Principles and Methods of Quantum Information Technologies (Lecture Notes in Physics, 911)

✍ Scribed by Yoshihisa Yamamoto (editor), Kouichi Semba (editor)

• Publisher: Springer
• Year: 2015
• Tongue: English
• Leaves: 615
• Edition: 1st ed. 2016
• Category: Library

✦ Synopsis

This book presents the research and development-related results of the “FIRST” Quantum Information Processing Project, which was conducted from 2010 to 2014 with the support of the Council for Science, Technology and Innovation of the Cabinet Office of the Government of Japan. The project supported 33 research groups and explored five areas: quantum communication, quantum metrology and sensing, coherent computing, quantum simulation, and quantum computing. The book is divided into seven main sections. Parts I through V, which consist of twenty chapters, focus on the system and architectural aspects of quantum information technologies, while Parts VI and VII, which consist of eight chapters, discuss the superconducting quantum circuit, semiconductor spin and molecular spin technologies.

Readers will be introduced to new quantum computing schemes such as quantum annealing machines and coherent Ising machines, which have now arisen as alternatives to standard quantum computers and are designed to successfully address NP-hard/NP-complete combinatorial optimization problems, which are ubiquitous and relevant in our modern life. The book offers a balanced mix of theory-based and experimentation-based chapters written by leading researchers. Extensive information is provided on Quantum simulation, which focuses on the implementation of various many-body Hamiltonians in a well-controlled physical system, Quantum key distribution, Quantum repeaters and quantum teleportation, which are indispensable technologies for building quantum networks with various advanced applications and require far more sophisticated experimental techniques to implement.

✦ Table of Contents

Preface
Contents
Part I Quantum Communication
1 Quantum Information Theory for Quantum Communication
1.1 Basic Rules of Quantum Mechanics
1.2 Density Operators
1.2.1 Measurement on a Subsystem
1.2.2 Marginal State of a Subsystem
1.2.3 Density Operators
1.2.4 Properties of Bipartite Pure States
1.2.5 Physical States and Density Operators
1.3 Qubits
1.3.1 Pauli Operators
1.3.2 General States of a Qubit
1.3.3 Orthogonal Measurement on a Qubit
1.3.4 Unitary Transformation on a Qubit
1.4 Generalized Measurements and Quantum Operations
1.4.1 Use of Auxiliary Systems
1.4.2 Physically Allowed Operations
1.4.3 Generalized Measurements
1.4.4 Quantum Operations
1.5 Communication Resources
1.5.1 Quantum Channels and Classical Channels
1.5.2 Entanglement as a Communication Resource
1.5.3 Properties of Maximally Entangled States
1.5.4 Quantum Dense Coding and Quantum Teleportation
1.5.5 Conversion Among the Resources
References
2 Quantum Communication for the Ultimate Capacity and Security
2.1 Introduction
2.2 Increasing the Capacity of an Optical Channel
2.3 QKD and Beyond
2.4 Future Outlook
References
3 Quantum Communication Experiments Over Optical Fiber
3.1 Evolution of Quantum Key Distribution Systems
3.2 Differential Phase Shift Quantum Key Distribution
3.2.1 Protocol
3.2.2 Experiments
3.3 Telecom-Band Entanglement and Applications
3.3.1 Telecom-Band Entanglement Sources
3.3.2 Long-Distance Entanglement Distribution and Entanglement-Based QKD
3.3.3 Entanglement Swapping
3.4 Summary and Future Outlook
References
4 Spin-Photon Entanglement in Semiconductor Quantum Dots: Towards Solid-State-Based Quantum Repeaters
4.1 Introduction: Quantum Repeaters
4.1.1 Quantum Key Distribution
4.1.2 Divide and Conquer: Quantum Repeaters
4.2 On Quantum Dots and Spins
4.3 All-Optical, Ultrafast Spin Manipulation in Quantum Dots
4.4 Spin-Photon Entanglement in Quantum Dots
4.5 Coherent Frequency/Wavelength Conversion in Quantum Dots
4.6 A High-Speed Link to Entangle Quantum Dot Spins
4.7 Conclusion
References
Part II Quantum Metrology and Sensing
5 Optical Lattice Clocks for Precision Time and FrequencyMetrology
5.1 Introduction
5.2 Operating Principles of an Optical Lattice Clock
5.3 Lamb-Dicke Spectroscopy in a Magic-Wavelength Lattice
5.4 Absolute Frequency Measurement of Optical Lattice Clocks With 87Sr
5.5 Frequency Comparison of Optical Lattice Clocks Near the Quantum Projection Noise Limit
5.6 Cryogenic Strontium Optical Lattice Clocks
5.7 Frequency Comparison Between Distant Optical Lattice Clocks Towards Relativistic Geodesy
5.8 Future Prospects
References
6 Cold Atom Magnetometers
6.1 Introduction
6.2 Control of Spinor Condensates
6.2.1 Experimental Setup
6.2.2 Rabi Oscillations and Ramsey Interferometry
6.2.2.1 Rotation by Radio Frequency Pulses
6.2.2.2 Mathematical Formalism of Spinor Rotation
6.2.2.3 Experimental Verification of Rotation by RF Pulses (Rabi Oscillation)
6.2.3 Ramsey Interferometry
6.2.4 Observation of Larmor Precession in an Inhomogeneous Magnetic Field
6.2.5 Effect of Spin Echo for Inhomogeneous Spin Precession
6.3 Ultracold Atom AC Magnetometry
6.4 Summary and Future Prospects
References
7 Photonic Quantum Metrologies Using Photons: Phase Super-sensitivity and Entanglement-Enhanced Imaging
7.1 Introduction
7.2 Two Photon Interference
7.2.1 Photons in Spatio-Temporal Modes
7.2.2 Two-Photon Quantum Interference at a Beam Splitter
7.2.3 Single-Photon and Multi-photon Interferometers
7.3 Optical Phase Measurement Exceeding the Standard Quantum Limit
7.4 An Entanglement-Enhanced Microscope: Application of the Phase Super-sensitivity to Microscopy
7.5 Quantum Optical Coherence Tomography
7.6 Summary
References
8 Counting Statistics of Single-Electron Transport
8.1 Introduction to Counting Statistics
8.2 Single-Electron Counting with a Quantum Dot
8.2.1 Charge Detection of a Quantum Dot
8.2.2 Data Correction for Finite Bandwidth
8.2.3 Counting Multiple Tunneling Processes
8.3 Bidirectional Counting with a Double Quantum Dot
8.3.1 Charge Detection of a Double Quantum Dot
8.3.2 Correlated Tunneling Current Through a DQD
8.4 Summary
References
Part III Coherent Computing
9 Some Recent Progress for Approximation Algorithms
9.1 Introduction
9.2 The Edge-Disjoint Paths Problem
9.3 Semi-definite Programming and Coloring
9.4 Conclusion
References
10 Coherent Computing with Injection-Locked Laser Network
10.1 Introduction
10.2 Concept and Basic Principle
10.2.1 Gottesman-Knill Theorem
10.2.2 Laser Phase Transition
10.2.3 Downward Search, Laternal Search and Upward Search
10.3 Analysis of Injection-Locked Laser Network
10.3.1 Proposed System
10.3.2 Theoretical Model
10.3.3 Mapping of the Ising Model
10.3.4 Alternative Picture of the Proposed Ising Machine
10.4 Benchmark on MAX-CUT Problems
10.4.1 MAX-CUT Problems
10.4.2 c-Number Langevin Equations
10.4.3 Self-Learning Steps
10.4.4 Benchmarking Results
10.5 The Proof of Concept Experiment Using Mutually Coupled Semiconducter Lasers
10.5.1 Experimental Setup
10.5.2 Observation of Ferromagnetic and Anti-ferromagnetic Phase Orders
10.5.3 Spontaneous Frequency Optimization of Mutually Coupled Slave Lasers
10.6 Mapping of Classical XY Models onto Laser Network
10.6.1 Steady State Distribution of Coupled Laser Network
10.6.2 Towards Large-Scale Implementation
10.7 Conclusion
References
11 A Degenerate Optical Parametric Oscillator Network for Coherent Computation
11.1 Introduction
11.2 A Single Degenerate OPO
11.3 A Degenerate OPO Network
11.3.1 Oscillation Threshold
11.3.2 Quadrature Components
11.3.3 Overall Photon Decay Rate
11.4 Two Coupled Degenerate OPOs
11.5 Computational Experiments
11.5.1 Numerical Method
11.5.2 Results
11.5.2.1 Solution Quality
11.5.2.2 Computation Time
11.5.3 Performance Improvement
11.6 Experimental Implementation
11.6.1 A Network of Four Degenerate OPOs
11.6.2 Towards the Implementation of Large-Scale Network
11.7 Quantum Mechanical Simulation
11.7.1 Theoretical Model
11.7.2 Simulation Result
11.8 Conclusion
References
12 A Coherent Ising Machine for MAX-CUT Problems: Performance Evaluation against Semidefinite Programming and Simulated Annealing
12.1 Introduction
12.2 A Multiple-pulse DOPO with Quantum Measurement-Feedback Control
12.2.1 Outline
12.3 c-Number Langevin Equations for the Multiple-pulse DOPO with Quantum Feedback Control
12.4 Numerical Studies for a Simple MAX-CUT-3 Problem
12.5 Computational Experiments Against G-Set Graphs and Complete Graphs
12.5.1 G-Set Graphs
12.5.2 Complete Graphs
12.6 Numerical Studies for Higher-Order Ising Problems
12.7 Conclusion
References
Part IV Quantum Simulation
13 Bose-Einstein Condensation: A Platform for Quantum Simulation Experiments
13.1 Introduction
13.2 Fundamental Concepts of Bose-Einstein Condensation
13.2.1 Order Parameter, Spontaneous Symmetry Breaking and Coherent State
13.2.2 Nambu-Goldstone Modes
13.2.3 Off-Diagonal Long Range Order
13.3 Bose-Einstein Condensation of an Ideal Gas
13.3.1 The Physical Picture Behind BEC
13.3.2 BEC Threshold in a Uniform System
13.3.2.1 Energy Density of States
13.3.2.2 BEC Critical Temperature and Density
13.3.2.3 Condensate Fraction
13.3.2.4 Volume Requirement for BEC
13.4 Bogoliubov Theory of a Weakly Interacting Bose Gas
13.4.1 Hamiltonian of a Weakly Interacting Bose Gas and the Lowest-Order Approximation
13.4.2 Bogoliubov Quasi-particles
13.4.3 Excitation Spectrum
13.4.3.1 Phase and Amplitude Modulation Modes
13.4.3.2 Healing Length and Mean-Field Energy Shift
13.4.3.3 Observation of the Bogoliubov Excitation Spectrum
13.4.4 Condensate Fragmentation
13.4.5 Population Fluctuations and Phase Locking
13.5 Superfluidity
13.5.1 Landau's Criteria of Superfluidity
13.5.2 Superfluid Velocity and Phase of the BEC Order Parameter
13.5.3 Quantized Vortices in Superfluids
13.5.4 Berezinskii-Kosterlitz-Thouless (BKT) Phase Transition
13.5.4.1 Bound Vortex-Pairs
13.5.4.2 BKT Phase Transition Temperature
13.5.4.3 Algebraic Decay of the First-Order Coherence Function
13.6 Useful Techniques for Quantum Simulation Experiments
13.6.1 Production of Atomic BEC
13.6.1.1 Cooling and Trapping
13.6.1.2 Evaporative Cooling to Quantum Degeneracy
13.6.1.3 Quantum Gases
13.6.2 Production of Exciton-Polariton Condensates
13.6.2.1 Cooling and Trapping
13.6.2.2 Polariton Fluids
13.6.3 Inter-atomic Interaction
13.6.3.1 Quantum Collision Regime
13.6.3.2 Scattering Length
13.6.3.3 Feshbach Resonance
13.6.4 Quantum Gases in an Optical Lattice
13.6.4.1 Optical Lattice
13.6.4.2 Hubbard Model
13.6.4.3 Two Ultimate Bose-Hubbard Model Regimes: Superfluid and Mott Insulator States
References
14 Quantum Simulation Using Ultracold Ytterbium Atoms in an Optical Lattice
14.1 Quantum Simulation Using Ultracold Atoms in an Optical Lattice: Background
14.2 Basic Properties of Two-Electron Atoms of Yb
14.2.1 Rich Variety of Isotopes
14.2.2 Novel Energy Structure
14.2.3 Interatomic Interaction
14.2.4 SU(N) Symmetry
14.3 Yb Atoms in an Optical Lattice
14.3.1 Strongly Interacting Bose-Fermi Mixtures in an Optical Lattice
14.3.1.1 Photoassociation Method for Probing of Pair Occupancies
14.3.1.2 Formation of Novel Quantum States
14.3.2 SU(6) Mott Insulator and Enhanced Atomic Pomeranchuk Cooling
14.3.2.1 Optical Stern-Gerlach Spin Separation
14.3.2.2 Formation of the SU(6) Mott Insulator
14.3.2.3 Enhanced Pomeranchuk Cooling for an Atomic Gas
14.3.3 High-Resolution Laser Spectroscopy
14.3.3.1 Spectroscopy for the Mott Insulating State
14.3.3.2 Spectroscopy for the Superfluid-Mott Insulator Transition
14.3.4 Yb-Li Atomic Mixture
14.3.4.1 Controlled Impurity System
14.3.4.2 Quantum Degenerate Mixture of Yb and Li in an Optical Lattice
14.3.4.3 Molecules with Spin Degrees of Freedom
14.4 Realization of Nonstandard Optical Lattices
14.4.1 Superlattice
14.4.2 Lieb Lattice
14.5 Development of Methods for Manipulation of Yb Interatomic Interaction
14.5.1 Optical Feshbach Resonance
14.5.2 Magnetic Feshbach Resonance
14.6 Conclusion
References
15 Quantum Simulation with Trapped Ions—Experimental Realization of the Jaynes-Cummings-Hubbard Model—
15.1 Introduction
15.2 Local Phonons in a Linear Trap and Phonon Hopping
15.3 Simulation of a JCH Model with Two Trapped Ions
15.3.1 JCH Model
15.3.2 JCH Model Using Two Trapped Ions with Two Excitations
15.3.3 Experimental
15.3.3.1 Experimental Setup
15.3.3.2 Results
15.4 Conclusion
References
16 Equilibrium to Nonequilibrium Condensation in Driven-Dissipative Semiconductor Systems
16.1 Introduction
16.2 BCS Theory and MSBE for Exciton-Polariton Systems
16.2.1 Model
16.2.2 Mean-Field Approximation
16.2.3 BCS Theory for Exciton-Polariton Condensation
16.2.4 MSBE for Semiconductor Lasers
16.3 BEC-BCS-LASER Crossover Theory
16.4 Second Thresholds, Band Renormalization, and Gain Spectra
16.5 Conclusions and Perspectives
Appendix 1: Excitonic Effects in the Low Density Limit
Appendix 2: Proof of Equivalence
References
17 High-Orbital Exciton-Polariton Condensation: Towards Quantum-Simulator Applications
17.1 Introduction
17.2 Microcavity Exciton-Polaritons
17.2.1 Exciton-Polaritons: Fundamentals
17.2.2 Experimental Techniques
17.2.3 Exciton-Polariton Condensation
17.3 Exciton-Polaritons in Two-Dimensional Lattices
17.3.1 Lattice Formation
17.3.2 Band Structure Calculation
17.3.3 Experimental Setup
17.3.4 High-Orbital Condensates
17.3.4.1 d-Wave Condensation in the Square Lattice
17.3.4.2 Vortex-Antivortex Order in the Honeycomb Lattice
17.3.5 Band Engineering
17.4 Exciton-Polariton Quantum Simulation
17.4.1 Present Status
17.4.2 Beyond the Single-Particle Physics
17.5 Conclusion
References
Part V Quantum Computing
18 Layered Architectures for Quantum Computers and Quantum Repeaters
18.1 Introduction to Quantum Architectures
18.1.1 Prior Work on Quantum Computer Architecture
18.1.2 Layered Framework
18.2 Physical Layer
18.2.1 Spin Qubits in Quantum Dots
18.2.2 Optical Spin Control
18.2.3 Dispersive Non-demolition Measurement
18.3 Virtualization Layer
18.3.1 Virtual Qubit
18.3.2 Virtual Gates
18.4 Quantum Error Correction Layer
18.4.1 Surface Code in the Layered Architecture
18.4.2 Pauli Frames
18.4.3 Resource Overhead for Error Correction
18.5 Logical Layer
18.5.1 Functions of the Logical Layer
18.5.2 Magic State Distillation
18.6 Application Layer
18.7 Quantum Repeaters
18.8 Conclusion
References
19 Analysis of an Atom-Optical Architecture for Quantum Computation
19.1 Introduction
19.2 The Photonic Module
19.3 Towards Fault-Tolerant Quantum Computation
19.3.1 A Modular Quantum Computer Architecture
19.3.2 Topological Error Correction
19.4 Topological Computation and Performance
19.4.1 Defining Qubits and Gates
19.4.1.1 Gates
19.4.2 Resource Optimisation and Estimation
19.5 Summary
References
20 Optical Hybrid Quantum Information Processing
20.1 Introduction
20.2 Qubits and Continuous Variables
20.2.1 Qubits
20.2.2 Continuous Variables
20.3 Quantum Teleportation and Quantum Computing
20.3.1 Quantum Teleportation
20.3.1.1 Basic Concept
20.3.1.2 Qubit Teleportation
20.3.1.3 CV Teleportation
20.3.2 Quantum Computing Based on Quantum Teleportation
20.3.2.1 Cluster-State Quantum Computation
20.3.2.2 Quantum Gate Based on Off-Line Scheme
20.4 Towards Hybrid Quantum Information Processing
20.4.1 Hybrid Quantum Teleportation
20.4.1.1 Proposal and Difficulties
20.4.1.2 Demonstration of Hybrid Teleportation
20.4.2 Hybrid Quantum Computing
20.4.2.1 Hybrid Approach to CV Universality
20.4.2.2 Hybrid Approach to Qubit Universality
20.5 Conclusion
References
Part VI Superconducting Qubits
21 Microwave Photonics on a Chip: Superconducting Circuits as Artificial Atoms for Quantum Information Processing
21.1 Introduction
21.2 Basic Types of Superconducting Qubit Circuits
21.3 Cavity Quantum Electrodynamics
21.4 Selecting Quantum Transitions
21.5 Electromagnetically Induced Transparency
21.6 State Population Inversion and Lasing
21.7 Cooling
21.8 Nanomechanical Resonators
21.9 Photon Generation
21.10 Quantum State Tomography
21.11 Dynamical Casimir Effect
21.12 Coherent Population Transfer
21.13 Tunable Mirrors and Interferometers
21.14 Quantum Nondemolition Measurements
21.15 Generating Squeezed States
21.16 Topological Phases
21.17 Bell Inequality
21.18 Leggett-Garg Inequality
21.19 Kochen-Specker Theorem
21.20 Nonlinear Optics
21.21 Final Summary
References
22 Achievements and Outlook of Research on Quantum Information Systems Using Superconducting Quantum Circuits
22.1 Introduction
22.2 Superconducting State and Josephson Junction
22.3 Eve of Josephson Qubit Realization
22.4 Development of Josephson Qubit
22.5 Progress on Gate Operation Accuracy and Decoherence
22.6 Quantum Logic Gates and Integration
22.7 Implementation of Quantum Algorithm
22.8 Qubit Readout
22.9 Outlook
References
23 Parametric Amplifier and Oscillator Based on Josephson Junction Circuitry
23.1 Introduction
23.2 Quantum Description of the Parametrically-Modulated Duffing Oscillator
23.2.1 Review of the Flux-Driven Josephson Parametric Amplifier
23.2.2 Hamiltonian and Equations of Motion
23.2.3 JPA Characteristics
23.2.3.1 Parametric Gain
23.2.3.2 Noise Temperature
23.2.4 Parametric Oscillator
23.3 Conclusions
References
24 Superconductor-Diamond Hybrid Quantum System
24.1 Introduction
24.2 Superconducting Flux Qubit
24.2.1 Superconducting Flux Qubit with Tunable Quantum Level Spacing
24.2.2 Coherence Property
24.2.3 Strong Coupling to a Quantum Harmonic Oscillator
24.2.4 Readout and Measurement Based Control via Josephson Bifurcation Amplifier
24.3 Single Spin, Photon and Charge Manipulation of NV Center in Diamond
24.3.1 NV Center in Diamond
24.3.2 Spin Coherence Time of NV Center
24.3.3 Electrical Control of Single Photon Emission and Charge State in Single NV Center
24.4 Superconducting Flux Qubit NV Center in a Diamond Hybrid Quantum System
24.4.1 Preparation of NV Center in Diamond
24.4.2 Coherent Coupling Between Flux Qubit and NV Spin Ensemble
24.4.3 Quantum Memory Operations in the Hybrid Quantum System
24.4.4 Observation of a Dark State with a Hybrid System Consisting of a Superconducting Flux Qubit and an Electron Spin Ensemble in Diamond
24.5 Conclusions
References
Part VII Semiconductor and Molecular Spin Qubits
25 Spin Qubits with Semiconductor Quantum Dots
25.1 Spin Qubit Made of Quantum Dots
25.2 Electron Spin Initialization and Detection
25.3 Electrical Manipulation of Single Electron Spins
25.3.1 Single Spin Manipulation
25.3.1.1 One-Qubit Gates
25.3.1.2 Principle of Electron Spin Resonance
25.3.2 Electric Dipole Spin Resonance
25.3.3 Strongly Driven EDSR
25.4 Two Spin Operations
25.4.1 Reduced Spin Dynamics Made of Two Spins
25.4.1.1 Exchange Qubits
25.4.1.2 SWAP Operation
25.5 Architecture for Spin-Qubit Quantum Computer
25.6 Other Techniques for Manipulating Single Electrons
25.6.1 Photon to Electron Spin Interface
25.6.1.1 Single Photoelectron Detection with a Single QD
25.6.1.2 Non-destructive Single Photoelectron Detection
25.6.1.3 Angular Momentum Transfer from Single Photons to Single Electrons
25.6.2 Transfer of Single Electrons Between Distant QDs
25.6.2.1 Electron Transfer Using Surface Acoustic Wave
25.7 Conclusions and Prospects
References
26 Silicon Quantum Information Processing
26.1 Introduction
26.2 Single Spin Versus Spin Ensemble
26.3 Initialization of Nuclear Spins
26.4 Coherence Times
26.4.1 Electron Spin Coherence Times T2e
26.4.2 Nuclear Spin Coherence Time T2n
26.5 Quantum Memory and Quantum Calculation by Nuclear Spin Ensemble Qubits
26.5.1 Entanglement of the Electron and Nuclear Spins of the 31P Donors
26.5.2 29Si Nuclear Spin Quantum Memory with a Spin Triplet Center
26.6 Single-Spin Qubit
26.7 Summary
References
27 Quantum Information Processing Experiments Using Nuclear and Electron Spins in Molecules
27.1 Introduction
27.2 Spin Qubit Control Techniques
27.2.1 Conventional Techniques
27.2.2 Numerical Synthesis
27.2.3 Control of the Electron Spins
27.2.4 Transient Compensation
27.3 Hyperpolarization of Spins
27.3.1 Hyperpolarization by Cooling
27.3.2 Dynamic Nuclear Polarization Using Photo-Excited Triplet Electrons
27.4 Sensitivity Enhancement by Spin Amplification
27.5 Summary: Toward Spin QIP Experiments
References
28 Molecular Spin Qubits: Molecular Optimization of Synthetic Spin Qubits, Molecular Spin AQC and Ensemble Spin Manipulation Technology
28.1 Introduction
28.2 Synthetic Approaches to Lloyd Model Electron Spin Scalable Qubit Systems
28.3 Controlled-NOT Gate Operations by Molecular Spin Qubits
28.4 Adiabatic Quantum Computation on a Molecular Spin QC
28.5 Multi-Spin Quantum Control Through Single Spin Manipulation
28.5.1 Theoretical Background
28.5.2 Indirect Application of a Quantum Gate on a Three-Spin System
28.6 Conclusions
Appendices
Appendix 28.1
Appendix 28.2
References