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

Simple matrix operations

As mentioned in the introduction to this chapter, the power of matrices is the operations defined on them. Here, we go through some of the basic operations for matrices that we will build on as the book progresses. You have already encountered some of these operations with vectors in the previous chapter, but we will now expand them to matrices.

Addition

Addition is one of the easiest operations, along with its inverse subtraction. You basically just perform addition on each entry of one matrix that corresponds with another entry in the other matrix, as shown in the following formula. Addition is only defined for matrices with the same dimensions:

Example

Here is an example of matrix addition:

Exercise 1

What is the sum of the following two matrices? (Answers to exercises are at the end of the chapter.)

Scalar multiplication

Scalar multiplication is also rather easy. A scalar is just a number, and so scalar multiplication...