Book Image

Essential Mathematics for Quantum Computing

By : Leonard S. Woody III
5 (1)
Book Image

Essential Mathematics for Quantum Computing

5 (1)
By: Leonard S. Woody III

Overview of this book

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.
Table of Contents (20 chapters)
1
Section 1: Introduction
4
Section 2: Elementary Linear Algebra
8
Section 3: Adding Complexity
13
Section 4: Appendices
Appendix 1: Bra–ket Notation
Appendix 2: Sigma Notation
Appendix 5: References

Quantum gates

In this section, I'd like to take the math you have learned in this chapter around matrices and connect it to actual quantum computing—namely, quantum gates. Please remember that this book is not about teaching you everything in quantum computing, but rather the mathematics needed to do and learn quantum computing. That being said, I want to connect the math to quantum computing and show the motivation for learning it. Do not be frustrated if this does not all make sense, and please consult the reference books in the appendix for more information on quantum gates.

Logic gates

In classical computing, we use logic gates to put together circuits that will implement algorithms, such as, adding two numbers. The logic gates represent Boolean logic. Here are some simple logic operations:

  • AND
  • OR
  • NOT

In a circuit, you have input, output, and logic gates. The input and outputs are represented by a binary number, with 1 being true and 0 being...