This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training.
The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition.
This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates.
Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X.
Author(s): Jack D. Hidary
Edition: 2
Publisher: Springer
Year: 2021
Language: English
Commentary: Vector PDF
Pages: 432
City: New York, NY
Tags: Machine Learning; Algorithms; Optimization; Random Number Generation; Linear Algebra; Fourier Transform; Quantum Mechanics; Random Walk; Complexity; Search Algorithms; Shor's Factoring Algorithm; Quantum Algorithms
Contents
Preface to the Second Edition
Preface to the First Edition
Acknowledgements
Navigating this Book
Part I Foundations
CHAPTER 1 Superposition, Entanglement and Reversibility
1.1 Superposition and Entanglement
1.2 The Born Rule
1.3 Schrödinger’s Equation
1.4 The Physics of Computation
CHAPTER 2 A Brief History of Quantum Computing
2.1 Early Developments and Algorithms
2.2 Shor and Grover
2.3 Defining a Quantum Computer
CHAPTER 3 Qubits, Operators and Measurement
Quantum Circuit Diagrams
3.1 Quantum Operators
Unary Operators
Binary Operators
Ternary Operators
3.2 Comparison with Classical Gates
3.3 Universality of Quantum Operators
3.4 Gottesman-Knill and Solovay-Kitaev
3.5 The Bloch Sphere
3.6 The Measurement Postulate
3.7 Computation-in-Place
CHAPTER 4 Complexity Theory
4.1 Problems vs. Algorithms
4.2 Time Complexity
4.3 Complexity Classes
4.4 Quantum Computing and the Church-Turing Thesis
Part II Hardware and Applications
CHAPTER 5 Building a Quantum Computer
5.1 Assessing a Quantum Computer
5.2 Neutral Atoms
5.3 NMR
5.4 NV Center-in-Diamond
5.5 Photonics
Semiconductor quantum transistor
Topological photonic chip
5.6 Spin Qubits
5.7 Superconducting Qubits
5.8 Topological Quantum Computation
5.9 Trapped Ion
5.10 Summary
CHAPTER 6 Development Libraries for Quantum Computer Programming
6.1 Quantum Computers and QC Simulators
6.2 Cirq
6.3 Qiskit
6.4 Forest
6.5 Quantum Development Kit
6.6 Dev Libraries Summary
Using the Libraries
Other Development Libraries
6.7 Additional Quantum Programs
Bell States
Gates with Parameters
CHAPTER 7 Teleportation, Superdense Coding and Bell’s Inequality
7.1 Quantum Teleportation
7.2 Superdense Coding
7.3 Code for Quantum Teleportation and Superdense Communication
7.4 Bell Inequality Test
Summary
CHAPTER 8 The Canon: Code Walkthroughs
8.1 The Deutsch-Jozsa Algorithm
8.2 The Bernstein-Vazirani Algorithm
The Bernstein-Vazirani Algorithm
8.3 Simon’s Problem
8.4 Quantum Fourier Transform
8.5 Shor’s Algorithm
RSA Cryptography
The Period of a Function
Period of a Function as an Input to a Factorization Algorithm
Classical order finding
Quantum order finding
Quantum arithmetic operations in Cirq
Modular exponential arithmetic operation
Using the modular exponential operation in a circuit
Classical post-processing
Quantum order finder
The complete factoring algorithm
8.6 Grover’s Search Algorithm
Grover’s Algorithm in Qiskit
3-Qubit Grover’s Algo
Summary
CHAPTER 9 Quantum Computing Methods
9.1 Variational Quantum Eigensolver
VQE with Noise
More Sophisticated Ansatzes
9.2 Quantum Chemistry
9.3 Quantum Approximate Optimization Algorithm (QAOA)
Example Implementation of QAOA
9.4 Machine Learning on Quantum Processors
9.5 Quantum Phase Estimation
Implemention of QPE
9.6 Solving Linear Systems
Description of the HHL Algorithm
Example Implementation of the HHL Algorithm
9.7 Quantum Random Number Generator
9.8 Quantum Walks
Implementation of a QuantumWalk
9.9 Unification Framework for Quantum Algorithms (QSVT)
9.10 Dequantization
9.11 Summary
CHAPTER 10 Applications and Quantum Supremacy
10.1 Applications
Quantum Simulation and Chemistry
Sampling from Probability Distributions
Linear Algebra Speedup with Quantum Computers
Optimization
Tensor Networks
10.2 Quantum Supremacy
Random Circuit Sampling
Other Problems for Demonstrating Quantum Supremacy
Quantum Advantage and Beyond Classical Computation
10.3 Quantum Error Correction
Context and Importance
Important Preliminaries
Motivating Example: The Repetition Code
The Stabilizer Formalism
10.4 Doing Physics with Quantum Computers
Conclusion
Part III Toolkit
CHAPTER 11 Mathematical Tools for Quantum Computing I
11.1 Introduction and Self-Test
11.2 Linear Algebra
Vectors
Introduction to Dirac Notation
Basic Vector Operations
The Norm of a Vector
The Dot Product
11.3 The Complex Numbers and the Inner Product
Complex Numbers
The Inner Product as a Refinement of the Dot Product
The Polar Coordinate Representation of a Complex Number
11.4 A First Look at Matrices
Basic Matrix Operations
The Identity Matrix
Transpose, Conjugate and Trace
Matrix Exponentiation
11.5 The Outer Product and the Tensor Product
The Outer Product as a Way of Building Matrices
The Tensor Product
11.6 Set Theory
The Basics of Set Theory
The Cartesian Product
Relations and Functions
Important Properties of Functions
11.7 The Definition of a Linear Transformation
11.8 How to Build a Vector Space From Scratch
Groups
Rings
Fields
The Definition of a Vector Space
Subspaces
11.9 Span, Linear Independence, Bases and Dimension
Span
Linear Independence
Bases and Dimension
Orthonormal Bases
CHAPTER 12 Mathematical Tools for Quantum Computing II
12.1 Linear Transformations as Matrices
12.2 Matrices as Operators
An Introduction to the Determinant
The Geometry of the Determinant
Matrix Inversion
12.3 Eigenvectors and Eigenvalues
Change of Basis
12.4 Further Investigation of Inner Products
The Kronecker Delta Function as an Inner Product
12.5 Hermitian Operators
Why We Can’t Measure with Complex Numbers
Hermitian Operators Have Real Eigenvalues
12.6 Unitary operators
12.7 The Direct Sum and the Tensor Product
The Direct Sum
The Tensor Product
12.8 Hilbert Space
Metrics, Cauchy Sequences and Completeness
An Axiomatic Definition of the Inner Product
The Definition of Hilbert Space
12.9 The Qubit as a Hilbert Space
CHAPTER 13 Mathematical Tools for Quantum Computing III
13.1 Boolean Functions
13.2 Logarithms and Exponentials
13.3 Euler’s Formula
CHAPTER 14 Dirac Notation
14.1 Vectors
14.2 Vector operations
Inner and Outer Products
14.3 Tensor Products
14.4 Notation for PDF and Expectation Value
CHAPTER 15 Table of Quantum Operators and Core Circuits
Works Cited
Index
