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Explorations in Quantum Computing [Multiple-component retail product]

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  • Formāts: Multiple-component retail product, 327 pages, 78 illus., Contains 1 Hardback and 1 CD-ROM
  • Izdošanas datums: 12-Dec-1997
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 038794768X
  • ISBN-13: 9780387947686
  • Multiple-component retail product
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  • Formāts: Multiple-component retail product, 327 pages, 78 illus., Contains 1 Hardback and 1 CD-ROM
  • Izdošanas datums: 12-Dec-1997
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 038794768X
  • ISBN-13: 9780387947686
As miniaturization in our modern worl deepens, and nanotechnology and its machines become more prevalent in the real world, the need to consider using quantum mechanical concepts to perform various tasks in computation increases. Such talks include: the teleporting of information, breaking heretofore "unbreakalbe" codes, communicating with messages that betray eavesdropping, and the generation of random munbers. To date, there has been no book written which applies quantum physics to the basic operations of a computer. This one does, thus presenting us with the ideal vehicle for explaining the complexities of quantum mechanics to students, researchers and computer engineers, alike, as they prepare to design and create the computing and information delivery systems of the future. This project evolved from a course taught by one of the authors, Colin Williams, to a group of students in teoretical computer science. Both authors have solid backgrounds in the subject matter at the theoretical and research level, as well as experience on a more practical plane. While intended for use as a textbook for senior/graduate level students in computer science, physics, and engineering, this book has its primary use as an up-to-date reference work in the emerging interdisciplinary field of quantum computing. It presumes no background in quantum physics, or theoretical computer science per se, but it does require knowledge of calculus and familiarity with the concept of the Turing machine. The authors have included visual imagery and graphics throughout the book. They also enlist the use of Mathematica code to support their technical discussions in their examples. These features are designed to help readers better grasp the very complex nature of the physical principles involved with quatum computing. The print presentation is enhanced by the availability of a cross-
Acknowledgments ix(2)
Preface xi(8)
CD-ROM Contents xix
Chapter
1. Computer Technology Meets Quantum Reality
1(16)
1.1 Computers as Physical Systems
2(5)
1.2 Technological Issues
7(4)
1.3 Economic and Environmental Issues
11(3)
1.4 Social and Political Pressures
14(1)
1.5 The 2020 Vision
14(3)
Chapter
2. The Capabilities of Computing Machinery
17(28)
2.1 How the Turing Machine Came About
18(3)
2.2 Deterministic Turing Machines
21(1)
2.3 Probabilistic Turing Machines
22(2)
2.4 Quantum Turing Machines
24(2)
2.5 Universality
26(1)
2.6 Computability
27(4)
2.7 Proving Versus Providing Proof
31(2)
2.8 Complexity
33(12)
Chapter
3. Quantum Mechanics and Computers
45(30)
3.1 Physics and Computers
45(4)
3.2 Taking the Quantum Leap
49(1)
3.3 Quantization: From Bits to Qubits
50(1)
3.4 State Vectors and Dirac Notation
50(2)
3.5 Superposition
52(2)
3.6 Probability Interpretation
54(1)
3.7 Alternative Bases
55(1)
3.8 Eigenstates
55(2)
3.9 State of a Quantum Memory Register
57(2)
3.10 Unitary Operators
59(2)
3.11 Schrodinger's Equation
61(1)
3.12 What Does the Hamiltonian Mean Physically and Computationally?
62(1)
3.13 Unitary Evolution
63(1)
3.14 Interference
63(6)
3.15 Observables as Hermitian Operators
69(1)
3.16 Measurement: Extracting Answers From Quantum Computers
70(1)
3.17 Benioff's Quantum Computer
71(1)
3.18 Feynman's Quantum Computer
72(1)
3.19 Deutsch's Quantum Computer
73(2)
Chapter
4. Simulating a Simple Quantum Computer
75(30)
4.1 What Computation Are We Going to Simulate?
76(1)
4.2 Representing a Computation as a Circuit
77(4)
4.3 Determining the Size of the Memory Register
81(3)
4.4 Computing the Hamiltonian Operator
84(3)
4.5 Computing the Unitary Evolution Operator
87(1)
4.6 Running the Quantum Computer for a Fixed Length of Time
88(5)
4.7 Running the Quantum Computer Until the Computation Is Done
93(2)
4.8 Extracting the Answer
95(1)
4.9 Putting It All Together
96(9)
Chapter
5. The Effects of Imperfections
105(8)
5.1 Imperfections in Preparation
106(2)
5.2 Imperfections in Evolution
108(3)
5.3 Imperfections in Measurement
111(2)
Chapter
6. Breaking Unbreakable Codes
113(34)
6.1 Codes and Code-Breakers
114(1)
6.2 Code Making
115(3)
6.3 Trapdoor Functions
118(1)
6.4 One-Time Pads
119(3)
6.5 The RSA Public Key Cryptography Scheme
122(5)
6.6 Code-Breaking on a Classical Computer
127(3)
6.7 Code-Breaking on a Quantum Computer
130(1)
6.8 A Trick From Number Theory
131(2)
6.9 Shor's Algorithm for Factoring on a Quantum Computer
133(4)
6.10 Simulation of Shor's Algorithm
137(5)
6.11 Shor's Algorithm Can Sometimes Fail
142(5)
Chapter
7. True Randomness
147(16)
7.1 The Concept of Randomness
148(1)
7.2 Does Randomness Exist in Nature?
149(2)
7.3 Uses of Random Numbers
151(4)
7.4 Randomness and Classical Computers
155(3)
7.5 The Plague of Correlations
158(1)
7.6 Randomness and Quantum Computers
159(1)
7.7 Simulation of a Quantum Computer Generating a True Random Number
160(3)
Chapter
8. Quantum Cryptography
163(20)
8.1 Heisenberg's Uncertainty Principle
164(3)
8.2 Polarization
167(2)
8.3 Using Polarized Photons to Encode a Message
169(1)
8.4 Measuring the Polarization of a Photon
169(1)
8.5 Uncertainty Principle for Polarized Photons
170(2)
8.6 Quantum Cryptography Using Polarized Photons
172(1)
8.7 Simulation of Quantum Cryptography in the Absence of Eavesdropping
172(3)
8.8 Simulation of Quantum Cryptography in the Presence of Eavesdropping
175(2)
8.9 The Working Prototype
177(1)
8.10 Other Approaches to Quantum Cryptography
178(5)
Chapter
9. Quantum Teleportation
183(30)
9.1 What Is Teleportation?
183(3)
9.2 Physics Behind Teleportation
186(1)
9.3 Local Versus Nonlocal Interactions
186(2)
9.4 Entanglement
188(2)
9.5 Spooky Action at a Distance
190(1)
9.6 Bell's Theorem
191(5)
9.7 How to Teleport One Qubit
196(4)
9.8 Teleportation Circuit for a Quantum Computer
200(5)
9.9 Simulation of Quantum Teleportation
205(2)
9.10 Experimental Status of Quantum Teleportation
207(1)
9.11 Other Uses of Entangled Qubits
208(5)
Chapter
10. Quantum Error Correction
213(28)
10.1 Decoherence and Dissipation
214(4)
10.2 Models of Errors
218(3)
10.3 Classical Versus Quantum Error Correction
221(1)
10.4 Elementary Error Correction Using Redundancy
222(2)
10.5 The Problem With a Quantum Version of Majority Voting
224(1)
10.6 Error Correction via Symmetrization
225(3)
10.7 Quantum Error-Correcting Codes
228(1)
10.8 Quantum Circuit for Correcting a Phase Shift and/or Bit Flip Error
229(7)
10.9 How Many Errors Can Be Tolerated?
236(2)
10.10 Computing Forever Without Error
238(3)
Chapter
11. How to Make a Quantum Computer
241(26)
11.1 Heteropolymer-Based Quantum Computers
241(10)
11.2 Ion Trap-Based Quantum Computers
251(5)
11.3 Cavity QED-Based Quantum Computers
256(2)
11.4 NMR-Based Quantum Computers
258(9)
Appendix. Using the Code Supplements 267(22)
Bibliography 289(14)
Index 303