| Contents |
Preface -- A note on references -- 1. Cbits and Qbits -- 1.1. What is a quantum computer? -- 1.2. Cbits and their states -- 1.3. Reversible operations on Cbits -- 1.4. Manipulating operations on Cbits -- 1.5. Qbits and their states -- 1.6. Reversible operations on Qbits -- 1.7. Circuit diagrams -- 1.8. Measurement gates and the Born rule -- 1.9. The generalized Born rule -- 1.10. Measurement gates and state preparation -- 1.11. Constructing arbitrary 1- and 2-Qbit states -- 1.12. Summary : Obits versus Cbits -- 2. General features and some simple examples -- 2.1. The general computational process -- 2.2. Deutsch's problems -- 2.3. Why additional Qbits needn't mess things up -- 2.4. The Bernstein-Vazirani problem -- 2.5. Simon's problem -- 2.6. Constructing Toffoli gates -- 3. Breaking RSA encryption -- 3.1. Period finding, factoring, and cryptography -- 3.2. Number-theoretic preliminaries -- 3.3. RSA encryption -- 3.4. Quantum period finding : preliminary remarks -- 3.5. The quantum Fourier transform -- 3.6. Eliminating the 2-Qbit gates -- 3.7. Finding the period -- 3.8. Calculating the periodic function -- 3.9. The unimportance of small phase errors -- 3.10. Period finding and factoring -- |
| Contents |
4. Searching with a quantum computer -- 4.1. The nature of the search -- 4.2. The Grover iteration -- 4.3. How to construct W -- 4.4. Generalization to several special numbers -- 4.5. Searching for one out of four items -- 5. Quantum error correction -- 5.1. The miracle of quantum error correction -- 5.2. A simplified example -- 5.3. The physics of error generation -- 5.4. Diagnosing error syndromes -- 5.5. The 5-Qbit error-correcting code -- 5.6. The 7-Qbit error-correcting code -- 5.7. Operations on 7-Qbit codewords -- 5.8. A 7-Qbit encoding circuit -- 5.9. A 5-Qbit encoding circuit -- 6. Protocols that use just a few Qbits -- 6.1. Bell states -- 6.2. Quantum cryptography -- 6.3. Bit commitment -- 6.4. Quantum dense coding -- 6.5. Teleportation -- 6.6. The GHZ puzzle -- |
| Contents |
Appendices -- A. Vector spaces : basic properties and Dirac notation -- B. Structure of the general 1-Qbit unitary transformation -- C. Structure of the general 1-Qbit state -- D. Spooky action at a distance -- E. Consistency of the generalized Born rule -- F. Other aspects of Deutsch's problem -- G. The probability of success in Simon's problem -- H. One way to make a cNOT gate -- I. A little elementary group theory -- J. Some simple number theory -- K. Period finding and continued fractions -- L. Better estimates of success in period finding -- M. Factoring and period finding -- N. Shor's 9-Qbit error-correcting code -- O. A circuit-diagrammatic treatment of the 7-Qbit code -- P. On bit commitment -- Index. |
| Bibliography note | Includes bibliographical references and index. |
| LCCN | 2007282225 |
| ISBN | 9780521876582 (cased) |
| ISBN | 0521876583 (cased) |
