Quantum information and quantum optics with superconducting circuits / Juan José García Ripoll, Institute of Fundamental Physics (IFF), CSIC.

Format:

Book

Author/Creator:

García Ripoll, Juan José, author.

Language:

English

Subjects (All):

Quantum theory.

Quantum optics.

Physical Description:

1 online resource (xiv, 302 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge : Cambridge University Press, 2022.

Summary:

Superconducting quantum circuits are among the most promising solutions for the development of scalable quantum computers. Built with sizes that range from microns to tens of metres using superconducting fabrication techniques and microwave technology, superconducting circuits demonstrate distinctive quantum properties such as superposition and entanglement at cryogenic temperatures. This book provides a comprehensive and self-contained introduction to the world of superconducting quantum circuits, and how they are used in current quantum technology. Beginning with a description of their basic superconducting properties, the author then explores their use in quantum systems, showing how they can emulate individual photons and atoms, and ultimately behave as qubits within highly connected quantum systems. Particular attention is paid to cutting-edge applications of these superconducting circuits in quantum computing and quantum simulation. Written for graduate students and junior researchers, this accessible text includes numerous homework problems and worked examples.

Contents:

Cover

Half-title

Title page

Copyright information

Contents

List of Figures

List of Tables

Notation

1 Introduction

1.1 The Book

1.2 Acknowledgments

2 Quantum Mechanics

2.1 Canonical Quantization

2.1.1 Hamiltonian Equations

2.1.2 Quantum Observables

2.1.3 Unitary Evolution

2.2 Two-Level Systems

2.3 Density Matrices

2.4 Measurements

3 Superconductivity

3.1 Microscopic Model

3.2 Macroscopic Quantum Model

3.3 Superfluid Current

3.4 Superconducting Phase

3.5 Gauge-Invariant Phase

3.6 Fluxoid Quantization

3.7 Josephson Junctions

4 Quantum Circuit Theory

4.1 Introduction

4.1.1 What Makes a Circuit Quantum

4.1.2 How Do We Work with Quantum Circuits?

4.2 Circuit Elements

4.2.1 Capacitor

4.2.2 Inductor

4.2.3 Josephson Junctions or "Nonlinear Inductors"

4.2.4 Other Elements

4.3 Quantization Procedure

4.4 LC Resonator

4.5 Transmission Line

4.6 Charge and Transmon Qubits

4.7 SQUIDs

4.7.1 rf-SQUID

4.7.2 dc-SQUID

4.8 Three-Junction Flux Qubit

4.9 Number-Phase Representation

Exercises

5 Microwave Photons

5.1 LC Resonator

5.1.1 Energy Quantization and Photons

5.1.2 Hamiltonian Diagonalization

5.1.3 Phase Space Dynamics

5.1.4 Are There Real Photons?

5.2 Transmission Lines or Waveguides

5.2.1 Periodic Boundary Conditions

5.2.2 λ/2 and λ/4 Microwave Cavities

5.2.3 Tunable Cavities

5.3 Three-Dimensional Cavities and Waveguides

5.4 Photon States

5.4.1 Fock States

5.4.2 Thermal States

5.4.3 Coherent States

5.4.4 Schrödinger Cat States

5.4.5 Single-, Two-, and Multimode Squeezed States

5.4.6 Wigner Functions and Gaussian States

5.5 Gaussian Control of Microwave Photons

5.5.1 Coherent Drivings and Displacement Operations

5.5.2 Coupling to an Environment.

5.5.3 Cavity Spectroscopy

5.5.4 Losses and Heating

5.5.5 Beam Splitters and Circulators

5.5.6 Amplification

5.5.7 Photon Quadrature Measurements

5.6 Conclusion

6 Superconducting Qubits

6.1 What Is a Qubit?

6.1.1 From Logical to Physical Qubits

6.1.2 Qubit Hamiltonian

6.1.3 Interaction Picture

6.1.4 Single-Qubit Gates

6.1.5 Decoherence and Dephasing

6.1.6 Relaxation and Heating

6.2 Charge Qubit

6.2.1 Coulomb Blockade

6.2.2 The Actual Superconducting Charge Qubit

6.2.3 Qubit Hyperbola

6.2.4 Charge Qubit History

6.3 Transmon Qubit

6.3.1 Moving Particle Picture and Energy Bands

6.3.2 Transmon as Anharmonic Oscillator

6.3.3 Josephson Junctions and the Mathieu Equation

6.3.4 Transmon as Qubit

6.4 Flux Qubit

6.4.1 Frustration and Current States

6.4.2 rf-SQUID Qubit

6.4.3 Persistent Current Qubit

6.4.4 General Operation

6.5 Qubit-Qubit Interactions

6.5.1 Dipolar Magnetic Interaction

6.5.2 Dipolar Electric Interaction

6.5.3 Coupling Tunability

6.5.4 Mediated Interactions and Tunable Couplers

6.6 Qubit Coherence

7 Qubit-Photon Interaction

7.1 Qubit-Line Interaction Models

7.1.1 Dipolar Interaction

7.1.2 Spin-Boson Hamiltonian

7.1.3 Spectral Function and Spin-Boson Regimes

7.1.4 Rotating Wave Approximation

7.2 Waveguide-QED

7.2.1 Wigner-Weisskopf Approximation

7.2.2 Input-Output Relations

7.2.3 Spontaneous Emission Spectrum

7.2.4 Single-Photon Scattering

7.2.5 Quantum Links

7.3 Cavity-QED

7.3.1 Quantum Rabi and Jaynes-Cummings Models

7.3.2 Jaynes-Cummings Ladder

7.3.3 Vacuum Rabi splitting

7.3.4 Rabi Oscillations: Weak and Strong Coupling

7.3.5 Ultrastrong Coupling

7.3.6 Multiple Qubits

7.3.7 Off-Resonant Qubits and Dispersive Coupling

7.4 Circuit-QED Control.

7.4.1 Direct Cavity Spectroscopy

7.4.2 Qubit Dispersive Measurement

7.4.3 Two-Tone Spectroscopy

7.4.4 Single-Photon Generation

7.4.5 Qubit Reset

7.4.6 Cavity Fock States Superpositions

7.4.7 Cavity Schrödinger Cats

8 Quantum Computing

8.1 Quantum Circuit Model

8.2 Quantum Registers

8.2.1 Measurements

8.2.2 Qubit Reset

8.2.3 Architectural Decisions

8.3 Gate Toolbox

8.3.1 Universal Set of Gates

8.3.2 Two-Qubit Exchange Gates (iSWAP)

8.3.3 Two-Qubit Tunable Frequency CZ Gate

8.3.4 Two-Qubit Tunable Coupling CZ Gate

8.4 Tomography and Error Characterization

8.4.1 Classes of Errors

8.4.2 Error Models: Completely Positive Maps

8.4.3 Error Quantification: Fidelity

8.4.4 Randomized Benchmarking

8.5 Fault-Tolerant Quantum Computers

8.5.1 Local Errors and Global Qubits

8.5.2 Passive versus Active Error Correction

8.5.3 Stabilizer Codes

8.5.4 Surface Code

8.5.5 Fault-Tolerant Thresholds and Outlook

8.6 Near-Term Intermediate Scale Quantum Computers

8.6.1 What Is NISQ?

8.6.2 Hybrid Quantum Computers

8.6.3 Quantum Volume

8.7 Outlook

9 Adiabatic Quantum Computing

9.1 Adiabatic Evolution

9.1.1 Landau-Zener and Qubit Adiabatic Control

9.1.2 The Adiabatic Theorem

9.1.3 Circuit-QED Applications of Adiabatic Theorem

9.2 Adiabatic Quantum Computing Model

9.2.1 The Adiabatic Quantum Computing Algorithm

9.2.2 Resource Accounting

9.3 The Choice of Hamiltonian

9.3.1 A Primer on Complexity Classes

9.3.2 QUBO and NP-Complete Hamiltonian Problems

9.3.3 QMA-Complete Problems

9.3.4 Scaling of Resources

9.4 D-Wave's Quantum Annealer

9.4.1 D-Wave's Architecture

9.4.2 Device Operation

9.4.3 Performance Analysis

9.5 Summary and Outlook

Appendix A Hamiltonian Diagonalizations.

A.1 Tridiagonal Matrix Diagonalization

A.1.1 Periodic Boundary Conditions

A.1.2 Open Boundary Conditions

A.2 Harmonic Chain Diagonalization

A.3 Schrieffer-Wolff Perturbation Theory

A.3.1 Nondegenerate Perturbation Theory

A.3.2 Degenerate Perturbation Theory

A.3.3 Considerations

Appendix B Open Quantum Systems

B.1 Nonunitary Evolution

B.2 Master Equations

B.2.1 Lindblad Equation

B.2.2 Linear System-Bath Coupling

B.2.3 System in a Thermal Bath: Cooling and Heating

B.2.4 Perturbations and Generalizations

B.2.5 Strong Nonlinearity and Multilevel systems

B.3 Input-Output Theory

B.3.1 Memory Function

B.3.2 Markovian Approximation: Decay Rate and Lamb Shift

B.3.3 Input-Output Relations

B.3.4 Spectroscopy

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 08 Aug 2022).

Includes bibliographical references and index.

Other Format:

Print version: García Ripoll, Juan José. Quantum information and quantum optics with superconducting circuits

ISBN:

1-316-80013-X

1-316-80524-7

1-316-77946-7

OCLC:

1331716631