Principles of Superconducting Quantum Computers

Explore the intersection of computer science, physics, and electrical and computer engineering with this discussion of the engineering of quantum computers
 
In Principles of Superconducting Quantum Computers, a pair of distinguished researchers delivers a comprehensive and insightful discussion of the building of quantum computing hardware and systems. Bridging the gaps between computer science, physics, and electrical and computer engineering, the book focuses on the engineering topics of devices, circuits, control, and error correction.
 
Using data from actual quantum computers, the authors illustrate critical concepts from quantum computing. Questions and problems at the end of each chapter assist students with learning and retention, while the text offers descriptions of fundamentals concepts ranging from the physics of gates to quantum error correction techniques.
 
The authors provide efficient implementations of classical computations, and the book comes complete with a solutions manual and demonstrations of many of the concepts discussed within. It also includes:
* A thorough introduction to qubits, gates, and circuits, including unitary transformations, single qubit gates, and controlled (two qubit) gates
* Comprehensive explorations of the physics of single qubit gates, including the requirements for a quantum computer, rotations, two-state systems, and Rabi oscillations
* Practical discussions of the physics of two qubit gates, including tunable qubits, SWAP gates, controlled-NOT gates, and fixed frequency qubits
* In-depth examinations of superconducting quantum computer systems, including the need for cryogenic temperatures, transmission lines, S parameters, and more
 
Ideal for senior-level undergraduate and graduate students in electrical and computer engineering programs, Principles of Superconducting Quantum Computers also deserves a place in the libraries of practicing engineers seeking a better understanding of quantum computer systems.

List of contents

1 Qubits, Gates, and Circuits 1
 
1.1 Bits and Qubits . . . . . . . . . . . . . . . . . . . . . . . . 1
 
1.1.1 Circuits in Space vs. Circuits in Time . . . . . . . 1
 
1.1.2 Superposition . . . . . . . . . . . . . . . . . . . . . 2
 
1.1.3 No Cloning . . . . . . . . . . . . . . . . . . . . . . 3
 
1.1.4 Reversibility . . . . . . . . . . . . . . . . . . . . . 4
 
1.1.5 Entanglement . . . . . . . . . . . . . . . . . . . . . 4
 
1.2 Single-Qubit States . . . . . . . . . . . . . . . . . . . . . . 5
 
1.3 Measurement and the Born Rule . . . . . . . . . . . . . . 6
 
1.4 Unitary Operations and Single-Qubit Gates . . . . . . . . 7
 
1.5 Two-Qubit Gates . . . . . . . . . . . . . . . . . . . . . . . 9
 
1.5.1 Two-Qubit States . . . . . . . . . . . . . . . . . . . 9
 
1.5.2 Two-Qubit Gates . . . . . . . . . . . . . . . . . . . 11
 
1.5.3 Controlled-NOT . . . . . . . . . . . . . . . . . . . 13
 
1.6 Bell State . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
 
1.7 No Cloning, Revisited . . . . . . . . . . . . . . . . . . . . 15
 
1.8 Example: Deutsch's Problem . . . . . . . . . . . . . . . . 17
 
1.9 Key Characteristics of Quantum Computing . . . . . . . . 20
 
1.10 Quantum Computing Systems . . . . . . . . . . . . . . . . 22
 
1.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
 
2 Physics of Single Qubit Gates 29
 
2.1 Requirements for a Quantum Computer . . . . . . . . . . 29
 
2.2 Single Qubit Gates . . . . . . . . . . . . . . . . . . . . . . 30
 
2.2.1 Rotations . . . . . . . . . . . . . . . . . . . . . . . 30
 
2.2.2 Two State Systems . . . . . . . . . . . . . . . . . . 38
 
2.2.3 Creating Rotations: Rabi Oscillations . . . . . . . 44
 
2.3 Quantum State Tomography . . . . . . . . . . . . . . . . 49
 
2.4 Expectation Values and the Pauli Operators . . . . . . . . 51
 
2.5 Density Matrix . . . . . . . . . . . . . . . . . . . . . . . . 52
 
2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
 
iii
 
iv CONTENTS
 
3 Physics of Two Qubit Gates 59
 
3.1 square root
 
iSWAP Gate . . . . . . . . . . . . . . . . . . . . . . . . 59
 
3.2 Coupled Tunable Qubits . . . . . . . . . . . . . . . . . . . 61
 
3.3 Fixed-frequency Qubits . . . . . . . . . . . . . . . . . . . 64
 
3.4 Other Controlled Gates . . . . . . . . . . . . . . . . . . . 66
 
3.5 Two-qubit States and the Density Matrix . . . . . . . . . 68
 
3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
 
4 Superconducting Quantum Computer Systems 73
 
4.1 Transmission Lines . . . . . . . . . . . . . . . . . . . . . . 73
 
4.1.1 General Transmission Line Equations . . . . . . . 73
 
4.1.2 Lossless Transmission Lines . . . . . . . . . . . . . 75
 
4.1.3 Transmission Lines with Loss . . . . . . . . . . . . 77
 
4.2 Terminated Lossless Line . . . . . . . . . . . . . . . . . . 82
 
4.2.1 Reflection Coefficient . . . . . . . . . . . . . . . . . 82
 
4.2.2 Power (Flow of Energy) and Return Loss . . . . . 84
 
4.2.3 Standing Wave Ratio (SWR) . . . . . . . . . . . . 85
 
4.2.4 Impedance as a Function of Position . . . . . . . . 86
 
4.2.5 Quarter Wave Transformer . . . . . . . . . . . . . 88
 
4.2.6 Coaxial, Microstrip, and Co-planar Lines . . . . . 89
 
4.3 S Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 92
 
4.3.1 Lossless Condition . . . . . . . . . . . . . . . . . . 93
 
4.3.2 Reciprocity . . . . . . . . . . . . . . . . . . . .

About the author

Daniel D. Stancil, PhD, is the Alcoa Distinguished Professor and Head of Electrical and Computer Engineering at North Carolina State University. In addition to quantum computing, his research interests include spin waves, and microwave and optical devices and systems.
Gregory T. Byrd, PhD, is Professor and Associate Head of Electrical and Computer Engineering at North Carolina State University. His research focuses on both classical and quantum computer architecture and systems.

Product details

• Authors: Gregory T Byrd, Gregory T. Byrd, Daniel D Stancil, Daniel D. Stancil, Daniel D. Byrd Stancil, Stancil Daniel D.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 05.04.2022
• EAN: 9781119750727
• ISBN: 978-1-119-75072-7
• No. of pages: 384
• Subjects: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering; Computertechnik, Quantencomputer, Quantum Computing, Computer Engineering, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Quantum Electronics, Quantenelektronik