Stancil, Daniel D., author.
Principles of superconducting quantum computers / Daniel D. Stancil, Gregory T. Byrd - First edition. - Hoboken, NJ, USA : John Wiley & Sons, Inc., c2022. - xxxi ; 346 pages : 26 cm
Includes bibliographical references.
Table of Contents
1 Qubits, Gates, and Circuits
Bits and Qubits
Circuits in Space vs. Circuits in Time
Superposition
No Cloning
Reversibility
Entanglement
Single-Qubit States
Measurement and the Born Rule
Unitary Operations and Single-Qubit Gates
Two-Qubit Gates
Two-Qubit States
Two-Qubit Gates
Controlled-NOT
Bell State
No Cloning, Revisited
Example: Deutsch’s Problem
Key Characteristics of Quantum Computing
Quantum Computing Systems
Exercises
2.Physics of Single Qubit Gates
Requirements for a Quantum Computer
Single Qubit Gates
Rotations
Two State Systems
Creating Rotations: Rabi Oscillations
Quantum State Tomography
Expectation Values and the Pauli Operators
Density Matrix
Exercises
3 Physics of Two Qubit Gates
√ iSWAP Gate
Coupled Tunable Qubits
Fixed-frequency Qubits
Other Controlled Gates
Two-qubit States and the Density Matrix
Exercises
4 Superconducting Quantum Computer Systems
Transmission Lines
General Transmission Line Equations
Lossless Transmission Lines
Transmission Lines with Loss
Terminated Lossless Line
Reflection Coefficient
Power (Flow of Energy) and Return Loss
Standing Wave Ratio (SWR)
Impedance as a Function of Position
Quarter Wave Transformer
Coaxial, Microstrip, and Co-planar Lines
Parameters
Lossless Condition
Reciprocity
Transmission (ABCD) Matrices
Attenuators
Circulators and Isolators
Power Dividers/Combiners
Mixers
Low-pass Filters
Noise
Thermal Noise
Equivalent Noise Temperature
Noise Factor and Noise Figure
Attenuators and Noise
Noise in Cascaded Systems
Low Noise Amplifiers
Exercises
5 Resonators: Classical Treatment
Parallel Lumped Element Resonator
Capacitive Coupling to a Parallel Lumped-Element Resonator
Transmission Line Resonator
Capacitive Coupling to a Transmission Line Resonator
Capacitively-Coupled Lossless Resonators
Classical Model of Qubit Readout
Exercises
6 Resonators: Quantum Treatment
Lagrangian Mechanics
Hamilton’s Principle
Calculus of Variations
Lagrangian Equation of Motion
Hamiltonian Mechanics
Harmonic Oscillators
Classical Harmonic Oscillator
Quantum Mechanical Harmonic Oscillator
Raising and Lowering Operators
Can a Harmonic Oscillator be used as a Qubit?
Circuit Quantum Electrodynamics
Classical LC Resonant Circuit
Quantization of the LC Circuit
Circuit Electrodynamic Approach for General Circuits
Circuit Model for Transmission Line Resonator
Quantizing a Transmission Line Resonator
Quantized Coupled LC Resonant Circuits
Schrödinger, Heisenberg, and Interaction Pictures
Resonant Circuits and Qubits
The Dispersive Regime
Exercises
7 Theory of Superconductivity
Bosons and Fermions
Bloch Theorem
Free Electron Model for Metals
Discrete States in Finite Samples
Phonons
Debye Model
Electron-Phonon Scattering and Electrical Conductivity
Perfect Conductor vs. Superconductor
Bardeen, Cooper and Schrieffer Theory of Superconductivity
Cooper Pair Model
Dielectric Function
Jellium
Scattering Amplitude and Attractive Electron-Electron Interaction
Interpretation of Attractive Interaction
Superconductor Hamiltonian
Superconducting Ground State
Electrodynamics of Superconductors
Cooper Pairs and the Macroscopic Wave Function
Potential Functions
London Equations
London Gauge
Penetration Depth
Flux Quantization
Chapter Summary
Exercises
8 Josephson Junctions
Tunneling
Reflection from a Barrier
Finite Thickness Barrier
Josephson Junctions
Current and Voltage Relations
Josephson Junction Hamiltonian
Quantized Josephson Junction Analysis
Superconducting Quantum Interference Devices (SQUIDs)
Josephson Junction Parametric Amplifiers
Exercises
9 Errors and Error Mitigation
NISQ Processors
Decoherence
State Preparation and Measurement Errors
Characterizing Gate Errors
State Leakage and Suppression using Pulse Shaping
Zero-Noise Extrapolation
Optimized Control using Deep Learning
Exercises
10 Quantum Error Correction
Review of Classical Error Correction
Error Detection
Error Correction: Repetition Code
Hamming Code
Quantum Errors
Detecting and Correcting Quantum Errors
Bit Flip
Phase Flip
Correcting Bit and Phase Flips: Shor’s 9-qubit Code
Arbitrary Rotations
Stabilizer Codes
Stabilizers
Stabilizers for Error Correction
Operating on Logical Qubits
Error Thresholds
Concatenation of Error Codes
Threshold Theorem
Surface Codes
Stabilizers
Error Detection and Correction
Logical X and Z Operators
Multiple Qubits: Lattice Surgery
CNOT
Single-Qubit Gates
Summary and Further Reading
Exercises
11 Quantum Logic: Efficient Implementation of Classical Computations
Reversible Logic
Reversible Logic Gates
Reversible Logic Circuits
Quantum Logic Circuits
Entanglement and Uncomputing
Multi-qubit gates
Qubit topology
Efficient Arithmetic Circuits: Adder
Quantum Ripple Carry Adder
In-place Ripple Carry Adder
Carry-Lookahead Adder
Adder Comparison
Phase Logic
Controlled-Z and Controlled-Phase Gates
Selective Phase Change
Phase Logic Gates
Summary and Further Reading
Exercises
12 Some Quantum Algorithms
Computational Complexity
Quantum Program Run-Time
Classical Complexity Classes
Quantum Complexity
Grover’s Search Algorithm
Grover Iteration
Quantum Implementation
Generalizations
Quantum Fourier Transform
Frequencies and Quantum-encoded Signals
Inverse QFT
Quantum Implementation
Computational Complexity
Quantum Phase Estimation
Quantum Implementation
Computational Complexity and Other Issues
Shor’s Algorithm
Hybrid Classical-Quantum Algorithm
Finding the Period
Computational Complexity
Variational Quantum Algorithms
Variational Quantum Eigensolver
Quantum Approximate Optimization Algorithm
Challenges and Opportunities
Summary and Further Reading
Exercises
"Digital systems that are most familiar are based on binary digits, or "bits." Each bit can take on either the value "1" or "0", and any arbitrary data can be represented by such a binary representation. In addition, any arbitrary logical operation can be implemented using bits. The text refers to these familiar systems as "classical" systems, since they are governed by the everyday laws of classical physics. Quantum computing is different from classical computing in a number of significant ways, as discussed in 'Principles of superconducting quantum computers'"-- Provided by publisher
In English text.
9781119750727 (hardback)
Quantum computers.
Superconducting quantum interference devices.
CIR QA 76.889 / S73 2022
Principles of superconducting quantum computers / Daniel D. Stancil, Gregory T. Byrd - First edition. - Hoboken, NJ, USA : John Wiley & Sons, Inc., c2022. - xxxi ; 346 pages : 26 cm
Includes bibliographical references.
Table of Contents
1 Qubits, Gates, and Circuits
Bits and Qubits
Circuits in Space vs. Circuits in Time
Superposition
No Cloning
Reversibility
Entanglement
Single-Qubit States
Measurement and the Born Rule
Unitary Operations and Single-Qubit Gates
Two-Qubit Gates
Two-Qubit States
Two-Qubit Gates
Controlled-NOT
Bell State
No Cloning, Revisited
Example: Deutsch’s Problem
Key Characteristics of Quantum Computing
Quantum Computing Systems
Exercises
2.Physics of Single Qubit Gates
Requirements for a Quantum Computer
Single Qubit Gates
Rotations
Two State Systems
Creating Rotations: Rabi Oscillations
Quantum State Tomography
Expectation Values and the Pauli Operators
Density Matrix
Exercises
3 Physics of Two Qubit Gates
√ iSWAP Gate
Coupled Tunable Qubits
Fixed-frequency Qubits
Other Controlled Gates
Two-qubit States and the Density Matrix
Exercises
4 Superconducting Quantum Computer Systems
Transmission Lines
General Transmission Line Equations
Lossless Transmission Lines
Transmission Lines with Loss
Terminated Lossless Line
Reflection Coefficient
Power (Flow of Energy) and Return Loss
Standing Wave Ratio (SWR)
Impedance as a Function of Position
Quarter Wave Transformer
Coaxial, Microstrip, and Co-planar Lines
Parameters
Lossless Condition
Reciprocity
Transmission (ABCD) Matrices
Attenuators
Circulators and Isolators
Power Dividers/Combiners
Mixers
Low-pass Filters
Noise
Thermal Noise
Equivalent Noise Temperature
Noise Factor and Noise Figure
Attenuators and Noise
Noise in Cascaded Systems
Low Noise Amplifiers
Exercises
5 Resonators: Classical Treatment
Parallel Lumped Element Resonator
Capacitive Coupling to a Parallel Lumped-Element Resonator
Transmission Line Resonator
Capacitive Coupling to a Transmission Line Resonator
Capacitively-Coupled Lossless Resonators
Classical Model of Qubit Readout
Exercises
6 Resonators: Quantum Treatment
Lagrangian Mechanics
Hamilton’s Principle
Calculus of Variations
Lagrangian Equation of Motion
Hamiltonian Mechanics
Harmonic Oscillators
Classical Harmonic Oscillator
Quantum Mechanical Harmonic Oscillator
Raising and Lowering Operators
Can a Harmonic Oscillator be used as a Qubit?
Circuit Quantum Electrodynamics
Classical LC Resonant Circuit
Quantization of the LC Circuit
Circuit Electrodynamic Approach for General Circuits
Circuit Model for Transmission Line Resonator
Quantizing a Transmission Line Resonator
Quantized Coupled LC Resonant Circuits
Schrödinger, Heisenberg, and Interaction Pictures
Resonant Circuits and Qubits
The Dispersive Regime
Exercises
7 Theory of Superconductivity
Bosons and Fermions
Bloch Theorem
Free Electron Model for Metals
Discrete States in Finite Samples
Phonons
Debye Model
Electron-Phonon Scattering and Electrical Conductivity
Perfect Conductor vs. Superconductor
Bardeen, Cooper and Schrieffer Theory of Superconductivity
Cooper Pair Model
Dielectric Function
Jellium
Scattering Amplitude and Attractive Electron-Electron Interaction
Interpretation of Attractive Interaction
Superconductor Hamiltonian
Superconducting Ground State
Electrodynamics of Superconductors
Cooper Pairs and the Macroscopic Wave Function
Potential Functions
London Equations
London Gauge
Penetration Depth
Flux Quantization
Chapter Summary
Exercises
8 Josephson Junctions
Tunneling
Reflection from a Barrier
Finite Thickness Barrier
Josephson Junctions
Current and Voltage Relations
Josephson Junction Hamiltonian
Quantized Josephson Junction Analysis
Superconducting Quantum Interference Devices (SQUIDs)
Josephson Junction Parametric Amplifiers
Exercises
9 Errors and Error Mitigation
NISQ Processors
Decoherence
State Preparation and Measurement Errors
Characterizing Gate Errors
State Leakage and Suppression using Pulse Shaping
Zero-Noise Extrapolation
Optimized Control using Deep Learning
Exercises
10 Quantum Error Correction
Review of Classical Error Correction
Error Detection
Error Correction: Repetition Code
Hamming Code
Quantum Errors
Detecting and Correcting Quantum Errors
Bit Flip
Phase Flip
Correcting Bit and Phase Flips: Shor’s 9-qubit Code
Arbitrary Rotations
Stabilizer Codes
Stabilizers
Stabilizers for Error Correction
Operating on Logical Qubits
Error Thresholds
Concatenation of Error Codes
Threshold Theorem
Surface Codes
Stabilizers
Error Detection and Correction
Logical X and Z Operators
Multiple Qubits: Lattice Surgery
CNOT
Single-Qubit Gates
Summary and Further Reading
Exercises
11 Quantum Logic: Efficient Implementation of Classical Computations
Reversible Logic
Reversible Logic Gates
Reversible Logic Circuits
Quantum Logic Circuits
Entanglement and Uncomputing
Multi-qubit gates
Qubit topology
Efficient Arithmetic Circuits: Adder
Quantum Ripple Carry Adder
In-place Ripple Carry Adder
Carry-Lookahead Adder
Adder Comparison
Phase Logic
Controlled-Z and Controlled-Phase Gates
Selective Phase Change
Phase Logic Gates
Summary and Further Reading
Exercises
12 Some Quantum Algorithms
Computational Complexity
Quantum Program Run-Time
Classical Complexity Classes
Quantum Complexity
Grover’s Search Algorithm
Grover Iteration
Quantum Implementation
Generalizations
Quantum Fourier Transform
Frequencies and Quantum-encoded Signals
Inverse QFT
Quantum Implementation
Computational Complexity
Quantum Phase Estimation
Quantum Implementation
Computational Complexity and Other Issues
Shor’s Algorithm
Hybrid Classical-Quantum Algorithm
Finding the Period
Computational Complexity
Variational Quantum Algorithms
Variational Quantum Eigensolver
Quantum Approximate Optimization Algorithm
Challenges and Opportunities
Summary and Further Reading
Exercises
"Digital systems that are most familiar are based on binary digits, or "bits." Each bit can take on either the value "1" or "0", and any arbitrary data can be represented by such a binary representation. In addition, any arbitrary logical operation can be implemented using bits. The text refers to these familiar systems as "classical" systems, since they are governed by the everyday laws of classical physics. Quantum computing is different from classical computing in a number of significant ways, as discussed in 'Principles of superconducting quantum computers'"-- Provided by publisher
In English text.
9781119750727 (hardback)
Quantum computers.
Superconducting quantum interference devices.
CIR QA 76.889 / S73 2022