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

Appendix 4: Probability

The study of gambling, specifically the throwing of dice, led to the mathematical field of probability. Probability is the study of how likely an event is to occur given a number of possible outcomes. A real number between 0 and 1 is assigned to each event where 0 signifies the event has no chance of happening and 1 signifies the event will always happen. You can also multiply these numbers by 100 to get a percentage that the event will happen. All the probabilities for all possible outcomes must sum to 1. For instance, the probability of a coin flip landing on heads is 0.5 or 50%. For tails, it is also 0.5 or 50%. Both of these numbers add up to 1. From these basics, this chapter will go over the probability needed in the study of quantum computing.

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

  • Definitions
  • Random variables