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Essential Mathematics for Quantum Computing
Essential Mathematics for Quantum Computing

Essential Mathematics for Quantum Computing: A beginner's guide to just the math you need without needless complexities

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Essential Mathematics for Quantum Computing

Chapter 1: Superposition with Euclid

Mathematics is the language of physics and the foundation of computer science. Since quantum computing evolved from these two disciplines, it is essential to understand the mathematics behind it. The math you need is linear in nature, and that is where we will start. By the time we are done, you will have the mathematical foundation to fundamentally understand quantum computing. Let's get started!

In this chapter, we are going to cover the following main topics:

  • Vectors
  • Linear combinations
  • Superposition
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Key benefits

  • 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

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.

Who is this book 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!

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

Product Details

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Publication date, Length, Edition, Language, ISBN-13
Publication date : Apr 22, 2022
Length: 252 pages
Edition : 1st
Language : English
ISBN-13 : 9781801070188
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Product Details

Publication date : Apr 22, 2022
Length: 252 pages
Edition : 1st
Language : English
ISBN-13 : 9781801070188
Category :
Languages :

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Table of Contents

14 Chapters
Section 1: Introduction Chevron down icon Chevron up icon
Chapter 1: Superposition with Euclid Chevron down icon Chevron up icon
Chapter 2: The Matrix Chevron down icon Chevron up icon
Section 2: Elementary Linear Algebra Chevron down icon Chevron up icon
Chapter 3: Foundations Chevron down icon Chevron up icon
Chapter 4: Vector Spaces Chevron down icon Chevron up icon
Chapter 5: Using Matrices to Transform Space Chevron down icon Chevron up icon
Section 3: Adding Complexity Chevron down icon Chevron up icon
Chapter 6: Complex Numbers Chevron down icon Chevron up icon
Chapter 7: EigenStuff Chevron down icon Chevron up icon
Chapter 8: Our Space in the Universe Chevron down icon Chevron up icon
Chapter 9: Advanced Concepts Chevron down icon Chevron up icon
Section 4: Appendices Chevron down icon Chevron up icon
Other Books You May Enjoy Chevron down icon Chevron up icon

Customer reviews

Top Reviews
Rating distribution
Full star icon Full star icon Full star icon Full star icon Half star icon 4.6
(19 Ratings)
5 star 89.5%
4 star 0%
3 star 0%
2 star 0%
1 star 10.5%
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Vlad Jan 15, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
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.
Subscriber review Packt
Omar Al Hathaf Jul 31, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Feefo Verified review Feefo
THEODOROS ZAFEIRIDIS May 20, 2024
Full star icon Full star icon Full star icon Full star icon Full star icon 5
perfect
Feefo Verified review Feefo
rory woods May 19, 2022
Full star icon Full star icon Full star icon Full star icon Full star icon 5
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.
Amazon Verified review Amazon
Brian K Apr 25, 2022
Full star icon Full star icon Full star icon Full star icon Full star icon 5
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.
Amazon Verified review Amazon
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