3 through Section 2.7 discusses an advanced topic.
Reader Tip. The reader might find some of this chapter to be “just boring math.” If you are eager to leap into the quantum world, we suggest reading the first two or three sections before moving on to Chapter 3. Return to Chapter 2 as a reference when needed (using the index and the table of contents of find specific topics).
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- Quantum Computing for Computer Scientists , pp. 29 - 73Publisher: Cambridge University PressPrint publication year: 2008
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