Essential Mathematics for Quantum Computing: A beginner’s guide to just the math you need without needless complexities
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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
11 reviews for Essential Mathematics for Quantum Computing: A beginner’s guide to just the math you need without needless complexities
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delbert –
in my quantum computing collaboration with literally hundreds of folks, the difficulty i most often see in getting started is that folks are overwhelmed by the math. thank goodness Woody wrote this book! the mysteries of Quantum Computing all come down to the math: Superposition? check out the first chapter. Entanglement? take a gander at Chapter 5. Interference? Phase Kickback? these two come in with the most beautiful equation in mathematics, covered primarily in Chapter 6. The latter chapters in the book take us into the rules that govern quantum mechanics and quantum computing — the rules of Hilbert Space. Woody’s reassuring Virginia drawl comes through on every page, reassuring you that you’ve got this. and exercises at each step along the way to *make sure* you’ve got this. (yes, sorry, you have to do the exercises to really get the math. some things never change) and finally, you’ve gotta love a book with a chapter entitled: Eigenstuff.
Colleen –
This book is an excellent overview of the linear algebra central to quantum circuits and quantum algorithms. Woody dives into the topics with clear examples, diagrams/images, and practice problems and covers the bulk of linear algebra and abstract algebra needed for an introductory quantum mechanics course. Readers will come away with enough of the math behind quantum computing to start a course in it.
However, Woody doesn’t always relate the material back to quantum computing, so those looking for a book on quantum computing might want to purchase a companion book as they work through the math in Woody’s book.
It would also serve as a great linear algebra course companion for students struggling with a linear algebra textbook. The explanations are clear and concise, and practice problems add to the understanding of concepts.
Brian K –
This book provides a fast, readable introduction (or review for those with a deeper knowledge of linear algebra) to the mathematics needed for Quantum Mechanics and Quantum Computing. Nicely developed visuals help explain key concepts.
There are practice exercises to help reinforce the topics being covered as well as the answers (though not worked through.)
Woody includes 5 appendices on further physical ideas (bra-ket notation) and other mathematical topics (trigonometry and probability.)
One drawback to this book, in my humble opinion, is a lack of connection to Quantum theory and why they are important to it.
But I think this book would be an asset to someone who wants to start reading on Quantum Mechanics and Computing and needs a good companion on linear algebra.
rory woods –
I’ve been programming for decades and quantum computing was always a topic of interest. I’ve read about it but always felt like I was missing something. This book finally gave me the foundation I needed. It provides that “one level down” insight needed to grok the higher subject. The author makes no assumptions about your existing math skills (so-so in my case). Instead, he starts with the basics and works you up from there. Suddenly you are reading about (and understanding) linear functionals and eigenvalues. An all-around great read for anyone in the space or interested in learning more.
Harry –
I have read about one-fourth and presentation is pretty clear. Note that I am a novice.
Nostromo500 –
This book is very well written and has great figures and examples. A must-read and a good reference book on quantum mathematics.
Sam Smith –
Very useful book. Topics are presented simply and practically. Also looks great on my book shelf- I look like a quantum genius!
Steven Fernandes –
The book is a student-friendly introduction to learning the basics of superposition, matrix operations, quantum gates, sets, functions, vector space, subspace, linear independence transformation inspired by Euclid, complex numbers, Eigenvectors, Tensor products, etc. The last chapter introduces advanced topics such as Gram-Schmidt, Spectral decomposition, Singular value decomposition, Polar decomposition, etc. Each chapter of the book contains exercise questions with solutions. The mathematical concepts are explained in a beginner-friendly manner, and anyone can understand them.
The drawbacks include the size of figures 1.6, 1.7, 1.8, 5.12, 5.13, etc., being too large and occupying almost complete pages, which wastes resources. In appendix 2 the summation symbol on page 202 occupies one entire page. To understand the practical implementation of quantum algorithms, I would recommend other Packt books written by Robert Loredo and Robert S. Sutor.
Wai –
I am interested in quantum computing for years but frustrated by the math. Finally found a book that enables me to learn essential mathematics for understanding quantum computing. Very grateful for the author to write this book.
joey –
Wow what a wonderful book with such relevant content! Much material from my younger engineering education and is a nice well organized volume for review of the old plus much new material needed for my understanding of the quantum computing process. As a retired engineer with much interest in computer science today, I have purchased about dozen quantum related books prior to getting this one which is proving to help solve my immediate hurdles with the needed math in the quantum computing path.
V –
Bravo, Leonard! Creating such a well-structured and breathtaking math book takes time and patience. I bet you invested a lot.
This book has roughly 200 pages but teaches you starting from elementary things, such as vectors, and ending up with more advanced concepts, such as tensors or matrix decompositions. You won’t find anything in this book about quantum physics or commercially available services; this is a 100% pure math book focusing on vectors/matrixes. You can enjoy it even if you know how to do addition, subtraction, multiplication, and division of real numbers only, which I hope the reader already acquired before middle school. Reading and doing all the exercises took me one and a half days. It has a few misprints (mainly incorrectly used signs), but the rest is top-quality. The only regret I have after reading is that I wasn’t able to read it 20 years ago as a student.