Dancing with qubits : how quantum computing works and how it can change the world / Robert S. Sutor.

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
Contents: 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
Contents: 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
Contents: 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
Contents: 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

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