## Quantum Computation and Quantum Communication:: Theory and ExperimentsThe attraction of quantum computation and quantum communica tion theory and experiments hes in the fact that we engineer both them themselves and the quantum systems they treat. This approach has turned out to be very resiUent. Driven by the final goal of calculating exponentially faster and communicating infinitely more securely than we do today, as soon as we encounter a limitation in either a theory or experiment, a new idea around the no-go emerges. As soon as the decoherence "demon" threatened the first computation models, quan tum error correction theory was formulated and applied not only to computation theory but also to communication theory to make it un conditionally secure. As soon as liquid-state nuclear magnetic resonance experiments started to approach their limits, solid-based nuclear spin experiments—the Kane computer—came in. As soon as it was proved that it is theoretically impossible to completely distinguish photon Bell states, three new approaches appeared: hyperentanglement, the use of continuous variables, and the Knill-Laflamme-Milburn proposal. There are many more such examples. What facilitated all these breakthroughs is the fact that at the present stage of development of quantum computation and communication, we deal with elementary quantum systems consisting of several two-level systems. The complexity of handling and controlHng such simple sys tems in a laboratory has turned out to be tremendous, but the basic physical models we follow and calculate for the systems themselves are not equally intricate. |

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### Contents

BITS AND QUBITS THEORY AND ITS IMPLEMENTATION | |

12 Definition of a Turing Machine | |

13 Turing Computability | 2 |

Boolean Algebra | 5 |

Transistors and Their Limits | 7 |

Logic Gates | 10 |

17 Reversible Gates | 12 |

Qubits | 15 |

23 LiquidState Nuclear Magnetic Resonance | 92 |

24 SiliconBased Nuclear Spins | 97 |

25 Ion Traps | 107 |

26 Future Experiments | 121 |

27 Quantum Communication Implementation | 123 |

PERSPECTIVES | 133 |

31 Quantum Network | 135 |

311 Laser | 136 |

19 Flying Qubits and Circular Polarization | 18 |

110 Superposition of Qubits | 20 |

111 BraKet Qubit Formalism | 22 |

112 Operators | 24 |

113 Detecting Qubits | 25 |

114 Quantum Gates and Circuits | 27 |

115 Qubit Computation and EBusiness | 29 |

116 Numbers and Bits | 34 |

117 Entangled Qubits | 37 |

118 General Single Qubit Formalism | 43 |

119 Other Qubits and Universal Gates | 49 |

120 Teleportation of Copies and the NoCloning Theorem | 54 |

121 Quantum Cryptography | 62 |

122 Quantum Error Correction | 70 |

123 Unconditional Security of Quantum Cryptography | 79 |

EXPERIMENTS | 85 |

312 OneAtom Laser and AtomCavity Coupling | 137 |

313 Single Photons on Demand | 138 |

314 Laser Dark States | 140 |

315 Cavity Dark States | 142 |

316 DarkState Teleportation | 144 |

317 Quantum Repeaters | 149 |

32 QuantumClassical Coupling | 157 |

322 KochenSpecker Setups | 165 |

33 Quantum Algorithms | 171 |

332 DeutschJozsa and BernsteinVazirani Algorithms | 174 |

333 Shors Algorithm | 178 |

334 Quantum Simulators | 184 |

34 Quantum Turing Machines vs Quantum Algebra | 188 |

References | 197 |

209 | |

### Other editions - View all

Quantum Computation and Quantum Communication:: Theory and Experiments Mladen Pavicic Limited preview - 2007 |

Quantum Computation and Quantum Communication:: Theory and Experiments Mladen Pavicic No preview available - 2014 |

### Common terms and phrases

algebra algorithm Alice apply approach assume atom beam splitter bits Boolean calculation called carry cavity circuit classical CNOT complexity consider containing correction corresponding cryptography defined described detection detector determine device diagram direction electron emission energy entangled equations error et al example experiment exponential expressed factor field Figure frequency function gate give given by Eq GNFS ground Hence implementation increase interaction laser beam lattice linear logic magnetic matrix means measurements nuclear obtain operator output pairs path Pavičić phase photon physical polarization positive possible presented probability problem procedure pulses quantum circuit quantum computer quantum mechanics qubits reads repeater requires resonator respectively result reversible rotating shown in Fig side single space step superposition theory transform transistor transition trap Turing machine turns values vectors wave

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