7.3 The complex math and physics of a single qubit

Includes bibliographical references and index

Cover -- Title Page -- Copyright -- Packt page -- Dedication -- Contributors -- Contents -- List of Figures -- Preface -- Chapter 1: Why Quantum Computing? -- 1.1 The mysterious quantum bit -- 1.2 I'm awake! -- 1.3 Why quantum computing is different -- 1.4 Applications to artificial intelligence -- 1.5 Applications to financial services -- 1.6 What about cryptography? -- 1.7 Summary -- I Foundations -- Chapter 2: They're Not Old, They're Classics -- 2.1 What's inside a computer? -- 2.2 The power of two -- 2.3 True or false? -- 2.4 Logic circuits -- 2.5 Addition, logically

2.6 Algorithmically speaking -- 2.7 Growth, exponential and otherwise -- 2.8 How hard can that be? -- 2.8.1 Sorting -- 2.8.2 Searching -- 2.9 Summary -- Chapter 3: More Numbers than You Can Imagine -- 3.1 Natural numbers -- 3.2 Whole numbers -- 3.3 Integers -- 3.4 Rational numbers -- 3.4.1 Fractions -- 3.4.2 Getting formal again -- 3.5 Real numbers -- 3.5.1 Decimals -- 3.5.2 Irrationals and limits -- 3.5.3 Binary forms -- 3.5.4 Continued fractions -- 3.6 Structure -- 3.6.1 Groups -- 3.6.2 Rings -- 3.6.3 Fields -- 3.6.4 Even greater abstraction -- 3.7 Modular arithmetic -- 3.8 Doubling down

3.9 Complex numbers, algebraically -- 3.9.1 Arithmetic -- 3.9.2 Conjugation -- 3.9.3 Units -- 3.9.4 Polynomials and roots -- 3.10 Summary -- Chapter 4: Planes and Circles and Spheres, Oh My -- 4.1 Functions -- 4.2 The real plane -- 4.2.1 Moving to two dimensions -- 4.2.2 Distance and length -- 4.2.3 Geometric figures in the real plane -- 4.2.4 Exponentials and logarithms -- 4.3 Trigonometry -- 4.3.1 The fundamental functions -- 4.3.2 The inverse functions -- 4.3.3 Additional identities -- 4.4 From Cartesian to polar coordinates -- 4.5 The complex ̀̀plane'' -- 4.6 Real three dimensions

4.7 Summary -- Chapter 5: Dimensions -- 5.1 R2 and C2 -- 5.2 Vector spaces -- 5.3 Linear maps -- 5.3.1 Algebraic structure of linear transformations -- 5.3.2 Example linear transformations on R2 -- 5.4 Matrices -- 5.4.1 Notation and terminology -- 5.4.2 Matrices and linear maps -- 5.5 Matrix algebra -- 5.5.1 Arithmetic of general matrices -- 5.5.2 Arithmetic of square matrices -- 5.6 Cartesian products -- 5.7 Length and preserving it -- 5.7.1 Dot products -- 5.7.2 Inner products -- 5.7.3 Euclidean norm -- 5.7.4 Reflections again -- 5.7.5 Unitary transformations

5.7.6 Systems of linear equations -- 5.8 Change of basis -- 5.9 Eigenvectors and eigenvalues -- 5.10 Direct sums -- 5.11 Homomorphisms -- 5.11.1 Group homomorphisms -- 5.11.2 Ring and field homomorphisms -- 5.11.3 Vector space homomorphisms -- 5.12 Summary -- Chapter 6: What Do You Mean ""Probably""? -- 6.1 Being discrete -- 6.2 More formally -- 6.3 Wrong again? -- 6.4 Probability and error detection -- 6.5 Randomness -- 6.6 Expectation -- 6.7 Markov and Chebyshev go to the casino -- 6.8 Summary -- II Quantum Computing -- Chapter 7: One Qubit -- 7.1 Introducing quantum bits -- 7.2 Bras and kets

Available to OhioLINK libraries

Explore the principles and practicalities of quantum computing Key Features Discover how quantum computing works and delve into the math behind it with this quantum computing textbook Learn how it may become the most important new computer technology of the century Explore the inner workings of quantum computing technology to quickly process complex cloud data and solve problems Book Description Quantum computing is making us change the way we think about computers. Quantum bits, a.k.a. qubits, can make it possible to solve problems that would otherwise be intractable with current computing technology. Dancing with Qubits is a quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. From there it moves on to a fuller description of classical computing and the mathematical underpinnings necessary to understand such concepts as superposition, entanglement, and interference. Next up is circuits and algorithms, both basic and more sophisticated. It then nicely moves on to provide a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments will affect you. Really understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is introduced and explained thoroughly, in clear English with helpful examples. What you will learn See how quantum computing works, delve into the math behind it, what makes it different, and why it is so powerful with this quantum computing textbook Discover the complex, mind-bending mechanics that underpin quantum systems Understand the necessary concepts behind classical and quantum computing Refresh and extend your grasp of essential mathematics, computing, and quantum theory Explore the main applications of quantum computing to the fields of scientific computing, AI, and elsewhere Examine a detailed overview of qubits, quantum circuits, and quantum algorithm Who this book is for Dancing with Qubits is a quantum computing textbook for those who want to deeply explore the inner workings of quantum computing. This entails some sophisticated mathematical exposition and is therefore best suited for those with a healthy interest in mathematics, physics, engineering, and comput..