Quantum Computation and Quantum Communication:: Theory and Experiments

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Springer Science & Business Media, 2006 - Computers - 221 pages
The 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
Index
209
Copyright

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