Wow! eBook
Essential Mathematics for Quantum Computing: A beginner's guide to just the math you need without needless complexities
Author(s): Leonard S. Woody III (Author)
- Publisher: Packt Publishing
- Publication Date: 22 April 2022
- Language: English
- Print length: 252 pages
- ISBN-10: 1801073147
- ISBN-13: 9781801073141
Book Description
Demystify quantum computing by learning the math it is built on
Key Features
- Build a solid mathematical foundation to get started with developing powerful quantum solutions
- Understand linear algebra, calculus, matrices, complex numbers, vector spaces, and other concepts essential for quantum computing
- Learn the math needed to understand how quantum algorithms function
Book Description
Quantum computing is an exciting subject that offers hope to solve the world’s most complex problems at a quicker pace. It is being used quite widely in different spheres of technology, including cybersecurity, finance, and many more, but its concepts, such as superposition, are often misunderstood because engineers may not know the math to understand them. This book will teach the requisite math concepts in an intuitive way and connect them to principles in quantum computing.
Starting with the most basic of concepts, 2D vectors that are just line segments in space, you’ll move on to tackle matrix multiplication using an instinctive method. Linearity is the major theme throughout the book and since quantum mechanics is a linear theory, you’ll see how they go hand in hand. As you advance, you’ll understand intrinsically what a vector is and how to transform vectors with matrices and operators. You’ll also see how complex numbers make their voices heard and understand the probability behind it all.
It’s all here, in writing you can understand. This is not a stuffy math book with definitions, axioms, theorems, and so on. This book meets you where you’re at and guides you to where you need to be for quantum computing. Already know some of this stuff? No problem! The book is componentized, so you can learn just the parts you want. And with tons of exercises and their answers, you’ll get all the practice you need.
What you will learn
- Operate on vectors (qubits) with matrices (gates)
- Define linear combinations and linear independence
- Understand vector spaces and their basis sets
- Rotate, reflect, and project vectors with matrices
- Realize the connection between complex numbers and the Bloch sphere
- Determine whether a matrix is invertible and find its eigenvalues
- Probabilistically determine the measurement of a qubit
- Tie it all together with bra-ket notation
Who this book is for
If you want to learn quantum computing but are unsure of the math involved, this book is for you. If you’ve taken high school math, you’ll easily understand the topics covered. And even if you haven’t, the book will give you a refresher on topics such as trigonometry, matrices, and vectors. This book will help you gain the confidence to fully understand quantum computation without losing you in the process!
Table of Contents
- Superposition with Euclid
- The Matrix
- Foundations
- Vector Spaces
- Using Matrices to Transform Space
- Complex Numbers
- Eigenstuff
- Our Space in the Universe
- Advanced Concepts
- Appendix 1 – Bra-ket Notation
- Appendix 2 – Sigma Notation
- Appendix 3 – Trigonometry
- Appendix 4 – Probability
- Appendix 5 – References
Editorial Reviews
Review
“This book offers a comprehensive and structured introduction to the mathematical foundations of quantum computing, making it an excellent resource for both beginners and those seeking to deepen their understanding. By starting with fundamental concepts like vectors and superposition and gradually building up to more advanced topics such as linear transformations, complex numbers, and Hilbert spaces, the book ensures a smooth learning curve. The inclusion of numerous exercises reinforces comprehension, while discussions on key topics like eigenvalues, quantum gates, and the Bloch sphere provide essential insights into quantum mechanics. With well-organized appendices covering crucial mathematical tools, this book serves as an invaluable guide for anyone looking to develop a strong mathematical intuition for quantum computing.”
Jayakumar Vaithiyashankar, Founder and CEO of Anuthantra, IBM Quantum Educator and Qiskit Advocate, Swayam-Nptel Instructor
“Essential Mathematics for Quantum Computing by Leonard S. Woody III, an excellent starting point for anyone wondering how to begin their journey in quantum computing. This book lays a solid mathematical foundation, covering everything from basic vector concepts to trigonometry, and beautifully bridges math with quantum principles.
If you’ve studied subjects like linear Algebra at university, this book will help you connect the dots and apply your existing knowledge in a quantum context. Highly recommended for all quantum enthusiasts!”
Yousra Farhani, Founder of Quantum Africa, Quantum Optimization and Machine Learning Researcher, Recipient of the Quantum Rising Star Award for Women in Quantum and the Arab Young Pioneers Award in Quantum (MENA Region)
About the Author
Leonard S. Woody III is a senior consultant with 20 years of experience explaining complex subjects to software development clients. For the last 3 years, he has worked at Microsoft, most currently as a program manager for Azure Quantum. He was awarded a BS in computer science and a BS in physics from the University of Virginia. He attained his MS in software engineering from George Mason University. Woody lives in Northern Virginia with his wife and four children. His biggest love is spending time with his family.
