Dancing with Qubits, 2nd Edition

Unlock the core math and understand the technical nuances of quantum computing in this detailed guide. Delve into the practicality of NISQ algorithms, and survey promising advancements in quantum machine learning. Key Features Discover how quantum computing works and delve into the math behind it with practical examples Learn about and assess the most up-to-date quantum computing topics including quantum machine learning Explore the inner workings of existing quantum computing technologies to understand how they may perform significantly better than their classical counterparts Book Description Dancing with Qubits, Second Edition, is a comprehensive quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. A full description of classical computing and the mathematical underpinnings of quantum computing follows, helping you better understand concepts such as superposition, entanglement, and interference. Next up are circuits and algorithms, both basic and sophisticated, as well as a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments may affect you. This new edition is updated throughout with more than 100 new exercises and includes new chapters on NISQ algorithms and quantum machine learning. Understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is explained thoroughly and with helpful examples, leaving you with a solid foundation of knowledge in quantum computing that will help you pursue and leverage quantum-led technologies. What you will learn Explore the mathematical foundations of quantum computing Discover the complex, mind-bending concepts that underpin quantum systems Understand the key ideas behind classical and quantum computing Refresh and extend your grasp of essential mathematics, computing, and quantum theory Examine a detailed overview of qubits and quantum circuits Dive into quantum algorithms such as Grover's search, Deutsch-Jozsa, Simon's, and Shor's Explore the main applications of quantum computing in the fields of scientific computing, AI, and elsewhere Who this book is for Dancing with Qubits, Second Edition, is a quantum computing textbook for all those who want to understand and explore the inner workings of quantum computing. This entails building up from basic to some sophisticated mathematics and is therefore best suited for those with a healthy interest in mathematics, physics, engineering, or computer science. I Foundations Why Quantum Computing Topics covered in this chapter 1.1 The mysterious quantum bit 1.2 I m awake 1.3 Why quantum computing is different 1.4 Applications to artificial intelligence 1.5 Applications to financial services 1.6 What about cryptography 1.7 Summary They re Not Old They re Classics Topics covered in this chapter 2.1 What s inside a computer 2.2 The power of two 2.3 True or false 2.4 Logic circuits 2.5 Addition logically 2.6 Algorithmically speaking 2.7 Growth exponential and otherwise 2.8 How hard can that be 2.9 Summary More Numbers Than You Can Imagine Topics covered in this chapter 3.1 Natural numbers 3.2 Whole numbers 3.3 Integers 3.4 Rational numbers 3.5 Real numbers 3.6 Structure 3.7 Modular arithmetic 3.8 Doubling down 3.9 Complex numbers algebraically 3.10 Summary Planes and Circles and Spheres Oh My Topics covered in this chapter 4.1 Functions 4.2 The real plane 4.3 Trigonometry 4.4 From Cartesian to polar coordinates 4.5 The complex “plane” 4.6 Real three dimensions 4.7 Summary Dimensions Topics covered in this chapter 5.1 R2 and C1 5.2 Vector spaces 5.3 Linear maps 5.4 Matrices 5.5 Matrix algebra 5.6 The determinant and trace 5.7 Length and preserving it 5.8 Unitary transformations 5.9 Change of basis 5.10 Eigenvectors and eigenvalues 5.11 Direct sums 5.12 Homomorphisms 5.13 Systems of linear equations 5.14 Summary 6 What Do You Mean “Probably” Topics covered in this chapter 6.1 Being discrete 6.2 More formally 6.3 Wrong again 6.4 Probability and error detection 6.5 Randomness 6.6 Expectation 6.7 Hellinger distance 6.8 Markov and Chebyshev go to the casino 6.9 Summary II Quantum Computing One Qubit Topics covered in this chapter 7.1 Introducing quantum bits 7.2 Bras and kets 7.3 The complex math and physics of a single qubit 7.4 A nonlinear projection 7.5 The Bloch sphere 7.6 Professor Hadamard meet Professor Pauli 7.7 Gates and unitary matrices 7.8 Summary Two Qubits Three Topics covered in this chapter 8.1 Tensor products 8.2 Entanglement 8.3 Multi-qubit gates 8.4 The cat 8.5 Summary Wiring Up the Circuits Topics covered in this chapter 9.1 So many gates 9.2 From gates to circuits 9.3 Building blocks and universality 9.4 Arithmetic 9.5 Welcome to Delphi 9.6 Amplitude amplification and interference 9.7 Searching with Grover 9.8 The Deutsch-Jozsa algorithm 9.9 The Bernstein-Vazirani algorithm 9.10 Simon s algorithm 9.11 Summary From Circuits to Algorithms Topics covered in this chapter 10.1 Quantum Fourier Transform 10.2 Factoring 10.3 How hard can that be again 10.4 Phase kickback 10.5 Eigenvalue and phase estimation 10.6 Order and period finding 10.7 Shor s factoring algorithm 10.8 Summary Getting Physical Topics covered in this chapter 11.1 That s not logical 11.2 What does it take to be a qubit 11.3 Quantum cores and interconnects 11.4 Decoherence 11.5 Error correction for physical qubits 11.6 Quantum benchmarks 11.7 The software stack and access 11.8 Simulation 11.9 Light and photons 11.10 Summary III Advanced Topics Considering NISQ Algorithms Topics covered in this chapter 12.1 Cost functions and optimization 12.2 Heuristics 12.3 Hermitian matrices again 12.4 Expectation and the variational principle 12.5 Time evolution 12.6 Parameterized circuits 12.7 The Hamiltonian 12.8 Quantum approximate optimization algorithm (QAOA) 12.9 Is NISQ worth it 12.10 Summary Introduction to Quantum Machine Learning Topics covered in this chapter 13.1 What is machine learning 13.2 Methods for encoding data 13.3 Quantum neural networks 13.4 Quantum kernels for SVMs 13.5 Other quantum machine learning research areas 13.6 Summary Questions about the Future Topics covered in this chapter 14.1 Ecosystem and community 14.2 Applications and strategy 14.3 Computing system access 14.4 Software 14.5 Hardware 14.6 Education 14.7 Workforce 14.8 Summary Afterword Topics covered in this chapter A.1 One qubit kets A.2 Two qubit kets A.3 Pauli gates and matrices A.4 Pauli strings of length 2 A.5 Greek letters B Notices Topics covered in this chapter B.1 Photos images and diagrams B.2 Marks B.3 Creative Commons Attribution-NoDerivs 2.0 Generic B.4 Creative Commons Attribution-ShareAlike 2.0 Germany B.5 Creative Commons Attribution 3.0 Unported B.6 Creative Commons Attribution-ShareAlike 3.0 Unported B.7 Los Alamos National Laboratory B.8 Python 3 license Topics covered in this chapter C.1 How this book was built C.2 Citing this book C.3 Python version C.4 LaTeX environment Other Books You May Enjoy References Index Work with fully explained algorithms and ready-to-use examples that can be run on quantum simulators and actual quantum computers with this comprehensive guideKey FeaturesGet a solid grasp of the principles behind quantum algorithms and optimization with minimal mathematical prerequisitesLearn the process of implementing the algorithms on simulators and actual quantum computersSolve real-world problems using practical examples of methodsBook DescriptionThis book provides deep coverage of modern quantum algorithms that can be used to solve real-world problems. You'll be introduced to quantum computing using a hands-on approach with minimal prerequisites. You'll discover many algorithms, tools, and methods to model optimization problems with the QUBO and Ising formalisms, and you will find out how to solve optimization problems with quantum annealing, QAOA, Grover Adaptive Search (GAS), and VQE. This book also shows you how to train quantum machine learning models, such as quantum support vector machines, quantum neural networks, and quantum generative adversarial networks. The book takes a straightforward path to help you learn about quantum algorithms, illustrating them with code that's ready to be run on quantum simulators and actual quantum computers. You'll also learn how to utilize programming frameworks such as IBM's Qiskit, Xanadu's PennyLane, and D-Wave's Leap. Through reading this book, you will not only build a solid foundation of the fundamentals of quantum computing, but you will also become familiar with a wide variety of modern quantum algorithms. Moreover, this book will give you the programming skills that will enable you to start applying quantum methods to solve practical problems right away.What you will learnReview the basics of quantum computingGain a solid understanding of modern quantum algorithmsUnderstand how to formulate optimization problems with QUBOSolve optimization problems with quantum annealing, QAOA, GAS, and VQEFind out how to create quantum machine learning modelsExplore how quantum support vector machines and quantum neural networks work using Qiskit and PennyLaneDiscover how to implement hybrid architectures using Qiskit and PennyLane and its PyTorch interfaceWho this book is forThis book is for professionals from a wide variety of backgrounds, including computer scientists and programmers, engineers, physicists, chemists, and mathematicians. Basic knowledge of linear algebra and some programming skills (for instance, in Python) are assumed, although all mathematical prerequisites will be covered in the appendices.