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Part VI: Quantum Computing: Implementations
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Part VI: Quantum Computing: Implementations
by Gerd Leuchs, Dagmar Bruss
Quantum Information, 2 Volume Set, 2nd Edition
Cover
Preface to the New Edition
Preface to Lectures on Quantum Information (2006)
Volume 1
Part I: Classical Information Theory
1 Classical Information Theory and Classical Error Correction
1.1 Introduction
1.2 Basics of Classical Information Theory
1.3 Linear Block Codes
1.4 Further Aspects
References
2 Computational Complexity
2.1 Basics
2.2 Algorithms and Time Complexity
2.3 Tractable Trails: The Class P
2.4 Intractable Itineraries: The Class NP
2.5 Reductions and NP‐Completeness‐Completeness
2.6 P Versus NP
2.7 Optimization
2.8 Complexity Zoo
References
Part II: Foundations of Quantum Information Theory
3 Discrete Quantum States versus Continuous Variables
3.1 Introduction
3.2 Finite‐Dimensional Quantum Systems
3.3 Continuous‐Variables
References
4 Approximate Quantum Cloning
4.1 Introduction
4.2 The No‐Cloning Theorem
4.3 State‐Dependent Cloning
4.4 Phase‐Covariant Cloning
4.5 Universal Cloning
4.6 Asymmetric Cloning
4.7 Probabilistic Cloning
4.8 Experimental Quantum Cloning
4.9 Summary and Outlook
References
5 Channels and Maps
5.1 Introduction
5.2 Completely Positive Maps
5.3 The Choi–Jamiolkowski Isomorphism
5.4 The Stinespring Dilation Theorem
5.5 Classical Systems as a Special Case
5.6 Channels with Memory
5.7 Examples
References
6 Quantum Algorithms
6.1 Introduction
6.2 Precursors
6.3 Shor's Factoring Algorithm
6.4 Grover's Algorithm
6.5 Other Algorithms
6.6 Recent Developments
References
7 Quantum Error Correction
7.1 Introduction
7.2 Quantum Channels
7.3 Using Classical Error‐Correcting Codes
7.4 Further Aspects
References
Part III: Theory of Entanglement
8 The Separability versus Entanglement Problem
8.1 Introduction
8.2 Bipartite Pure States: Schmidt Decomposition
8.3 Bipartite Mixed States: Separable and Entangled States
8.4 Operational Entanglement Criteria
8.5 Non‐operational Entanglement Criteria
8.6 Bell Inequalities
8.7 Quantification of Entanglement
8.8 Classification of Bipartite States with Respect to Quantum Dense Coding
8.9 Multipartite States
Acknowledgments
References
9 Quantum Discord and Nonclassical Correlations Beyond Entanglement
9.1 Introduction
9.2 Quantumness Versus Classicality (of Correlations)
9.3 Quantifying Quantum Correlations – Quantum Discord
9.4 Interpreting Quantum Correlations – Local Broadcasting
9.5 Alternative Characterizations of Quantum Correlations
9.6 General Desiderata for Measures of Quantum Correlations
9.7 Outlook
References
10 Entanglement Theory with Continuous Variables
10.1 Introduction
10.2 Phase‐Space Description
10.3 Entanglement of Gaussian States
10.4 More on Gaussian Entanglement
References
11 Entanglement Measures
11.1 Introduction
11.2 Manipulation of Single Systems
11.3 Manipulation in the Asymptotic Limit
11.4 Postulates for Axiomatic Entanglement Measures: Uniqueness and Extremality Theorems
11.5 Examples of Axiomatic Entanglement Measures
Acknowledgments
References
12 Purification and Distillation
12.1 Introduction
12.2 Pure States
12.3 Distillability and Bound Entanglement in Bipartite Systems
12.4 Bipartite Entanglement Distillation Protocols
12.5 Distillability and Bound Entanglement in Multipartite Systems
12.6 Entanglement Purification Protocols in Multipartite Systems
12.7 Distillability with Noisy Apparatus
12.8 Applications of Entanglement Purification
12.9 Summary and Conclusions
Acknowledgments
References
13 Bound Entanglement
13.1 Introduction
13.2 Distillation of Quantum Entanglement: Repetition
13.3 Bound Entanglement – Bipartite Case
13.4 Bound Entanglement: Multipartite Case
13.5 Further Reading: Continuous Variables
Exercises
References
14 Multipartite Entanglement
14.1 Introduction
14.2 General Theory
14.3 Important Classes of Multipartite states
14.4 Specialized Topics
Acknowledgments
References
Part IV: Quantum Communication
15 Quantum Teleportation
15.1 Introduction
15.2 Quantum Teleportation Protocol
15.3 Implementations
References
16 Theory of Quantum Key Distribution (QKD)
16.1 Introduction
16.2 Classical Background to QKD
16.3 Ideal QKD
16.4 Idealized QKD in Noisy Environment
16.5 Realistic QKD in Noisy and Lossy Environment
16.6 Improved Schemes
16.7 Improvements in Public Discussion
16.8 Conclusion
References
17 Quantum Communication Experiments with Discrete Variables
17.1 Aunt Martha
17.2 Quantum Cryptography
17.3 Entanglement‐Based Quantum Communication
17.4 Conclusion
References
18 Continuous Variable Quantum Communication with Gaussian States
18.1 Introduction
18.2 Continuous‐Variable Quantum Systems
18.3 Tools for State Manipulation
18.4 Quantum Communication Protocols
References
Volume 2
Part V: Quantum Computing: Concepts
19 Requirements for a Quantum Computer
19.1 Classical World of Bits and Probabilities
19.2 Logically Impossible Operations?
19.3 Quantum World of Probability Amplitudes
19.4 Interference Revisited
19.5 Tools of the Trade
19.6 Composite Systems
19.7 Quantum Circuits
19.8 Summary
20 Probabilistic Quantum Computation and Linear Optical Realizations
20.1 Introduction
20.2 Gottesman/Chuang Trick
20.3 Optical Background
20.4 Knill–Laflamme–Milburn (KLM) Scheme
References
21 One‐Way Quantum Computation
21.1 Introduction
21.2 Simple Examples
21.3 Beyond Quantum Circuit Simulation
21.4 Implementations
21.5 Recent Developments
21.6 Outlook
Acknowledgments
Exercises
References
22 Holonomic Quantum Computation
22.1 Geometric Phase and Holonomy
22.2 Application to Quantum Computation
References
Part VI: Quantum Computing: Implementations
23 Quantum Computing with Cold Ions and Atoms: Theory
23.1 Introduction
23.2 Trapped Ions
23.3 Trapped Neutral Atoms
References
24 Quantum Computing Experiments with Cold Trapped Ions
24.1 Introduction to Trapped‐Ion Quantum Computing
24.2 Paul Traps
24.3 Ion Crystals and Normal Modes
24.4 Trap Technology
Acknowledgements
References
25 Quantum Computing with Solid‐State Systems
25.1 Introduction
25.2 Concepts
25.3 Electron Spin Qubits
25.4 Superconducting Qubits
References
26 Time‐Multiplexed Networks for Quantum Optics
26.1 Introduction
26.2 Multiplexing
26.3 Photon‐Number‐Resolving Detection with Time Multiplexing
26.4 Quantum Walks in Time
26.5 Conclusion
References
27 A Brief on Quantum Systems Theory and Control Engineering
27.1 Introduction
27.2 Systems Theory of Closed Quantum Systems
27.3 Toward a Systems Theory for Open Quantum Systems
27.4 Relation to Numerical Optimal Control
27.5 Outlook on Infinite‐Dimensional Systems
27.6 Conclusion
Acknowledgments
References
28 Quantum Computing Implemented via Optimal Control: Application to Spin and Pseudospin Systems
28.1 Introduction
28.2 From Controllable Spin Systems to Suitable Molecules
28.3 Scalability
28.4 Algorithmic Platform for Quantum Control Systems
28.5 Applied Quantum Control
28.6 Worked Example: Unitary Controls for Classifying Knots by NMR
28.7 Conclusions
Acknowledgments
References
Part VII: Quantum Interfaces and Memories
29 Cavity Quantum Electrodynamics: Quantum Information Processing with Atoms and Photons
29.1 Introduction
29.2 Microwave Cavity Quantum Electrodynamics
29.3 Optical Cavity Quantum Electrodynamics
29.4 Conclusions and Outlook
References
30 Quantum Repeater
30.1 Introduction
30.2 Concept of the Quantum Repeater
30.3 Proposals for Experimental Realization
30.4 Summary and Conclusions
Acknowledgments
References
31 Quantum Interface Between Light and Atomic Ensembles
31.1 Introduction
31.2 Off‐Resonant Interaction of Light with Atomic Ensemble
31.3 Entanglement of Two Atomic Clouds
31.4 Quantum Memory for Light
31.5 Multiple Passage Protocols
31.6 Atoms‐Light Teleportation and Entanglement Swapping
31.7 Quantum Cloning into Atomic Memory
31.8 Summary
Acknowledgment
References
32 Echo‐Based Quantum Memory
32.1 Overview of Photon Echo Techniques
32.2 Platforms for Echo‐Based Quantum Memory
32.3 Characterization
32.4 Demonstrations
32.5 Outlook
References
33 Quantum Electrodynamics of a Qubit
33.1 Quantum Electrodynamics of a Qubit in a Spherical Cavity
33.2 Suppression of Radiative Decay of a Qubit in a Photonic Crystal
References
34 Elementary Multiphoton Processes in Multimode Scenarios
34.1 A Generic Quantum Electrodynamical Model
34.2 The Multiphoton Path Representation
34.3 Examples
34.4 Conclusion
Appendix Evaluation of the Field Commutator
References
Part VIII: Towards Quantum Technology Applications
35 Quantum Interferometry with Gaussian States
35.1 Introduction
35.2 The Interferometer
35.3 Interferometer with Coherent States of Light
35.4 Interferometer with Squeezed States of Light
35.5 Fundamental Limits
35.6 Summary and Discussion
Problems
References
36 Quantum Logic‐Enabled Spectroscopy
36.1 Introduction
36.2 Trapping and Doppler Cooling of a Two‐Ion Crystal
36.3 Coherent Atom–Light Interaction and State Manipulation
36.4 Quantum Logic Spectroscopy for Optical Clocks
36.5 Photon Recoil Spectroscopy
36.6 Quantum Logic with Molecular Ions
36.7 Nonclassical States for Spectroscopy
36.8 Future Directions
Acknowledgments
References
37 Quantum Imaging
37.1 Introduction
37.2 The Quantum Laser Pointer
37.3 Manipulation of Spatial Quantum Noise
37.4 Two‐Photon Imaging
37.5 Other Topics in Quantum Imaging
37.6 Conclusion and Perspectives
Acknowledgment
References
38 Quantum Frequency Combs
38.1 Introduction
38.2 Parametric Down Conversion of a Frequency Comb
38.3 Experiment
38.4 Experimental Results
38.5 Application to Quantum Information Processing
38.6 Application to Quantum Metrology
38.7 Conclusion
Acknowledgment
References
Index
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22 Holonomic Quantum Computation
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23 Quantum Computing with Cold Ions and Atoms: Theory
Part VI
Quantum Computing: Implementations
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