| |
| |
| Preface | |
| |
| |
| A note on references | |
| |
| |
| |
| Cbits and Qbits | |
| |
| |
| |
| What is a quantum computer? | |
| |
| |
| |
| Cbits and their states | |
| |
| |
| |
| Reversible operations on Cbits | |
| |
| |
| |
| Manipulating operations on Cbits | |
| |
| |
| |
| Qbits and their states | |
| |
| |
| |
| Reversible operations on Qbits | |
| |
| |
| |
| Circuit diagrams | |
| |
| |
| |
| Measurement gates and the Born rule | |
| |
| |
| |
| The generalized Born rule | |
| |
| |
| |
| Measurement gates and state preparation | |
| |
| |
| |
| Constructing arbitrary 1- and 2-Qbit states | |
| |
| |
| |
| Summary: Qbits versus Cbits | |
| |
| |
| |
| General features and some simple examples | |
| |
| |
| |
| The general computational process | |
| |
| |
| |
| Deutsch's problem | |
| |
| |
| |
| Why additional Qbits needn't mess things up | |
| |
| |
| |
| The Bernstein-Vazirani problem | |
| |
| |
| |
| Simon's problem | |
| |
| |
| |
| Constructing Toffoli gates | |
| |
| |
| |
| Breaking RSA encryption | |
| |
| |
| |
| Period finding, factoring, and cryptography | |
| |
| |
| |
| Number-theoretic preliminaries | |
| |
| |
| |
| RSA encryption | |
| |
| |
| |
| Quantum period finding: preliminary remarks | |
| |
| |
| |
| The quantum Fourier transform | |
| |
| |
| |
| Eliminating the 2-Qbit gates | |
| |
| |
| |
| Finding the period | |
| |
| |
| |
| Calculating the periodic function | |
| |
| |
| |
| The unimportance of small phase errors | |
| |
| |
| |
| Period finding and factoring | |
| |
| |
| |
| Searching with a quantum computer | |
| |
| |
| |
| The nature of the search | |
| |
| |
| |
| The Grover iteration | |
| |
| |
| |
| How to construct W | |
| |
| |
| |
| Generalization to several special numbers | |
| |
| |
| |
| Searching for one out of four items | |
| |
| |
| |
| Quantum error correction | |
| |
| |
| |
| The miracle of quantum error correction | |
| |
| |
| |
| A simplified example | |
| |
| |
| |
| The physics of error generation | |
| |
| |
| |
| Diagnosing error syndromes | |
| |
| |
| |
| The 5-Qbit error-correcting code | |
| |
| |
| |
| The 7-Qbit error-correcting code | |
| |
| |
| |
| Operations on 7-Qbit codewords | |
| |
| |
| |
| A 7-Qbit encoding circuit | |
| |
| |
| |
| A 5-Qbit encoding circuit | |
| |
| |
| |
| Protocols that use just a few Qbits | |
| |
| |
| |
| Bell states | |
| |
| |
| |
| Quantum cryptography | |
| |
| |
| |
| Bit commitment | |
| |
| |
| |
| Quantum dense coding | |
| |
| |
| |
| Teleportation | |
| |
| |
| |
| The GHZ puzzle | |
| |
| |
| Appendices | |
| |
| |
| |
| Vector spaces: basic properties and Dirac notation | |
| |
| |
| |
| Structure of the general 1-Qbit unitary transformation | |
| |
| |
| |
| Structure of the general 1-Qbit state | |
| |
| |
| |
| Spooky action at a distance | |
| |
| |
| |
| Consistency of the generalized Born rule | |
| |
| |
| |
| Other aspects of Deutsch's problem | |
| |
| |
| |
| The probability of success in Simon's problem | |
| |
| |
| |
| One way to make a cNOT gate | |
| |
| |
| |
| A little elementary group theory | |
| |
| |
| |
| Some simple number theory | |
| |
| |
| |
| Period finding and continued fractions | |
| |
| |
| |
| Better estimates of success in period finding | |
| |
| |
| |
| Factoring and period finding | |
| |
| |
| |
| Shor's 9-Qbit error-correcting code | |
| |
| |
| |
| A circuit-diagrammatic treatment of the 7-Qbit code | |
| |
| |
| |
| On bit commitment | |
| |
| |
| Index | |