| Preface | p. xi |
| A note on references | p. xv |
| Cbits and Qbits | p. 1 |
| What is a quantum computer? | p. 1 |
| Cbits and their states | p. 3 |
| Reversible operations on Cbits | p. 8 |
| Manipulating operations on Cbits | p. 11 |
| Qbits and their states | p. 17 |
| Reversible operations on Qbits | p. 19 |
| Circuit diagrams | p. 21 |
| Measurement gates and the Born rule | p. 23 |
| The generalized Born rule | p. 28 |
| Measurement gates and state preparation | p. 30 |
| Constructing arbitrary 1- and 2-Qbit states | p. 32 |
| Summary: Qbits versus Cbits | p. 34 |
| General features and some simple examples | p. 36 |
| The general computational process | p. 36 |
| Deutsch's problem | p. 41 |
| Why additional Qbits needn't mess things up | p. 46 |
| The Bernstein-Vazirani problem | p. 50 |
| Simon's problem | p. 54 |
| Constructing Toffoli gates | p. 58 |
| Breaking RSA encryption | p. 63 |
| Period finding, factoring, and cryptography | p. 63 |
| Number-theoretic preliminaries | p. 64 |
| RSA encryption | p. 66 |
| Quantum period finding: preliminary remarks | p. 68 |
| The quantum Fourier transform | p. 71 |
| Eliminating the 2-Qbit gates | p. 76 |
| Finding the period | p. 79 |
| Calculating the periodic function | p. 83 |
| The unimportance of small phase errors | p. 84 |
| Period finding and factoring | p. 86 |
| Searching with a quantum computer | p. 88 |
| The nature of the search | p. 88 |
| The Grover iteration | p. 89 |
| How to construct W | p. 94 |
| Generalization to several special numbers | p. 96 |
| Searching for one out of four items | p. 98 |
| Quantum error correction | p. 99 |
| The miracle of quantum error correction | p. 99 |
| A simplified example | p. 100 |
| The physics of error generation | p. 109 |
| Diagnosing error syndromes | p. 113 |
| The 5-Qbit error-correcting code | p. 117 |
| The 7-Qbit error-correcting code | p. 121 |
| Operations on 7-Qbit codewords | p. 124 |
| A 7-Qbit encoding circuit | p. 127 |
| A 5-Qbit encoding circuit | p. 128 |
| Protocols that use just a few Qbits | p. 136 |
| Bell states | p. 136 |
| Quantum cryptography | p. 137 |
| Bit commitment | p. 143 |
| Quantum dense coding | p. 146 |
| Teleportation | p. 149 |
| The GHZ puzzle | p. 154 |
| Appendices | p. 159 |
| Vector spaces: basic properties and Dirac notation | p. 159 |
| Structure of the general 1-Qbit unitary transformation | p. 168 |
| Structure of the general 1-Qbit state | p. 173 |
| Spooky action at a distance | p. 175 |
| Consistency of the generalized Born rule | p. 181 |
| Other aspects of Deutsch's problem | p. 183 |
| The probability of success in Simon's problem | p. 187 |
| One way to make a cNOT gate | p. 189 |
| A little elementary group theory | p. 193 |
| Some simple number theory | p. 195 |
| Period finding and continued fractions | p. 197 |
| Better estimates of success in period finding | p. 201 |
| Factoring and period finding | p. 203 |
| Shor's 9-Qbit error-correcting code | p. 207 |
| A circuit-diagrammatic treatment of the 7-Qbit code | p. 210 |
| On bit commitment | p. 216 |
| Index | p. 218 |
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