Essential Mathematics for Quantum Computing

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

1. Superposition with Euclid
2. The Matrix
3. Foundations
4. Vector Spaces
5. Using Matrices to Transform Space
6. Complex Numbers
7. Eigenstuff
8. Our Space in the Universe
9. Advanced Concepts
10. Appendix 1 – Bra-ket Notation
11. Appendix 2 – Sigma Notation
12. Appendix 3 – Trigonometry
13. Appendix 4 – Probability
14. Appendix 5 – References

Review

“A Quantum Book Like No Other”, — Quantum Zeitgeist

One of the fundamental challenges for those new to the Quantum Computing field is getting a grip on the maths that is so fundamental to the understanding of what is actually happening in the weird world of Quantum. Getting a firm grasp of those fundamentals is not necessarily that easy and not all the machinery is taught unless you take a graduate programme in Quantum Physics. The new book from Leonard Woody who is a program manager with Microsoft Quantum Azure has the aim to be an all in one-stop-shop to understanding the mathematics that drive the next Quantum industrial revolution, without much requisite maths. But there is another duality to the book, for those who have perhaps forgotten some of the fundamentals and want to get into the quantum field.

With this book, you could literally use it to fully understand those key quantum operations such as kets, matrices, measurement, tensor products… [He gets] the reader from grade school maths into understanding quantum computing and I mean getting at the depth and you wont need to look things up in a half a different books, you can simply use Essential Mathematics for Quantum Computing to give you the operational knowledge. So if you want an easy entree into the world of Quantum, you will feel inspired with Woody.

I wish books like this existed when I was at school, because this is a “theme” book, which will no doubt encourage readers and students to learn the maths because they want to get into the quantum space. What better motivation to learn the maths. Often the opposite of the way maths is taught in school, ie. without application or a real purpose, which I’ve often thought turns students off. That is what is refreshing about this title.

— Quantum Zeitgeist, tinyurl.com/Math4QCReview

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.