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Preface 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 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 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 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 5 Dimensions 6 What Do You Mean "Probably"? II Quantum Computing 7 One Qubit 8 Two Qubits, Three 9 Wirina Up the Circuits 10 From Circuits to Algorithms 11 Getting Physical 12 Questions about the Future Afterword Appendices A Quick Reference B Symbols C Notices D Production Notes Other Books You May Enjoy Index